1. Cell Biology
  2. Physics of Living Systems
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A physical mechanism of TANGO1-mediated bulky cargo export

  1. Ishier Raote  Is a corresponding author
  2. Morgan Chabanon
  3. Nikhil Walani
  4. Marino Arroyo
  5. Maria F Garcia-Parajo
  6. Vivek Malhotra  Is a corresponding author
  7. Felix Campelo  Is a corresponding author
  1. Centre for Genomic Regulation (CRG), The Barcelona Institute of Science and Technology, Spain
  2. ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Spain
  3. Universitat Politècnica de Catalunya-BarcelonaTech, Spain
  4. Institute for Bioengineering of Catalonia, The Barcelona Institute of Science and Technology, Spain
  5. Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Spain
  6. ICREA, Spain
  7. Universitat Pompeu Fabra (UPF), Spain
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Cite this article as: eLife 2020;9:e59426 doi: 10.7554/eLife.59426

Abstract

The endoplasmic reticulum (ER)-resident protein TANGO1 assembles into a ring around ER exit sites (ERES), and links procollagens in the ER lumen to COPII machinery, tethers, and ER-Golgi intermediate compartment (ERGIC) in the cytoplasm (Raote et al., 2018). Here, we present a theoretical approach to investigate the physical mechanisms of TANGO1 ring assembly and how COPII polymerization, membrane tension, and force facilitate the formation of a transport intermediate for procollagen export. Our results indicate that a TANGO1 ring, by acting as a linactant, stabilizes the open neck of a nascent COPII bud. Elongation of such a bud into a transport intermediate commensurate with bulky procollagens is then facilitated by two complementary mechanisms: (i) by relieving membrane tension, possibly by TANGO1-mediated fusion of retrograde ERGIC membranes and (ii) by force application. Altogether, our theoretical approach identifies key biophysical events in TANGO1-driven procollagen export.

Introduction

Multicellularity requires not only the secretion of signaling proteins –such as neurotransmitters, cytokines, and hormones– to regulate cell-to-cell communication, but also of biomechanical matrices composed primarily of proteins such as collagens, which form the extracellular matrix (ECM) (Kadler et al., 2007; Mouw et al., 2014). These extracellular assemblies of collagens are necessary for tissue biogenesis and maintenance. Collagens, like all conventionally secreted proteins, contain a signal sequence that targets their entry into the endoplasmic reticulum (ER). After their glycosylation, procollagens fold and trimerize into a characteristic triple-helical, rigid structure, which, depending on the isoform, may extend several hundred nm in length (McCaughey and Stephens, 2019). These bulky procollagens are then exported from the ER at specialized export domains, termed ER exit sites (ERES), in a COPII-dependent manner. ERES are a fascinating subdomain of the ER, but a basic understanding of how these domains are created and segregated from the rest of the ER for the purpose of cargo export still remains a challenge. At the ERES, the formation of canonical COPII-coated carriers relies on the polymerization on the membrane surface of a large-scale protein structure: the protein coat. Polymerized coats, such as COPI, COPII, and clathrin coats, usually adopt spherical shapes –which bend the membrane underneath to form small vesicles of ~60–90 nm in diameter (Faini et al., 2013), although helical arrangements of COPII coats have been observed (Zanetti et al., 2013; Ma and Goldberg, 2016). Membrane bending by coats is promoted when the energy gain of coat polymerization is larger than the elastic energy of membrane deformation (Derganc et al., 2013; Scheve et al., 2013; Kozlov et al., 2014; Saleem et al., 2015; Day and Stachowiak, 2020). However, how COPII components function specifically to export procollagen remains unclear. The discovery of TANGO1 as a key ERES-resident player has made the processes of procollagen export and the organization of ERES amenable to molecular analysis (Bard et al., 2006; Saito et al., 2009; Wilson et al., 2011).

In the lumen of the ER, the SH3-like domain of TANGO1 binds procollagen via HSP47 (Saito et al., 2009; Ishikawa et al., 2016; Figure 1A). On the cytoplasmic side, TANGO1 has a proline-rich domain (PRD) and two coiled-coil domains (CC1 and CC2) (Figure 1A). The PRD of TANGO1 interacts with the COPII components Sec23A and Sec16 (Saito et al., 2009; Ma and Goldberg, 2016; Maeda et al., 2017); the CC1 domain binds the NBAS/RINT1/ZW10 (NRZ) tethering complex to recruit ER-Golgi intermediate compartment (ERGIC) membranes and also drives self-association amongst TANGO1 proteins (Santos et al., 2015; Raote et al., 2018); and the CC2 domain oligomerizes with proteins of the TANGO1 family (such as cTAGE5) (Saito et al., 2011; Maeda et al., 2016). Both cytosolic and lumenal activities of TANGO1 are critical for its function. For instance, a recent report identified a disease-causing mutation in TANGO1 in a human family, which results in a substantial fraction of TANGO1 protein being truncated and lacking its cytosolic functions, leading to collagen export defects (Lekszas et al., 2020). Recently, we visualized procollagen export domains with high lateral spatial resolution using stimulated emission depletion (STED) nanoscopy in mammalian tissue cultured cells (Raote et al., 2017; Raote et al., 2018). These studies revealed that TANGO1 organizes at the ERES into ring-like structures, of ~200 nm in lumenal diameter, that corral COPII components. Moreover, two independent studies showed that TANGO1 rings are also present in Drosophila melanogaster (Liu et al., 2017; Reynolds et al., 2019).

Figure 1 with 1 supplement see all
Physical model of TANGO1 ring formation.

(A) Schematic representation of the domain structure and topology of TANGO1, indicating the SH3 domain, a lumenal coiled-coiled domain (CC), the one and a half transmembrane region (TM), the coiled-coiled 1 (CC1) and 2 (CC2) domains, and the PRD. (B) Schematic description of the TANGO1 ring formation model (top view). ERES consisting of COPII subunits assemble into in-plane circular lattices (orange), whereas proteins of the TANGO1 family assemble into filaments by lateral protein-protein interactions (light blue). The competition between the affinity of the TANGO1 filament to bind COPII subunits (promoting capping of peripheral COPII subunits) and the resistance of the filament to be bent (promoting uncapping) controls the capping-uncapping transition. Only when TANGO1 caps the COPII lattice, it acts as a linactant by stabilizing the peripheral COPII subunits. (C) Schematic representation of individual proteins that constitute a TANGO1 filament and of how filament bending is associated with elastic stress generation. Individual TANGO1 family proteins (blue shapes) bind each other in a way that is controlled by the structure of protein-protein binding interfaces, leading to formation of an unstressed filament of a certain preferred curvature, c0 (left cartoon, showing the case where c0 = 0). Filament bending can be caused by the capping of TANGO1 filament to peripheral COPII machinery (orange area), which generates a stressed bent filament of a certain radius of curvature, ρ=1/c (right cartoon). Such deviations from the preferred shape (shown in light blue) are associated with elastic stress generation (red arrows point to the direction of the generated bending torque, which correspond to the direction of recovery of the filament preferred shape).

To further extend these findings, we combined STED nanoscopy with genetic manipulations and established that TANGO1 rings are organized by (i) lateral self-interactions amongst TANGO1-like proteins, (ii) radial interactions with COPII subunits, and (iii) tethering of small ER-Golgi intermediate compartment (ERGIC) vesicles to assist in the formation of a procollagen-containing export intermediate (Raote et al., 2018). Overall, the data suggest a mechanism whereby TANGO1 assembles into a ring, which selectively gathers and organizes procollagen, remodels COPII budding machinery, and recruits ERGIC membranes for the formation of a procollagen-containing transport intermediate. However, the biophysical mechanisms governing these events and how they are regulated by TANGO1 remain unknown.

Here, we put forward a biophysical framework to investigate how TANGO1 rings assemble around polymerizing COPII-coated structures for procollagen export. This general theoretical approach allows us to address: (i) the physical mechanisms by which TANGO1 and its interactors can assemble into functional rings at ERES, forming a fence around COPII coat components and (ii) whether and how a TANGO1 fence can couple COPII polymerization, membrane tension, and force to create an export route for procollagens at the ERES. In particular, we implement this theory in the form of two complementary models: a computational dynamic model that provides us with a general picture of the process of TANGO1-assisted transport intermediate formation; and a simplified but more tractable analytical equilibrium model that allows us to get clearer physical insights.

Overall, our results support a model where TANGO1 temporally and spatially orchestrates the export of procollagen through biophysical interactions with procollagen, COPII components, ERGIC, and the ER membrane.

Model development

In this section, we present the central hypotheses underlying our general modeling approach. These hypotheses are common to the two models that we subsequently describe: a dynamic computational model (Model A), and an equilibrium analytical model (Model B). We present here a qualitative overview of these models, highlighting their specificities, limitations and strengths. The detailed description of each model is provided in Appendix 1 and Appendix 2, respectively.

Fundamental hypotheses

To assess and rationalize mechanisms of TANGO1 assembly into rings at ERES and their contribution to procollagen export, we formulate general hypotheses built on accumulated experimental data that will serve as the foundation for our two modeling approaches.

Hypothesis 1: TANGO1 family of proteins and COPII coat proteins are described as two distinct membrane-bound species. Given the complexity of the system and the lack of quantitative biochemical data regarding the interactions amongst the different TANGO1 and COPII components, we assume for our modeling purposes that the TANGO1 family of proteins (TANGO1, cTAGE5 and TANGO1-Short) can be effectively described as a single species, to which we will simply refer as TANGO1. Similarly, for simplicity, we describe all the subcomponents of the COPII inner and outer coats as a single species. For our purpose, a more detailed description would only add complexity and free parameters without providing relevant biophysical insights.

Hypothesis 2: COPII subunits polymerize on the ER membrane forming a coat of specific curvature. COPII coat assembly at the ERES is relatively well characterized (Peotter et al., 2019). Polymerization of COPII subunits into spherical lattices induces curvature on the underlying membrane, typically resulting in spherical carriers of 60–90 nm (Faini et al., 2013; Aridor, 2018; Peotter et al., 2019). However, for bulky cargoes such as procollagens, complementary mechanisms are required to prevent the premature completion of the small carriers and to enable the packaging of large molecules.

Hypothesis 3: TANGO1 molecules have a propensity to assemble into rings as a result of protein-protein interactions between TANGO1-family proteins. This hypothesis is based on the observations that: (i) TANGO1 is seen in ring-like filamentous assemblies of specific size by STED nanoscopy (Raote et al., 2017; Roux, 2018); (ii) there is a direct 1:1 binding between TANGO1 and cTAGE5 CC2 domains (Saito et al., 2011); (iii) TANGO1-Short and cTAGE5 can form oligomers and oligomeric complexes together with Sec12 and TANGO1 (Maeda et al., 2016); (iv) TANGO1 and TANGO1-Short can directly homo-dimerize by their CC1 domains (Raote et al., 2018); and (v) super-resolution live lattice SIM imaging of TANGO1 in D. melanogaster larval salivary gland shows filament growth in ring formation (Reynolds et al., 2019). A physical consequence of this hypothesis is that deviations from the preferred TANGO1 ring curvature are associated to an elastic energetic cost: the ring is subject to internal strains and stresses and therefore resists bending away from its preferred curvature (Figure 1B,C).

Hypothesis 4: TANGO1 has a binding affinity to the peripheral COPII coat subunits, helping stabilize the COPII domain boundary by effectively reducing its line energy. This hypothesis is supported by the observations that proteins of the TANGO1 family bind to the COPII components Sec23, Sec16, and Sec12 (Saito et al., 2009; Ma and Goldberg, 2016; Hutchings et al., 2018; Raote et al., 2018). In physical terms, this hypothesis is equivalent to state that TANGO1 acts as a linactant by filling unsatisfied binding sites of the COPII coat edges and therefore effectively lowering its line tension (Figure 1B; Trabelsi et al., 2008, Saleem et al., 2015; Glick, 2017). Combined with hypothesis 1, another consequence of the TANGO1-COPII affinity is the mechanical coupling between the COPII coat edge and TANGO1.

 Qualitatively, our generic model for TANGO1 ring assembly can be described as a competition between two different driving forces: the resistance to bending of TANGO1 filamentous assemblies (hypothesis 3) and the binding affinity of TANGO1 proteins for peripheral COPII subunits (hypothesis 4). In the case of low TANGO1 bending resistance and/or high TANGO1-COPII binding affinity, TANGO1 will easily assemble around COPII patches, forming a ring. In the following, we refer to this process as capping of the COPII patch by TANGO1, the analogue to ‘wetting’ in soft-matter physics (Figure 1B,C). As a result of capping, the linactant effect of TANGO1 on COPII-coated ERES reduces the line energy, thus limiting further growth of the COPII lattice and the size of the TANGO1 rings (Figure 1B). In contrast, in the case of high TANGO1 rigidity and/or low TANGO1-COPII affinity (for instance, in cells expressing mutants of TANGO1 with reduced or abrogated interaction to COPII proteins), capping of COPII coats by TANGO1 rings will be energetically unfavorable, preventing any linactant effect (Figure 1B).

Model A: dynamic computational model

Here, we summarize our dynamic model of transport intermediate formation at ERES. The detailed, mathematical description of the model is presented in Appendix 1. The model extends the work of Tozzi et al., 2019 to include two membrane-bound species representing TANGO1 and COPII, respectively.

The ER membrane is represented as a continuous elastic surface on which both protein species can diffuse, interact, and induce membrane curvature. To account for these coupled chemical-mechanical processes, we follow Onsager’s variational formalism of dissipative dynamics (Arroyo and Desimone, 2009; Arroyo et al., 2018). The first step is to define the free energy of the system, which in our case is the sum of the following mechanical and chemical-related energetic contributions:

  1. Membrane bending energy: the energetic cost to bend the membrane away from a preferred spontaneous curvature, known as Helfrich energy (Helfrich, 1973). Here, we assume that the spontaneous curvature is proportional to the COPII surface density, so that when the surface is saturated with COPII species (fully polymerized lattice), the membrane tends to adopt a given total curvature of 2/Rc (where Rc is the radius of curvature of the polymerized COPII coat).

  2. TANGO1 ring elastic energy: the energetic cost to bend a TANGO1 filament away from a preferred ring curvature.

  3. Entropic free energy: the energetic cost for COPII and TANGO1 to mix or phase separate, here represented by a Flory-Huggins type of mixing free energy.

  4. Species self-interaction energy: the energetic gain for COPII and TANGO1 to self-recruit or self-repel.

  5. Interfacial energy: the energetic cost for COPII and TANGO1 domains to have an interface, physically similar to a line energy.

  6. TANGO1-COPII affinity energy.

  7. TANGO1 affinity for COPII domain interfaces (linactant effect), effectively reducing COPII line energy.

Next, we identify the dissipative mechanisms such as those associated with protein diffusion on the membrane surface, and with membrane in-plane shear stress. In addition, the system exchanges energy in the form of external supply of species (fixed chemical potential at the boundaries) and mechanical power. Finally, membrane inextensibility is ensured with a Lagrange multiplier field that has the physical interpretation of the membrane tension.

With these definitions (see Appendix 1), we obtain the rate of change of the system at each time point by numerically minimizing the rate of free energy release, energy dissipation, and energy exchange by the system. To facilitate the computational scheme, we formulate the problem in axisymmetric conditions. Note that this is not a limitation of the model’s physics itself but only of its numerical implementation.

The generality of Model A allows us to explore in a thermodynamically consistent manner a large range of possible dynamics of the system, including protein phase-separation, self-organization, spontaneous bud growth, and accessible stable states. However, the cost of this generality is a relative complexity that makes the physical understanding of the system more challenging. For this reason, in the next section, we describe a simplified but analytically tractable model.

Model B: equilibrium analytical model

To develop a theoretical model of transport intermediate formation at an ERES, we extend and adapt the approach from Saleem et al., 2015 on clathrin-coated vesicle formation to include the contributions of TANGO1 proteins in modulating COPII-dependent carrier formation. The detailed mathematical description is given in Appendix 2.

The main simplifying assumptions of this model are that (i) the system is at mechanical and thermodynamic equilibrium; (ii) the COPII coat is assumed to be much more rigid that the lipid bilayer, and therefore imposes a fixed radius of curvature leading to formation of spherical membranes of fixed radius Rc; and (iii) the buds are supposed axisymmetric. The second assumption allows us to limit the family of possible shapes to partial spheres connected to a flat surface, and greatly simplifies the theoretical treatment of the system. As shown below, this assumption is supported by the type of geometries obtained from Model A, which does not assume any a priori geometry.

We consider a continuous lipid membrane with a bending rigidity (κb), under a certain lateral membrane tension (σ). COPII assembly into a coat is driven by a binding chemical potential (μc0) and is opposed by the membrane bending energy. We consider that the major contribution to the binding chemical potential comes from coat-coat polymerization and not from coat-membrane binding (Saleem et al., 2015), so the binding energy μc0 represents the polymerization energy due to COPII-COPII binding, and will be referred to as the COPII polymerization energy in what follows. COPII units can therefore freely exchange with the rest of the membrane, which acts as the reservoir of COPII units at a fixed chemical potential. The edge of the COPII lattice has a line tension (λ0) due to free COPII polymerization sites. TANGO1 protein interactions are assumed to favor the formation of a linear filament of preferred curvature (c0) and bending rigidity (κT). Due to its affinity to COPII coat peripheral subunits, TANGO1 filaments can satisfy a fraction (ω) of the edge length, effectively reducing the COPII coat line tension by Δλ. Finally, we also account for the mechanical work of an outward-directed force (N) which favors transport intermediate elongation.

The main advantage of this model is that the assumption on the carrier geometry allows us to analytically express the dependency of given quantities of interest on the model parameters, facilitating the physical interpretation of the system. For instance, writing the above mechanisms in terms of the free energy of the system, and taking a bare flat membrane as the reference state, the total free energy change of the system accounting for TANGO1 and COPII can be written as (see Appendix 2):

(1) Δfc=σ(AmAp1)(μc02κbRc2)AcAp+[λ0ωΔλ+ωκT2(1ρc0)2]2πρApN zmaxAp,

where Am is the membrane surface area, Ac is the membrane surface area coated by COPII, Ap is the surface area of the carrier projection onto the flat membrane, ρ is the radius of the neck of the COPII coat, and zmax is the height of the carrier (see Appendix 2—figure 1). For practical reasons, we define the dimensionless shape parameter η=zmax/(2 Rc), so that η=1 for a single sphere of COPII spontaneous curvature. Equation 1 is plotted in Figure 1—figure supplement 1 for capped (ω=1) and uncapped (ω=0) carriers, highlighting the influence of COPII binding chemical potential on the energetically accessible shapes of the system.

Results

TANGO1 rings self-assemble to stabilize COPII shallow buds

We first make use of the generality of the computational dynamic model (Model A) to study the formation of TANGO1 assemblies at ERES. We start by investigating the ability of COPII complexes alone to generate spherical carriers. This corresponds to the control case where TANGO1 is treated as an inert species that only contributes to the entropic energy (no chemical nor mechanical interaction with COPII, the membrane, nor with itself). As shown in Figure 2A, after an initial nucleation stage (see Appendix 1), the COPII coat grows by recruiting more COPII species as it bends the membrane into a bud (Figure 2A(i–iii), Figure 2—video 1). As a metric to follow the bud growth with time, we track the height of the bud (zmax) as a function of time. As seen in Figure 2A, for inert TANGO1, the shape parameter – which we have earlier defined as η=zmax/(2 Rc) – increases continuously until η1 (Figure 2(ii)), before an abrupt event where η jumps to 1.4 and then drops back to 1. This event corresponds to the neck closure (Appendix 1, Figure 2A(iii)), characterized by a snap-through instability (Hassinger et al., 2017).

Figure 2 with 2 supplements see all
Computational dynamic model (Model A) recapitulates TANGO1 ring self-organization around COPII coats and highlights its role in stabilizing incomplete transporters.

Shape factor (η) and height (zmax) of the transport intermediate as a function of time for (A) inert TANGO1 and (B) functional TANGO1. (i-iii) Snapshots of the buds at the times indicated in the left graphs. All results obtained for parameters as given in Appendix 1—table 1, with χc=-2kBT and σ=0.006 kBT/nm2. Gray areas correspond to the coat nucleation stages (see Appendix 1 for details). See corresponding Figure 2—video 1 and Figure 2—video 2 for a dynamic representation of the simulations shown in (A) and (B), respectively.

In contrast, functional TANGO1 drastically modifies the dynamics and outcome of bud formation (see Figure 2B and Figure 2—video 2). First, the nucleation stage is shortened, suggesting that TANGO1 can facilitate the nucleation of the COPII coat in the presence of a small force perturbation at the membrane. Second, instead of growing to the point where the neck closes, we find that the shape parameter reaches a maximum around η0.9, before slightly decreasing to a stable height around η0.8. As seen from the corresponding snapshots (Figure 2B(i–iii)), this dynamic evolution is accompanied by the self-assembly of a high-density TANGO1 ring-like structure around the COPII coat that stabilizes the bud into a shallow, incomplete transport intermediate. These simulation results are in agreement with experimental observations of TANGO1 rings encircling COPII components in procollagen-rich membrane patches (Raote et al., 2017; Raote et al., 2018).

Transient reduction of membrane tension in TANGO1-stabilized buds facilitates the formation of large transport intermediates

To test if the formation of a stable incomplete transporter is compatible with the hypothesis that TANGO1 facilitates the biogenesis of large transport intermediate for procollagen export, we applied transient membrane tension reductions to shallow buds stabilized by TANGO1 rings. Such scenario is motivated by our previous experimental data showing that (i) ERGIC53-containing vesicles are recruited to the ERES by TANGO1 via tethering complexes (Nogueira et al., 2014; Santos et al., 2015; Raote et al., 2018), presumably enabling their fusion to the ER membrane and (ii) cells depleted of the tethering factors recruited by TANGO1 to ERES showed a reduction of ~70–80% in collagen secretion (Raote et al., 2018).

To mimic the presence of procollagen molecules inside the growing carrier preventing the total closure of the neck, we arbitrarily set a minimum neck radius threshold of 7.5 nm (see Appendix 1 for details). Starting from a stable shallow bud of shape parameter, η0.8, at a large membrane tension of σ=0.006 kBT/nm2 (Figure 3D(i)), we apply an ad hoc transient tension reduction as follows. First, the tension is reduced to σ=0.003 kBT/nm2, leading to bud re-growth. Second, when the bud height reaches η=1.5 (just after the beginning of neck closure), the membrane tension is gradually set back to its original value of σ=0.006 kBT/nm2 over a 10 ms time ramp (Figure 3A–C). We find that the carrier reaches a new equilibrium state at η2.8, corresponding to a 'key-hole' shape of about 195 nm height (Figure 3D(ii)). Next, continuing from this new equilibrium state, we repeat the transient tension reduction protocol, this time initiating the ramp to recover high tension for η=3.5, just after a new neck is formed. This time, the bud continues growing in a pearled shape despite the recovery of high membrane tension (Figure 3D(iii,iv), and Figure 3—video 1). Interestingly, the '2-pearl' shape corresponds to a height of about 300 nm, a typical length of trimerized procollagen I molecules (McCaughey and Stephens, 2019).

Figure 3 with 1 supplement see all
Transient membrane tension reduction in TANGO1-stabilized buds enables the formation of large procollagen-containing transport intermediates.

A transient decrease of membrane tension mimicking ERGIC membrane recruitment by TANGO1 enables the sequential growth of COPII-TANGO1 transport intermediates. (A) Computational protocol for the applied membrane tension as a function of time. When an equilibrium state is reached, σ is transiently reduced from 0.006 kBT/nm2 to 0.003 kBT/nm2 until the transport intermediate grows to either η=1.5 or η=3.5 Then σ is progressively restored to 0.006 kBT/nm2 following a linear ramp of ~10 ms. (B) Resulting shape parameter, η, as a function of time. Double-barred lines indicate that the system can remain at equilibrium for an arbitrarily long time. (C) Shape parameter as a function of membrane tension, σ. Gray regions in (A–C) correspond to low-tension regimes. (D) Three-dimensional rendering of the shape of the transport intermediate and protein surface distribution at the respective points indicated in panels (A–C). Parameters as in Appendix 1—table 1, with χc=-2kBT (see Appendix 1 for details, and Figure 3—video 1 for a dynamic representation of the simulation).

Altogether, our computational results support the scenario by which TANGO1 self-organizes around COPII coats and stabilizes shallow buds at physiological membrane tensions. This mechanism is enabled by TANGO1 affinity to COPII, TANGO1 filament bending rigidity, and the modulation of COPII coat line energy. The stability of shallow buds might facilitate procollagen recruitment and packaging by TANGO1 as well as the recruitment of ERGIC membranes to the ERES. We suggest that procollagen located at the neck of the growing carrier acts as a means to sterically prevent carrier scission. Transient membrane tension reduction, possibly mediated by fusing ERGIC membranes to the ER, allows the buds to grow from shallow to elongated pearled transport intermediates of sizes compatible with the encapsulation of procollagen molecules.

Analytical model explains transition from incomplete buds to large transport intermediates as a ratchet-like mechanism

Although the generality of Model A allows us to explore ranges of possible dynamic behaviors of the TANGO1-COPII system, its computational nature and inherent complexity makes its complete and rigorous analysis prohibitively challenging. To overcome this difficulty and gain a deeper physical insight, we developed an analytically tractable model that relies on two key simplifying assumptions: (i) given the shapes obtained with Model A (Figures 2 and 3), we constrain our analysis to carrier geometries that can be approximated by a stack of spheres connected to a flat membrane patch; and (ii) we focus on the local equilibrium states of the system. The details of this equilibrium analytic model (Model B) are summarized in the Model Development section and detailed in Appendix 2.

We start by examining the effect of membrane tension on the accessible equilibrium configurations of the system as a function of the two degrees of freedom of Model B: the transport intermediate shape characterized by the shape parameter (η), and the capping fraction (ω). This geometric simplification allows to write the free energy change per unit area (Equation 1) as (see Appendix 2):

(2) Δfc={σημ1η+λ(ω)η(1η)+ωκTη(1η)(1η(1η)4c0Rc),η1/24σ[n+(ηn)2]4μη+4λ(ω)(ηn)(1η+n) +4ωκT(1(ηn)(1η+n)4c0Rc),η1/2,

where μ~=μc0-2κb/Rc2+N/(2πRc) is the effective chemical potential, which depends on the polymerization energy of the coat on the membrane, μc0, the bending rigidity of the membrane, κb, and the applied pulling/pushing force, N; λ~ω=λ0-ωΔλ/Rc+4ωκ~Tc0Rc2, is the effective line tension of the coat; κ~T=κT/8Rc3 is the renormalized bending rigidity of the TANGO1 filament; and n is the number of fully-formed buds (see Appendix 2).

We plot in Figure 4A the free energy per unit area, Δfc (Equation 2), as a function of the shape parameter η, at two membrane tensions corresponding to experimentally measured value of the ER membrane, σER=0.003kBT/nm2, and of Golgi membranes, σGC=0.0012kBT/nm2, respectively (Upadhyaya and Sheetz, 2004). In each case, the free energy per unit area for complete capping (TANGO1 rings forming around COPII patches, ω=1) and no capping (no TANGO1 rings around COPII patches, ω=0) are shown. The free energy per unit area of the transport intermediate, Δfc, presents multiple local minima separated by energy barriers, indicating that global and locally stable shapes can coexist for a given set of parameters. At 'high' (ER) membrane tension, the global minimum of the free energy corresponds to a capped shallow bud (η0.35), while locally stable shapes are also found for complete spherical buds connected to a capped shallow bud (η1.5). In contrast, at 'low' (Golgi) membrane tension, the global free energy minimum is shifted to the capped complete spherical bud shape (pearled tube), while the incomplete bud state is now a local minimum. It should be noted that due to the geometric restriction of Model B, the energy barrier separating locally stable shapes tends to infinity for fully capped coats. However, our results indicate that the uncapping of the coat reduces the energy barrier, suggesting that a capping-uncapping transition might be necessary for a bud to grow. Alternatively, growth of a pearled structure from a shallow bud could also occur through unduloid-like shapes with a fully capped neck, which are not considered by model B, but are indeed observed with model A (see e.g. Figure 3D). The parameters controlling the capping-uncapping transition are studied in a later section.

Figure 4 with 1 supplement see all
Equilibrium analytic model explains tension-mediated carrier growth in terms of energetically accessible configurations.

(A) Free energy per unit area of the transport intermediate-TANGO1 system, Δfc, as a function of the shape parameter, η, at typical ER membrane tension (left), and Golgi membrane tension (right), for fully capped (ω=1, sly blue curves), and non-capped (ω=0, orange curves) cases. Solid lines indicate the locally stable states (lower free energy). Schematics of the transport intermediate shapes for the optimal shape parameters, η1,2*, are represented at the global and local equilibrium states. (B) Optimal shape parameters, η1,2*, as a function of the membrane tension, σ. Globally stable shapes are indicated with solid lines, while locally stables shapes are shown by dashed lines. A transient reduction in the membrane tension (green arrows from point (1) to point (2)) can lead to the growth of the transport intermediate (black vertical arrow), whereas recovery of the tension to the initial value (green arrows from point (2) to point (3)) can keep the system in a kinetically arrested metastable configuration. The capping-uncapping transition is depicted by the orange-to-sky blue gradient line. (C) The free energy barriers separating the incomplete bud from the large intermediate morphologies, Δf1,2 (blue line), and Δf2,1 (vermillion line) as defined in (A), plotted as a function of the membrane tension, σ. The arrow illustrates how a decrease in membrane tension reduces the energy barrier for growth of the transport intermediate. All parameter values are reported in Appendix 2—table 1, with no applied force, N=0.

To better visualize the effect of membrane tension on the shift in globally and locally stable shapes, we plot the optimal shape parameters, η*, (Figure 4B) and energy barriers between stable incomplete buds (η<1) and large transport intermediates (η>1) (Figure 4C) as a function the membrane tension. The effect of a transient decrease in membrane tension from σER to σGC on a capped stable shallow bud is represented by the green arrows in Figure 4B. Upon tension reduction, the initially globally-stable shallow bud becomes a local but not global minimum (Figure 4A,B). Concomitantly, the free energy barrier to transition from an incomplete bud to a large transport intermediate, f1,2, is reduced, and the reciprocal free energy barrier to transition back from a large to shallow bud, f2,1, is increased (Figure 4C). At low membrane tension, the growth of the metastable bud can be triggered by a small perturbation – such as thermal fluctuations or a mechanical perturbation in the system – and might be facilitated by transient uncapping (Figure 4A). By assuming Arrhenius kinetics, we can estimate an average transition time as τ1,2=t0eF1,2/kBT, where t0~1 ms is a characteristic time scale of membrane shape dynamics (Campelo et al., 2017); and F1,2f1,2 πRc2 is the overall free energy barrier of the shape transition. For the conditions detailed in Figure 4C, we obtain F1,2σER33 kBT and F1,2σGC8 kBT, and hence the transition time is decreases drastically upon tension reduction, from τ1,2σER~109 min to τ1,2σGC~0.1 min. Note that our equilibrium model can only predict the free energy barriers but not the actual dynamics of the transitions between metastable and stable states. Then, as the membrane tension recovers the 'high' ER value, the free energy barrier to transition back to a shallow bud remains relatively large (f2,1(σER)>f1,2(σGC)), preventing the carrier to recover its shallow, globally stable shape and hence possibly being kinetically trapped in a metastable configuration. Similar estimations as above, give that F2,1σER25 kBT, and τ2,1σER~106 min. By increasing these energy barriers, TANGO1 capping can contribute to preventing large transport intermediates from shrinking back to shallow shapes during subsequent cycles of membrane tension reduction. Overall, the tension-mediated growth of large transport intermediates is effectively a ratchet-like mechanism, where the difference between the energy barriers guarantees an almost unidirectional evolution of the system leading to the transport intermediate growth.

TANGO1 expands the parameter space of accessible stable incomplete carriers

The previous results were computed for a typical set of parameters of the TANGO1-COPII system (see Appendix 2—table 1). Next, we studied how robust was the stabilization of an incomplete carrier by a TANGO1 ring with respect to the COPII polymerization energy. To do so, we computed the local minima of the overall energy per unit area (Equation 2) for a range of values of the COPII polymerization energy, μc0, and the membrane tension, σ. The results are shown in Figure 5A in the form of a shape diagram for the optimal shape parameter, η*. We find that at low COPII polymerization energy, the coat fails to bend the membrane into a bud, resulting in a flat membrane (η*=0). At high COPII polymerization energy, however, the system adopts a fully budded structure. Interestingly, we identify a range of intermediate COPII binding energies, (0.0285 kBT/nm2<μc0<0.0315 kBT/nm2) at which a stable shallow bud (η*<1) can be brought to a large pearled shape (η*>1) by membrane tension reduction. Although this range of parameters might seem relatively narrow, similar narrow ranges have been shown to regulate clathrin-coated vesicle formation (Saleem et al., 2015; Hassinger et al., 2017).

TANGO1 widens the parameter space at which membrane tension regulation can trigger the growth of a stable incomplete carrier.

(A) Phase diagram obtained with Model B displaying the optimal shape parameter as a function of the COPII coat binding energy, μc0, and of the membrane tension, σ. Different shapes can be identified, from flat uncoated membranes, η*=0, to incomplete coated buds, η*<1/2, and to large transport intermediates, η*>1. Unless otherwise specified, parameters used for all the calculations are listed in Appendix 2—table 1. ER and Golgi membrane tensions are marked by yellow dashed lines. (B) Shape factor (color code) and final state (symbol) obtained with Model A as a function of membrane tension (σ) and COPII self-interaction (χc). (i) Inert TANGO1 but functional COPII. (ii) Functional TANGO1 and COPII. Each symbol represents the final state of a dynamic simulation, while iso-contours and colors are interpolated from the values at each symbol. (C) Snapshots of final states obtained for functional TANGO1 at σ=0.006 kBT/nm2 as indicated in panel (B). Note that (i) and (ii) reached local equilibrium states.

As a comparison, we made use of the dynamic computational model (Model A) to compute the final carrier states and shape parameters for various values of the membrane tension, σ, and the COPII self-interaction coefficient, χc. The resulting shape diagrams are shown in Figure 5B for both inert and functional TANGO1. Note that the COPII self-interaction parameter χc in Model A is conceptually equivalent to μc0 in the equilibrium Model B. In agreement with the results obtained with Model B (Figure 5A), we find that at low COPII self-interaction, the COPII coat either does not nucleate during the initial perturbation stage, or does nucleate but cannot provide enough bending energy to stabilize the membrane curvature against the membrane tension, thus resulting in a flat membrane (η*=0). At high COPII self-interaction, the nucleated coat successfully works against membrane tension to generate membrane curvature, generating a closed spherical bud. At intermediate COPII self-interaction, we find a transition region where the deformed membrane stabilizes as an open, shallow bud. Interestingly, the presence of functional TANGO1 dramatically widens the parameter space at which stable shallow buds are obtained. Importantly, the phase boundary at the transition from shallow to closed bud now spans a larger range of membrane tension and COPII self-interaction values (Figure 5B,C).

Overall, despite the different assumptions underlying the computational dynamic and equilibrium models, their qualitative agreement highlights the relevance of their common underlying physical mechanisms to TANGO1-mediated assembly of procollagen-containing transport intermediates.

TANGO1 properties control accessible membrane shapes through capping transition

As seen in Figures 4 and 5, the capping-uncapping transition of COPII coat by TANGO1 plays an important role in determining the transition between equilibrium-budded states. Therefore, we set out to examine the influence of TANGO1 model parameters on its capping ability.

We define ηtr as the shape parameters at which the different capping-uncapping transitions occur, which corresponds to the solutions to the equation Δfcηtr,ω=0=Δfcηtr,ω=1. Similarly, it is also informative to define the neck opening radius at which the capping-uncapping transition occurs, ρtr, which can be analogously found as the stationary points of the free energy (Equation 1) with respect to the capping fraction (Δfc/ω=0). From these equivalent definitions we obtain

(3) ηtr=n+12(1±1ξ2Rc2(1+c0ξ)2),
(4) ρtr=ξ1+c0ξ,

for c0>-1/ξ. Here ξ=κT/(2Δλ)22nm is a TANGO1-related length-scale (see parameter values in Appendix 2—table 1). These analytical results highlight how capping of COPII components by TANGO1 is promoted by large values of the TANGO1-COPII interaction, Δλ, and prevented by large TANGO1 filament bending rigidities, κT (Figure 6—figure supplement 1A). Additionally, if the bud opening radius ρ is equal to the radius of curvature imposed by the spherical polymerization of COPII, Rc, we can define a critical value of the TANGO1 linactant strength below which there is no capping Δλtr=κT21Rc-c02. This is illustrated in Figure 6A where the value of the critical COPII boundary radius ρtr (Equation 4) is plotted as a function of TANGO1 filament bending rigidity (κT) and linactant strength (Δλ). For ρ>ρtr, TANGO1 caps the COPII domains, whereas for ρ<ρtr, no capping nor ring formation occurs.

Figure 6 with 2 supplements see all
Capping is controlled by TANGO1 bending rigidity and linactant strength.

(A) Capping-uncapping phase diagram where the membrane neck radius at the radius at the trasition, ρtr (color-coded), given by Equation 4, is plotted against TANGO1 linactant strength, Δλ, and the bending rigidity, κT, for a filament of zero spontaneous curvature. Below the critical value of TANGO1 linactant strength, Δλtr, no capping occurs (no functional TANGO1 rings). Isolines for different values of ρtr are indicated by the denoted dashed lines. (B,C) Shape diagrams indicating the shape of minimal free energy, represented by the optimal shape parameter, η* (color-coded), as a function of the COPII coat polymerization energy, μc0, and of the TANGO1 linactant strength, λ (B), or the TANGO1 filament bending rigidity, κT (C). Capping-uncapping transitions are marked by thick, dashed, white lines, whereas the different shape transitions are denoted by the different dashed lines.

We then computed the optimal shape parameter and wetting fraction for a large range of values of TANGO1 bending rigidity, κT, linactant strength, Δλ, and spontaneous curvature, c0. These are presented in the form of shape diagrams in Figure 6B,C and Figure 6—figure supplement 2A. We find that, although none of these properties control the transition between shallow buds (η<1/2) and large intermediates (η>1), they are key in determining the capping-uncapping transition. Remarkably, we find once again that TANGO1 capping significantly expands the regions where stable shallow buds are energetically favored. In addition, the presence of a TANGO1 ring capping COPII subunits induced the formation of shapes with larger neck radii (Figure 6B,C, and Figure 6—figure supplement 1B). These results provide further support to our hypothesis that by capping COPII coats, TANGO1 stabilizes the formation of open buds preventing therefore the formation of fully budded spherical carriers. Such a stable wide neck would facilitate procollagen packing into the nascent intermediate.

Outward force facilitates the transition from TANGO1-stabilized buds to large transport intermediates

Finally, we examined how the application of a force directed toward the cytosolic side of the bud can facilitate the growth of a TANGO1-capped transport intermediate. The existence of such a force, although speculative in the context of procollagen export, could have several possible origins. For instance, molecular motors linking the membrane to the cytoskeleton could potentially produce such pulling forces. Another hypothetical source of force is linked to the folding of triple-helical procollagen in the ER lumen. TANGO1 recruits procollagen by binding its chaperone HSP47 (Ishikawa et al., 2016), which preferentially interacts with triple-helical procollagen (Tasab et al., 2000). Procollagen folds into a rigid triple-helix from the C terminus to the N terminus in a zipper-like manner (Engel and Prockop, 1991). Therefore, HSP47, and correspondingly TANGO1, binding sites are generated on the procollagen as it folds. We thus hypothesize that the interface between TANGO1/HSP47 and procollagen could act as a zipper helping in the elongation of triple helical rigid procollagen. The C termini of procollagens are often associated with the ER membrane (Beck et al., 1996). It is therefore possible that a ring of TANGO1 would constrain the procollagens in a bundle with the folded C termini oriented toward the growing tip of the bud. As procollagens fold, newly generated HSP47/TANGO1-binding sites will be more distant to the growing tip of the bud. The net result of this process would be procollagen applying a force directed toward the cytosol (and exerting an opposite reaction force on the TANGO1 ring). The isotropic TANGO1 ring structure would prevent the generation of any net torque and therefore of any tilt of the procollagen molecules.

Following the same protocol as above, we computed the optimal shape parameter as a function of the intensity of an outward point force for various COPII polymerization energies and membrane tensions. As shown in Figure 7A,B, we found that having a point force shifts the capping-uncapping and transport intermediate growth transitions toward lower COPII binding energies and higher membrane tensions. Interestingly, we can obtain an analytical estimate of the transition between incomplete shallow buds and large transport intermediates. To that end, we consider the situation where the free energy of an incomplete bud of shape parameter η, is equal to the free energy of a larger intermediate with an extra pearl, given by the shape parameter η+1. Equation 2 then gives

(5) μc02κbRc2+N2πRcσ=0,

which is independent of the structural details of the TANGO1 ring, as we have seen before (Figure 6B,C). The solution to this parametric equation is represented by the plane in light blue shown in Figure 7C. For completeness, in Figure 7C we also show the numerically found transition surfaces between flat membranes and shallow buds (dark blue surface, Figure 7C) and between large capped intermediates and full uncapped intermediates (orange surface, Figure 7C). Additionally, we rely on Equation 5 to define the critical force N*=2πRcσ-μc0+2κb/Rc2 at which the transition to a large transport intermediate is triggered. For the experimental values reported in Appendix 2—table 1and μc0=0.03kBT/nm2, we obtain N*~ 0.34kBTnm=1.4 pN, which, for comparison, is in the same order of magnitude of the force generated by molecular actin polymerization (Footer et al., 2007), and an order of magnitude smaller than typical force required to extract a membrane tethers (Derényi et al., 2002). Taken together, our results indicate that the formation of large transport intermediates can be greatly facilitated in the presence of TANGO1 by forces of physiological ranges oriented toward the cytosol. This mechanism could be complementary to the membrane tension regulation mechanism described above.

Outward force shifts capping transitions and facilitates bud formation.

(A, B) Shape diagrams showing the optimal shape parameter, η* (color coded), as a function of the applied force, N, and the COPII coat polymerization energy, μc0, for σ=σER=0.003 kBT/nm2 (A); or the membrane tension, σ, for μc0=0.03 kBT/nm2 (B). (C) Three-dimensional shape diagram, indicating the transition zones between flat membranes (η*=0), incomplete buds (η*<0), and large transport intermediates (η*>1) – as given by Equation 5 (light blue surface) and by numerical solution of model B (dark blue and orange surfaces) –, as a function of the COPII coat polymerization energy, μc0, membrane tension, σ, and applied force, N. Unless otherwise specified, the elastic parameters used for all the calculations shown in (A–C) are listed in Appendix 2—table 1.

Discussion

A model for TANGO1-mediated procollagen export from the ER

Here we delineated a feasible biophysical mechanism of how TANGO1 contributes to the formation of procollagen-containing transport intermediates at the ER. In particular, we presented two complementary models to study this process. The first model (Model A) is a dynamic model that does not impose any particular geometry for the intermediate shape. We next complemented this dynamic model with a more simplified but analytically tractable equilibrium model (Model B), which assumes that COPII polymerizes into lattices of spherical geometry. Physically, these models can be understood in terms of a competition between different driving forces. Each of these forces can either prevent or promote the elongation of procollagen-containing transport intermediates. The results obtained with these two complementary models of large transport intermediate formation reinforce the notion that TANGO1 rings serve to modulate the formation of COPII carriers for the export of bulky cargoes.

We previously showed that TANGO1 forms rings at ERES surrounding COPII components (Raote et al., 2017). We also revealed interactions that are required for TANGO1 ring formation, which are also important to control TANGO1-mediated procollagen export from the ER (Raote et al., 2018). However, it still remained unclear how TANGO1 rings organize and coordinate the budding machinery for efficient procollagen-export. Here, we propose that TANGO1 rings form at ERES by assembling as a filamentous structure made of different components of the TANGO1 family of proteins (Figure 1B,C). Evidence for the existence of linear assemblies of transmembrane proteins has indeed been reported in the context of transmembrane actin-associated (TAN) lines that couple outer nuclear membrane components to actin cables (Luxton et al., 2010). The components of the TANGO1 filament have an affinity for COPII subunits (Saito et al., 2009), leading to a capping of the periphery of a COPII lattice (Glick, 2017; Raote et al., 2018). This effectively reduces the line energy of the COPII coat and therefore we propose that, by capping COPII lattices, TANGO1 filaments can act as linactants (Figure 1B,C). In the context of HIV gp41-mediated membrane fusion, linactant compounds, such as vitamin E, lower the interfacial line tension between different membrane domains to inhibit HIV fusion (Yang et al., 2016).

When the association of TANGO1 with COPII subunits was abrogated –either by expressing TANGO1-∆PRD or by silencing the expression of SEC23A–, TANGO1 formed either smaller rings or long linear filamentous structures or planar clusters (Raote et al., 2018). In cells expressing TANGO1-∆PRD, the interaction between one of the filament components, TANGO1, and the COPII subunits is abolished. However, a TANGO1 filament can still be formed because this mutant still interacts with other TANGO1 or cTAGE5 proteins (Raote et al., 2018). In this situation, the filament proteins cTAGE5 (Saito et al., 2011; Saito et al., 2014) and TANGO1-Short (Maeda et al., 2016) can still bind the COPII component Sec23A. Because the affinity to bind to the peripheral COPII subunits is reduced, the filaments should be less line-active, and therefore less able to cap COPII components. Our theoretical results presented here predict that decreasing the TANGO1 filament linactant strength, λ, prevents capping of the peripheral COPII components and therefore results in a lower probability of having open carriers (Figure 6), which can lead to the observed defects in terms of ring structure and procollagen export.

Our results show that the formation of TANGO1 rings helps stabilize the COPII bud neck (Figures 2 and 5). This, we suggest, could allow for an efficient recruitment of procollagen molecules by TANGO1 to the exit site. It is not clear how long it takes for a procollagen molecule to fully fold into an export-competent triple helix after its translation into the ER, and it is possible that TANGO1 can act as a sensor of procollagen folding to couple it with the export machinery. However, in experiments where type I procollagen triple-helical stabilization and ER export were synchronized, fully folded procollagen required ~15 min to reach the early Golgi compartment (McCaughey et al., 2019). Since the half-lives of COPII components on the ER membrane are of the order of a few seconds (Forster et al., 2006), it seems likely that there is a mechanism in place to stabilize open nascent carriers, which helps to fully pack complex cargoes. Our theoretical results (Figure 2) support the proposed mechanism by which TANGO1 rings arrest the growth of standard COPII carriers and stabilize open shallow buds for the efficient packaging of procollagens (Figure 8A,B).

Schematic working model of TANGO-mediated bulky cargo export.

(A) In absence of functional TANGO1, COPII-coated (orange) spherical vesicles assemble normally, generating spherical carriers of between 60–90 nm in size. In absence of TANGO1, procollagens (magenta) cannot be packed into such small carriers. (B) In presence of a functional TANGO1 (light blue), a filament forms capping the base of a growing COPII patch (see top view in the top right subpanel) and packages procollagens to the export sites. At the high membrane tension of the ER, our results showed that this TANGO1 fence stabilizes a shallow bud, which might allow the efficient packaging of export-competent procollagens. (C) The NRZ complex (dark blue), which is recruited to the procollagen export sites by the TANGO1 TEER domain, tethers ERGIC53-containing membranes. (D) A possible outwards-directed force (magenta arrow) facilitates the generation of a large transport intermediate. (E) A combination of membrane tension decrease (possibly mediated by fusion of ERGIC membranes), outwards-directed force, and the polymerization of COPII lattices, contribute to the growth of a large transport intermediate commensurate with long semi-rigid procollagen molecules. The actual shape of the transport intermediate and whether it is fully or only partially coated still remain unknown.

Once a TANGO1 ring forms and stabilizes a shallow bud, the results of our model indicate that carrier expansion can proceed via at least two different, non-exclusive scenarios (Figure 8C,D): (i) local reduction of the membrane tension (Figures 35) and (ii) appearance of a directed force applied at the growing carrier and pointing toward the cytosol (Figure 7). Additionally, it is also possible that carrier growth occurs by an increase in the polymerization ability of COPII coats (Figure 5). It is possible that TANGO1 can directly or indirectly control each of these mechanisms (Ma and Goldberg, 2016; Raote et al., 2018). Notably, the TANGO1 ring properties, such as the linactant strength or the filament bending rigidity, are not drivers for the incomplete bud to large transport intermediate transition (Figure 6) but rather, they enhance the regions of the parameter space where carrier shapes with wide-open necks are stabilized, as opposed to fully formed vesicles or unassembled coats (Figure 5A,B).

The results of our models indicate that a transient reduction of the ER membrane tension can induce a transition from a stable shallow bud encircled by a TANGO1 ring to a large transport intermediate, that is not reabsorbed upon recovery of the tension (Figures 3 and 4). It is worth noting that, despite the different modeling and implementation choices taken in these two approaches, the values of the membrane tension at which the predictions agree only differ by a factor two. This difference could certainly be further reduced by undergoing a thorough analysis of the computational model's parameter space. However, given the computational cost of such study and the uncertainty of the experimental estimates for the ER and Golgi membrane tensions, seeking such a quantitative match between two qualitative models would only bring very limited insights. Finally, whether and how such tension regulation occurs at the level of the ERES still remains to be fully resolved. Nevertheless, we suggest a possible way by which TANGO1 could act as the membrane tension regulator at the ERES. We propose that the fusion of ERGIC53-containing membranes tethered by the TANGO1 TEER domain (Raote et al., 2018) would be the trigger for carrier growth. In particular, the ER-specific SNARE protein Syntaxin18 and the SNARE regulator SLY1, both of which are involved in membrane fusion reactions at the ER, are also required for procollagen export in a TANGO1-dependent manner (Nogueira et al., 2014). Fusion of ERGIC membranes to the sites of procollagen export would lead to a local and transient reduction of the membrane tension (Sens and Turner, 2006). In this scenario, TANGO1 would act as a regulator of membrane tension homeostasis to control procollagen export at the ERES (Figure 8C,E). We have recently proposed that ERGIC membranes fuse directly or adjacently to the growing transport intermediate to allow for membrane addition and tension release; and showed that compartment mixing can be arrested by the TANGO1 ring serving as a diffusion barrier (Raote et al., 2020). In our models, we have not included the effects of a partial diffusion barrier at the base of the growing carrier. Although these effects could lead to changes in the dynamics of carrier growth as discussed below, we do not expect any major qualitative changes in our proposed mechanisms of carrier elongation.

From the free energy profile shown in Figure 4A, we also noticed that the system needs to overcome an energy barrier to reach the globally stable state. Hence, depending on the dynamics of the system, this can be kinetically trapped into a locally stable deep bud (yellow shape in Figure 4A, right panel). Although our analytical equilibrium model cannot account for the dynamics of such transitions, we can give some estimates. First, mechanical equilibration of the membrane shape (τmech) can be theoretically estimated to be of the order of milliseconds (see e.g. Campelo et al., 2017; Sens and Rao, 2013), which is also in accordance to our own results from model A, where shape changes are found within few milliseconds (Figure 3). Second, the diffusive behavior of membrane tension has been measured at the plasma membrane of HeLa cells, with a diffusion coefficient of Dσ=0.024 μm2/s (Shi et al., 2018), which gives a characteristic diffusion time of the order of τσ~1 s (using characteristic length scales of 100500 nm). Since τστmech, membrane shape equilibrates much faster than the recovery of the membrane tension. Moreover, our recent findings that TANGO1 can induce a diffusion barrier at the base of the growing bud (Raote et al., 2020), suggest that the dynamics of tension equilibration can be even slower.

In parallel, we also hypothesize a situation where TANGO1 rings help pushing procollagen molecules into the growing carrier and couple this pushing force to procollagen folding, through the chaperone HSP47 (Figure 8D,E). Because HSP47 chaperone assists in folding (and hence in rigidifying) procollagen, it is tempting to speculate that the trimerization of procollagen occurs concomitantly to the its export and that the physical interaction between TANGO1 rings and procollagen/HSP47 could serve as a means to couple procollagen folding to force production. Although the existence of this pushing force is largely speculative, it could, according to our model, promote formation of a large intermediate and hence TANGO1 could act as a sensor of procollagen folding to couple it with the export machinery.

Finally, the results of our dynamic model show that the shape of the elongated carrier is a pearled tubule (Figure 3D and Figure 3—video 1). The fission of the upstream pearls is prevented in our model by a steric hindrance of the procollagen molecules packed inside the tubule (Figure 8E). Since TANGO1 is the receptor molecule that binds procollagen and packs it to facilitate its export (Saito et al., 2009), TANGO1 is indirectly required to prevent the fission of upstream necks. The results of our dynamic model indicate that during the elongation of the structure (Figure 3D and Figure 3—video 1). We previously proposed that the large transport intermediate is converted into a tunnel connecting ER to the ERGIC/early Golgi cisternae (Raote and Malhotra, 2019). If so, an appealing possibility is that, at this stage, the role of a TANGO1 ring would be to prevent lipid mixing between these transiently connected organelles by acting as a diffusion barrier (Raote et al., 2020). Finally, after procollagen delivery to the acceptor compartment, fission of the neck between the first two pearls of the tubule would not be sterically prevented anymore and therefore the tunnel could be disconnected. Future work will be required to help elucidate the precise control of the timing between these proposed fusion and fission events.

What controls organelle size in the context of intracellular trafficking? There has been a lot of work on what set the size of organisms, the size of tissues in an organism, and the size of cells in a tissue (Guertin and Sabatini, 2006; Marshall et al., 2012). However, there has been less work toward elucidating what sets the size of organelles relative to the cell. Extensive cargo transfer while trafficking bulky cargoes such as collagens leads to large amounts of membrane being transferred from one organelle to another. To maintain organelle homeostasis, loss of membrane from a compartment has to be concomitantly compensated by membrane acquisition from the biosynthetic pathway or by trafficking from other organelles; the arrival and departure of membrane at each compartment has to be efficiently balanced. How is this homeostatic balance controlled? Changes in membrane tension have been described to affect rates of exocytosis and endocytosis at the plasma membrane (Apodaca, 2002; Kosmalska et al., 2015; Wu et al., 2017) and of growth of membrane buds and tubes in general (Derényi et al., 2002; Cuvelier et al., 2005). Interestingly, a theoretical model has also established a crucial role for membrane tension in modulating the budding of clathrin-coated vesicles (Hassinger et al., 2017). Furthermore, it has been recently proposed that Atlastin-mediated maintenance of ER membrane tension is required for the efficient mobility of cargo proteins (Niu et al., 2019); and that the formation of intra-lumenal vesicles in endosomes is also regulated by membrane tension (Mercier et al., 2020). However, control of endomembrane trafficking by membrane tension still remains challenging to study experimentally and hence remains incompletely understood. We suggest that inter-organelle hubs, such as a TANGO1-scaffolded ERES-ERGIC, control the local tension homeostasis at specific membrane sub-domains and regulate the membrane flux between these organelles.

Proposal of experimental approaches to test the model

We have proposed and analyzed a theory by which TANGO1 assembles into a ring at the ERES to facilitate cargo export. The results of the theoretical biophysical models presented are compatible with our current understanding of the biology of this complex process. Importantly, our analyses are meant to help design experiments to further test our hypotheses. We speculate that a TANGO1 ring functions as a hub to collect and concentrate procollagens, to stabilize open COPII lattices, and to recruit and fuse membranes thus alleviating the ERES tension while promoting the export of procollagens from the ER. Although many of these individual events are based on experimental evidence, we lack an understanding of how collagens are collected and then percolated into the growing intermediate, whether the binding of TANGO1 to the rims of growing COPII coats acts as a linactant, the involvement of tension, the mechanism of tension sensing, and finally how these events are coordinated to cause procollagen export. It is important to be able to ask these questions because they highlight the gaps in our understanding of the process of cargo export at the ER. We propose a set of experimental procedures to test our hypotheses. The new experimental data will undoubtedly improve our understanding of how cells engage to export cargoes based on their size, volume, and the overall cellular needs.

Does TANGO1 form a linear or quasi-linear filament held together by lateral protein-protein interactions?

Although our hypothesis 3 (see Model Development section) is based on a number of indirect experimental observations, to our knowledge, there is no direct evidence for the existence of TANGO1 filaments. A first step to address this question will be to resolve the stoichiometry of the TANGO1 family proteins within a TANGO1 ring. Controlled photobleaching (Lee et al., 2012) or DNA-PAINT (Stein et al., 2019) of the single-labeled, endogenously expressed proteins could allow the recording of the number and spatial positions of single fluorophores in individual TANGO1 rings. These results, after complete quantitative reconstruction of all the single molecule signals, should provide an absolute stoichiometry and ultra-resolved structure of TANGO1 organization in the ERES. Ultimately, in vitro reconstitution of TANGO1 ring formation in synthetic lipid bilayers by using recombinant proteins will be of paramount importance to experimentally observe the formation of TANGO1 filaments, assess the minimal components required for their formation, and eventually measure the elastic properties of a TANGO1 filament.

Does the TANGO1-directed fusion of ERGIC membranes modulate the ERES membrane tension for procollagen export?

Future efforts in applying cutting-edge, super-resolution multicolor live-cell microscopy (Bottanelli et al., 2016; Ito et al., 2018; Liu et al., 2018; Schroeder et al., 2019) will help monitor the fusion of ERGIC membranes to the ER and couple these events to the formation of procollagen-containing transport intermediates. In addition, our hypothesis of TANGO1-mediated regulation of membrane tension is based upon the premise that fusion of ERGIC-53-containing vesicles to the procollagen export sites locally decreases the membrane tension. A recently established fluorescent membrane tension sensor (Colom et al., 2018; Goujon et al., 2019) could provide a means to monitor such effects in relation to procollagen export.

Is there an outwards-directed force contributing to transport intermediate elongation?

It has been shown that procollagen export from the ER does not require the presence of an intact microtubule network (McCaughey et al., 2019). However, the involvement of other force-producing agents, such as actin-myosin networks, remains unknown. The identification of additional physiological interactors of TANGO1 by proximity-dependent labeling assays, such as BioID (Roux, 2018), and the subsequent screening for candidates that can exert such forces could help identify possible molecular players involved in force-generation. However, it is important to stress that our model can explain the formation of large transport intermediates even in the absence of an applied force (Figure 7).

What is the shape of the transport intermediate that shuttles collagens from the ER to the ERGIC/Golgi complex?

Our full dynamic model predicts that the TANGO1-mediated procollagen-containing transport intermediates are shaped as a pearled tubule (Figure 3D). That this prediction holds true in tissue cultured cells, or alternatively that the transport intermediates have a more cylindrical geometry, as proposed from in vitro data of COPII polymerization in the presence of PPP sequences, such as those in the TANGO1 PRD (Ma and Goldberg, 2016; Hutchings et al., 2018), will reveal how TANGO1 modulates COPII polymerization and coat flexibility. To this end, three-dimensional, multicolor super-resolution microscopy techniques, such as 3D single molecule localization microscopy (3D-SMLM) or 3D stimulated emission depletion (3D-STED) microscopy, could provide sufficient resolution to map the three-dimensional morphology of the transport intermediates. Recent efforts by using 3D-SMLM and correlative light and electron microscopy (CLEM) have revealed the existence of large procollagen-containing structures (Gorur et al., 2017; Yuan et al., 2018). However, a recent report suggested that those structures were directed for lysosomal degradation and not for trafficking to the Golgi complex (Omari et al., 2018). By contrast, direct transport of procollagen between the ER and the Golgi complex by a short-loop pathway in the absence of large vesicles has been recently proposed (McCaughey et al., 2019), opening to the possibility of a direct tunneling mechanism for trafficking proteins between compartments (Raote and Malhotra, 2019). Eventually, the use of modern electron microscopy techniques such as cryo-electron tomography (Beck and Baumeister, 2016) or focused ion beam-scanning electron microscopy (FIB-SEM) (Nixon-Abell et al., 2016) will help solve this issue on the morphology of the transport intermediates that shuttle procollagens from the ER to the Golgi complex.

Concluding summary

In summary, we proposed a theoretical mechanical model that explains how TANGO1 molecules form functional rings at ERES, and how these TANGO1 rings assemble the machinery required to form a large transport intermediate commensurate with the size of procollagens. We envision that our hypotheses and the predictions of our model will guide new lines of experimental research to unravel mechanisms of COPII coats organization for the export of complex cargoes out of the ER.

Appendix 1

Computational dynamic model of TANGO1-mediated bulky cargo export (Model A)

In this Appendix, we derive a dynamic model of a lipid bilayer whose spontaneous curvature is dictated by the diffusion and interaction of two membrane-bound species, and specialize it to COPII and TANGO1.

The proposed model extends the work of Tozzi et al., 2019 to account for a second membrane-bound species and apply it to TANGO1-COPII complex assembly. We therefore focus our exposé on this novel aspect, and direct readers interested in the detailed underlying theory to Tozzi et al., 2019; Arroyo et al., 2018; Rahimi and Arroyo, 2012; Torres-Sánchez et al., 2019.

Onsager’s variational approach: energetics, dissipation, and power input

Our modeling approach is based on Onsager’s variational formalism of dissipative dynamics (Arroyo et al., 2018; Rahimi and Arroyo, 2012). The fundamental principle consists in describing the time evolution of the system through a minimization process of energy released, energy dissipated, and energy exchanged by the system. In other words, if ˙ is the rate of change of free energy, 𝒟 is the total dissipation potential, and 𝒫ext is the power input, the rate of change of the system can be obtained by minimizing at each time point the Rayleighian functional

(A1) =˙+𝒟+𝒫ext.

In this section, we define the energetic contributions to each of these quantities.

Free energy

We consider a lipid bilayer as a material surface parametrized by 𝐫(θα,t), where (θ1,θ2) are the Lagrangian surface coordinates, and t is the time. The state variable associated with the mechanical energy of the system is 𝐫, while the state variables associated with the chemical energy of the systems are the local area fractions of COPII and TANGO1, ϕc and ϕt, respectively. Note that these latter are bounded and should satisfy ϕc>0, ϕt>0, and 0ϕc+ϕt1.

Mechanical energy

The bending energy of the membrane is described by the classical Helfrich model with spontaneous curvature (Helfrich, 1973; Campelo et al., 2014; Chabanon et al., 2017)

(A2) bend=Γκ2(J-Ccϕc)2𝑑S,

where κ is the bending modulus, J is the total curvature (twice the mean curvature, H) of the membrane, and the integration is performed over the entire membrane patch, Γ. Here we consider a local spontaneous curvature Ccϕc resulting from the presence of COPII complexes. We assume a linear dependence of the spontaneous curvature on COPII local coverage, with Cc=2/Rc being the maximum spontaneous curvature induced by a full coverage of COPII (ϕc=1) with preferred radius of curvature Rc.

Appendix 1—figure 1
Schematic of a shallow COPII/TANGO1 bud and definition of the geometrical parameters favored by the proteins.

The total curvature J is a function of the state variable 𝐫. Briefly, from standard differential geometry (Deserno, 2015; do Carmo, 2016) we have that the tangent vectors at each point of the membrane are 𝐠α=𝐫/θα. They define the natural basis of the tangent space, from which the covariant components of the metric tensor are obtained gαβ=𝐠α𝐠β. Additionally, the unit normal to the surface is 𝐧=(𝐠1×𝐠2)/g, where g=det(gαβ). From these definitions, one gets the components of the second fundamental form kαβ=𝐧𝐠α/θα, whose invariants are the total curvature J=tr 𝐤=kαβgαβ, and the Gaussian curvature K=det𝐤=kαβgβγ. Here gβγ are the components of the inverse of the metric tensor, obtained from gαβgβγ=δαγ. Note that for simplicity, we have neglected the contribution of the Gaussian curvature to the bending energy in Equation (A2).

Based on our experimental observations (Raote et al., 2018), TANGO1 proteins are assumed to favor a ring-like conformation with a specific radius of curvature ρt and a preferred angle with the plane of the ring θt (see Appendix 1—figure 1). As detailed later, we will restrict the model to axisymmetric shapes. Therefore for clarity, here we directly write an axisymmetric expression of the functional for the TANGO1 ring stiffness as

(A3) stif=Γ[κρ2(1ρ-1ρt)2+κθ2(θ-θt)2]ϕt𝑑S,

where κρ and κθ are, respectively, the stiffness coefficients associated with the ring curvature 1/ρ and angle with the membrane θ.

Chemical energy

We consider two distinct membrane-bound species representing COPII and TANGO1 proteins. They are described by continuous surface fractions ϕc and ϕt, respectively. We consider the entropic mixing energy of the two proteins to be represented by a Flory–Huggins type energy such as

(A4) ent=ΓkBTap[ϕclnϕc+ϕtlnϕt+(1-ϕc-ϕt)ln(1-ϕc-ϕt)]𝑑S,

where ap is the molecular area of the proteins, assumed for simplicity to be identical for both proteins. The self-interaction and line energy of COPII proteins are

(A5) c=Γχc2apϕc2+Λc2ap|ϕc|2dS,

where χc is negative for attractive interactions. The parameter Λc ensures a length-scale associated with the interface of the COPII domain: the spatial gradient of ϕc is smoother for large values of Λc.

Similarly, we write the self-interaction and line energy of TANGO1 proteins as

(A6) t=Γχt2apϕt2+Λt2ap|ϕt|2dS.

Finally, the interactions between COPII and TANGO1 proteins are

(A7) ct=Γχct2apϕcϕt+Λct2apϕt|ϕc|2dS,

where the first term represents the affinity between the two proteins and the second term represents the affinity of TANGO1 for the COPII coat boundary. Combining the second term of Equation (A7) with the second term of Equation (A5), one can see that TANGO1 modulates the interfacial energy of COPII with an effective parameter Λc+Λctϕt.

The total free energy is the sum of the protein and membrane contributions:

(A8) =bend+stif+ent+c+t+ct.

Dissipation mechanisms

Dissipation of mechanical energy occurs through in-plane shear stress of the lipid bilayer as it dynamically deforms under the action of a Lagrangian velocity of the membrane 𝐕=𝐫/t=𝐯+vn𝐧, where 𝐯 and vn are its tangential and normal components respectively. This membrane ‘flow’ results in the time evolution metric tensor, whose time derivative in Lagrangian setting is the rate-of-deformation tensor of the surface (Torres-Sánchez et al., 2019)

(A9) d=12gt=12(v+vT)vnk.

The first term, involving the membrane tangential velocity 𝐯 represents the contribution of the tangential flow to the membrane deformation. The last term, involving the normal velocity vn, accounts for the shape change of the membrane. The rate of change of local area is tr(𝐝)=𝐯-vnJ, which is zero for an inextensible membrane. We consider the lipid bilayer to be in a fluid phase that can be approximated by an interfacial viscous Newtonian fluid (Arroyo and Desimone, 2009). Neglecting intermonolayer friction, and assuming membrane inextensibility, the dissipation potential by in-plane shear stress takes the form

(A10) 𝒟mech=Γηm𝐝:𝐝dS,

where ηm is the in-plane viscosity of the lipid bilayer.

Dissipation of chemical energy occurs by protein diffusion along the membrane surface, described by the species diffusive velocities relative to the Lagrangian coordinates, wc and wt for COPII and TANGO1, respectively. Assuming for simplicity that the two proteins have the same molecular drag coefficient ξ and surface area ap, the chemical dissipative potential of the system is

(A11) 𝒟chem=Γξ2ap(ϕc|𝐰c|2+ϕt|𝐰t|2)𝑑S.

Given that the typical length scale of our system is well below the Saffman-Delbrück length scale (∼1–10 µm), we can safely neglect dissipation arising from the friction between the membrane and the cytosol [Arroyo and Desimone, 2009]. The total dissipation potential of the system is 𝒟=𝒟mech+𝒟chem.

Power supplied

Mechanical power can only be supplied to our system through the boundary of the membrane patch Γ in the form of edge tractions and moments. Defining 𝝉 as the unit tangent vector along Γ so that 𝝂=𝝉×𝐧, the boundary tractions and moment power inputs are

(A12) mech=Γ(Fτvτ+Fνvν+Fnvn)dl+ΓMνn˙dl,

where Fτ, Fν and Fn are the traction components at the boundary, M is the bending moment per unit length, and 𝐧˙ is the material time derivative of the surface normal.

In this model, we assume that all proteins are membrane bound and provided at the boundary of the domain by a protein reservoir of fixed chemical potential. The chemical power supply is therefore written

(A13) 𝒫chem=Γ(μ¯c0apϕc𝐰c+μ¯t0apϕt𝐰t)𝝂𝑑l,

where μ¯c0 and μ¯t0 are the fixed boundary chemical potentials of COPII and TANGO1, respectively. The total power supplied to the system is 𝒫ext=𝒫mech+𝒫chem.

Governing dynamics

Protein surface transport

Based on the definitions of the free energies, we define the energy density W as =ΓW𝑑S. The chemical potentials of the two species can be written as μ¯i=ap(Wϕi-Wϕi), with i={c,t} (Tozzi et al., 2019). Here Wϕi and Wϕi are the partial derivatives of W with respect to ϕi and ϕi, respectively. The chemical potentials for each species are therefore

(A14) μ¯c=apκCc(JCcϕc)+kBTln(ϕc1ϕcϕt)+χcϕc(Λc+Λctϕt)2ϕc+χct2ϕtΛctϕtϕc,

and

(A15) μ¯t=ap2[κρ(1ρ-1ρt)+κθ(θ-θt)]+kBTln(ϕt1-ϕc-ϕt)+χtϕt-Λt2ϕt+χct2ϕc+Λct2|ϕc|2,

respectively. The diffusive velocity of the species i can be expressed as a function of the species chemical potential μ¯i by minimizing the Rayleighian with respect to 𝐰i, giving 𝐰i=-μ¯i/ξ (Tozzi et al., 2019). The strong form of the transport equations for the proteins on an incompressible surface is therefore

(A16) ξϕi˙(ϕiμ¯i)=0with i={c,t},

with the diffusive flux for each species given by

(A17) ϕcμ¯c=[apκCcJχct2ϕt]ϕc[(χc+apκCc2Λct2ϕt)ϕc+kBT1ϕt1ϕcϕt]ϕc+2Λctϕtϕc2ϕc+[(Λc+Λctϕt)ϕc](2ϕc),

and

(A18) -ϕtμ¯t=-[apSρθ+χct2ϕc+Λctϕc2ϕc]ϕt-[χtϕt+kBT1-ϕc1-ϕc-ϕt]ϕt+(Λtϕt)(2ϕt),

respectively. Here, we defined Sρθ=κρ(1/ρ-1/ρt)(1/ρ)+κθ(θ-θt)θ and 2 is the surface Laplacian. These expressions highlight that COPII transport explicitly depends on the membrane curvature through the J term, while TANGO1 transport explicitly depends on the ring radius and its angle with the membrane through Sρθ.

Membrane dynamics

To enforce local membrane incompressibility we introduce a Lagrange multiplier field σ that can be interpreted as the membrane tension (Rangamani et al., 2014). Consequently, we aim at minimizing the Lagrangian functional

(A19) =+Γσtr(𝐝)𝑑S=˙+𝒟+𝒫ext+Γσtr(𝐝)𝑑S,

where is the Rayleighian defined in Equation (A1). Following Tozzi et al., 2019, the dissipation rate of the free energy ˙ and the local area constraints can be expressed as functionals of the rate variables (𝐰,𝐯,vn). The governing equations for the membrane mechanics are obtained by minimizing Equation (A19) with respect to (𝐰,𝐯,vn), and maximizing it with respect to σ. In the case of W=Wbend, this results in the well-known shape equation and incompressibility condition (Zhong-can and Helfrich, 1989; Steigmann et al., 2003). A full analysis of the governing equation for the total energy density of the COPII/TANGO1 system is out of the scope of this paper. For practical purposes, in what follows we proceed to a numerical minimization of Equation (A19).

Model implementation

Axisymmetric parametrization and numerical scheme

Details of the model implementation for a single species can be found in Tozzi et al., 2019. Briefly, we formulate the model in axisymmetric coordinates so that each material point of the membrane is expressed in terms of the distance to the axis of symmetry ρ(u,t) and of the axis of symmetry coordinate z(u,t). Here, u[0,1] is the Lagrangian coordinate along the membrane arclength, and t is time. The Dirichlet boundary conditions in the axisymmetric system take the form

(A20) ρ(0,t)=0;z(0,t)=0;z(1,t)=0;z(1,t)=0.

The fixed chemical potentials at the open boundary are ensured by

(A21) ϕc(1,t)=ϕc0;ϕc(1,t)=0;ϕt(1,t)=ϕt0;ϕt(1,t)=0,

where ϕc0 and ϕt0 are the imposed protein densities of COPII and TANGO1, respectively, at the open boundary, mimicking protein reservoirs far from the budding site.

To solve numerically the coupled chemo-mechanical system, we employ a staggered approach where at each time step, we first solve the protein density field for a given membrane shape, and then update the shape at fixed membrane density distribution. The state variables are discretized using B-splines with cubic B-spline basis functions. The chemical problem is solved with the finite element method using a backward Euler discretization in time of the protein transport equations Equation (A16), and Newton’s method to solve the resulting non-linear system. The mechanical problem is solved for a given distribution of proteins by minimizing the incremental Lagrangian from Equation (A19) with respect to space variables and maximizing with respect to the Lagrange multiplier.

Simulation and analysis protocols

After a preliminary parameter analysis informed by the physics of the problem (see also the main text for a discussion on parameters), we chose the reference set of parameters given in Appendix 1—table 1. Except stated otherwise, all results are obtained for these parameter values. All computations are done on an initially flat membrane patch of 250 nm radius.

Appendix 1—table 1
Model parameters.
SymbolParameterValue
Material parameters
κMembrane bending rigidity20 kBT
RcPreferred radius of curvature of COPII35 nm
CcCOPII spontaneous curvature-2/Rc nm−1
ρtTANGO1 preferred radius of curvature45 nm
θtTANGO1 preferred angle of curvatureπ/4
κρTANGO1 ring radius rigidity120 kBT
κθTANGO1 ring angle rigidity6.4×10-4 kBT nm−2
apCharacteristic area of a protein100 nm2
χcCOPII self-interaction coefficient−2 kBT
χtTANGO1 self-interaction coefficient−1.2 kBT
χctAffinity coefficient between COPII and TANGO 1−0.4 kBT
ΛcCOPII interfacial coefficienttwo kBT
ΛtTANGO1 interfacial coefficient0.4 kBT
ΛctCoupling interfactial coefficient0.4 kBT
ηmMembrane viscosity5×10-9 N s m−1
ξMolecular drag coefficient (=2πηm)3.14×10-8 N s m−1
Model constraints
ϕc0COPII protein surface fraction at the open boundary0.1
ϕt0TANGO1 protein surface fraction at the open boundary0.02
σMembrane tension0.004–0.0096 kBT/nm2
NVertical axial force (applied for nucleation)0–0.56 kBT/nm
ρcolMinimal neck radius in presence of procollagen molecules7.5 nm
Stable equilibrium

We assume that an equilibrium shape is reached if the maximum displacement between two time-steps of each material points is below 5 × 10−3 nm for more than 10 time-steps in a row over a cumulative time larger than 1 ms.

Shape parameter

To facilitate a quantitative comparison between the end-states of the system obtained for different sets of parameters, we use the shape parameter, which is essentially the maximum height of the bud normalized by the preferred diameter of curvature of COPII η=zmax/2Rc (see also main text).

Coat nucleation

In our system, the flat membrane state is a locally (sometimes globally) stable equilibrium state. This means that a perturbation needs to be applied to initiate the nucleation of COPII coats. To ensure a reproducible perturbation protocol, we define a criteria for COPII coat nucleation such as the average surface density of COPII within a surface area Anuc=π(25nm)2 around the axis of symmetry must satisfy Anucϕc𝑑S>0.75Anuc. Starting from a flat membrane patch with homogeneous distribution of species, a small upward point force of N= 0.16 kBT/nm is applied at ρ=0. The force induces membrane deformation and initiates the recruitment of COPII. If the force is sufficient to nucleate a COPII coat as defined above, the point force is set back to zero, and the system is free to evolve. Alternatively, if an equilibrium is reached but the nucleation criteria is not satisfied, we gradually increase N until either a COPII coat is nucleated or until N> 0.56 kBT/nm, in which case we assume the flat membrane to be the stable state. The up-ward point force is implemented within the arclength parametrization by setting Fn(0,t)=N in the power supply Equation (A12).

Neck closure

In the cases where the transport carrier closes, no equilibrium is reached. Consequently, we assume that if the neck radius goes below 5 nm, we reach the small length scale limit of the continuum modeling approach, and assume neck closure. Because the neck closure event happens at different times after the neck snap-through, in order to facilitate the comparison of the carrier height in a systematic manner in the equilibrium shape phase diagrams, we take η at the minimum bud height after the neck snaps.

Prevention of neck closure by procollagen molecules

In simulations where procollagen molecules prevent the total closure, an energy penalty Γ10-3κ/(ρ-ρcol)2𝑑S is imposed on the portion of the membrane u[0.1;0.8] using a hyperbolic tangent of the form 0.5[tanh(100(u-0.1))-tanh(100(u-0.8))].

Appendix 2

Equilibrium analytical model of TANGO1-assisted transport intermediate formation (Model B)

Detailed description of the physical model of TANGO1-dependent transport intermediate formation

Here, we present the detailed description and derivation of the physical model of TANGO1-dependent transport intermediate formation presented in the main text. Our model builds on a previously presented mechanical model for clathrin-coated vesicle formation (Saleem et al., 2015), which includes the contributions from the coat polymerization on the membrane, the line tension of the polymerized coat, the membrane resistance to bending, and the membrane tension. We extended this model to allow for the growth of larger transport intermediates by incorporating (i) the effects of TANGO1 rings on COPII coats; and (ii) an outward-directed force (Appendix 2—figure 1A).

Analogously to the clathrin vesicle model by Saleem et al., 2015, we consider that the free energy per unit area of coat polymerization onto the membrane, μc, has a bipartite contribution arising from the positive chemical potential of COPII binding to the membrane, μc0, and from the negative contribution of membrane deformation by bending, so μc=μc0-2κbRc2, where κb is the bending rigidity of the lipid bilayer, and Rc is the radius of curvature imposed by the spherically polymerized COPII coat. We define the COPII chemical potential, μc0, as the free energy gain of polymerization of a COPII unit area on the ER membrane, which includes the contributions of the interactions between the coat and the membrane (μc-m) and between the coat subunits (actual polymerization interactions, μc-c). For clathrin-coated vesicle formation, Saleem et al., 2015 showed that the direct coat-coat interactions are the major contributors to the assembly of the coat. Based on this, we consider the simplified situation where the binding energy μc0 represents the polymerization energy due to COPII-COPII binding, and therefore the reservoir of COPII is the rest of the membrane (as is the case also for our dynamic model, see Appendix 1). An additional term associated to the possible elastic deformation of the COPII coat could be considered as μcoat,bend=-12κcoat2Rc-2Rcoat2, where κcoat is the coat rigidity and Rcoat is the spontaneous radius of curvature of the coat (Iglic et al., 2007; Boucrot et al., 2012). However, we assume here, for simplicity, that the coat is considerably more rigid than the membrane, κcoatκb, so there is no coat deformation and Rc=Rcoat. Alternatively, coat contribution to membrane bending has also been tackled by using a spontaneous curvature-based model (Agrawal and Steigmann, 2009; Hassinger et al., 2017). In our analytical model, we follow the approach of Saleem et al., 2015, which allows us to define the preferred spherical architecture of the polymerized coat. A spontaneous curvature-based approach was followed for our computational analysis of carrier shapes (Appendix 1). In summary, the free energy per unit area of the initially undeformed membrane due to COPII polymerization, fcoat, can be expressed as

(B1) fcoat=μc AcAp,

where Ac is the surface area of the membrane covered by the COPII coat, and Ap is the projected area of the carrier, that is, the area of the initially undeformed membrane under the carrier (Saleem et al., 2015; Appendix 2—figure 1B). We express all the free energies per unit area of the initially flat membrane and consider that there is a densely packed assembly of TANGO1 rings, as have been experimentally observed in cells (Raote et al., 2017; Raote et al., 2018). We also consider that the amounts of TANGO1 and COPII units are non-limiting. We next consider a line energy for the coat subunits laying at the edge of the polymerizing structure. This line energy per unit area reads as

(B2) fline0=λ0lAp,

where λ0 is the line tension of the bare coat, and l=2πρ is the length of the carrier edge, associated to the opening radius at the base of the carrier, ρ (Appendix 2—figure 1C). Next, we consider the contribution of the membrane tension, σ, to the free energy per unit area of the system, which reads as

(B3) ftension=σAmAp,

where Am is the surface area of the entire membrane after deformation (Appendix 2—figure 1B).

The following step is to expand on this model to include the contributions by which TANGO1 can modulate the formation of a transport intermediate. TANGO1 filaments are described by their length, LT, and by their persistence length, ξp=κTkBT, –where κT is the filament bending rigidity and kBT is the thermal energy, equal to the Boltzmann constant times the absolute temperature (Doi and Edwards, 1986)–, which describes how stiff the filament is. As long as the filament length is not much larger than the persistence length, the bending energy of the TANGO1 filament can be expressed as Fbend=κT2LT c-c02dl, where c and c0 are the actual and spontaneous curvature of the filament, respectively, and the integral is performed over the entire filament length. We define positive spontaneous curvatures of the filament as those where the TANGO1-COPII interacting domains lie on the concave side of the filament, and negative when they lie on the convex side. For a TANGO1 filament of length LT, that is bound to the circular boundary length of a COPII patch (of radius ρ), the filament bending energy per unit length can be written as fbend=κT2(1/ρ-c0)2ω, where we assumed that any existing filaments not adsorbed to the COPII patches adopt the preferred curvature, c0, and where ω is the capping fraction: the fraction of COPII domain boundary length covered ('capped') by TANGO1 molecules. Hence, analogously to our discussion for the free energy of coat binding to the membrane, Equation (B1), we can write the free energy per unit area of a TANGO1 filament as

(B4) fT,bend=μT lAp,

where μT=-fbend includes the negative contribution of the filament bending energy. A positive contribution of the filament assembly chemical potential, μT0, is not considered here since we assume that the assembly chemical potential is independent of whether the filament is capping or not a COPII patch and hence the fraction of TANGO1 monomers forming a filament is independent of the capping fraction. Moreover, we want to stress that the bending energy penalty of the filament diverges when the bud approaches closure, meaning that either there is uncapping of the TANGO1 filament from the edge of the COPII coat at narrow necks or the shape transition of the carrier goes through intermediate shapes with a relatively large bud neck, such as Delaunay shapes (e.g. unduloids) (Naito and Ou-Yang, 1997). This second option is analyzed with our model A, detailed in Appendix 1. In addition, TANGO1 proteins have an affinity to bind COPII components, and hence adsorb to the boundary of the COPII domains by binding the most external subunits. We therefore consider an extra free energy term associated to this TANGO1-COPII interaction, which is proportional to the boundary length of the COPII domain capped by TANGO1, and hence reads as

(B5) fTANGO1COPII=Δλ ωlAp,

where Δλ is the interaction strength between TANGO1 and COPII. We can write together Equations B2 and B5 as

(B6) fline=λlAp,

where λ=λ01-Δλλ0ω can be understood as the effective line tension of the COPII coat, in which Δλ is the reduction in the line tension due to TANGO1 capping, and hence is a measure of the linactant power of TANGO1.

Finally, the mechanical work performed by the outward-directed force, N, is also included in the free energy of the system, as

(B7) ff=N zmaxAp,

where zmax is the length of the carrier (Appendix 2—figure 1C). At this stage, for the sake of simplicity, we disregard the effects of the growth-shrinkage dynamics of the polymerizing COPII lattice. Hence, the total free energy per unit area of the carrier, fc, is the sum of all these contributions Equations B1,3,4,6,7,

(B8) fc=fcoat+fline+ftension+fT,bend+ff.

This free energy per unit area using a bare flat membrane as the reference state is presented in Equation 1 in the main text.

Geometry of the problem

Based on the proposed geometries for the growing carrier we can distinguish three geometries, depending on how complete the transport intermediate is: shallow buds, deep buds, and pearled intermediates (Appendix 2—figure 1C, panels (i) to (iii), respectively). This restricted family of shapes allows us to calculate as a function of the carrier morphology the geometric parameters that enter in Equation 1, namely, the area of the coat, Ac, the area of the membrane, Am, the projected area, Ap, and the opening radius at the coat rim, ρ (Saleem et al., 2015; Appendix 2—figure 1B). A convenient quantity to parametrize the shape of the carrier is the height of the carrier, zmax, which we will use in a dimensionless manner by normalizing it to the diameter of the spherical COPII bud, η=zmax /2Rc.

(i) Shallow bud

For a shallow bud (Appendix 2—figure 1B (i)), which corresponds to buds smaller than a hemisphere, we can write that Ac=Am=2πRc2 (1-cosθ), where 0<θ<π/2 is the opening angle of the bud (see Appendix 2—figure 1B (i)). In addition, Ap=πρ2=πRc2sin2θ; and zmax=Rc1-cosθ. Expressing these quantities as a function of the shape parameter, η, we obtain

(B9) Ac=Am=4πRc2η : η<12,
(B10) Ap=4πRc2η (1η) : η<12,
(B11) ρ=2Rcη(1η) : η<12.
(ii) Deep bud

For a deep bud (Appendix 2—figure 1B (ii)), which corresponds to buds larger than a hemisphere, we can write that Ac=2πRc2 (1-cosθ), where π/2<θ<π. In addition, Am=πRc2 (1+1-cosθ2); Ap=πRc2; and zmax=Rc1-cosθ. Expressing these quantities as a function of the shape parameter, η, which in this case ranges between 12<η<1, we obtain

(B12) Ac=4πRc2η : 12<η<1,
(B13) Am=πRc2(1+4η2) : 12<η<1,
(B14) Ap=πRc2 : 12<η<1,
(B15) ρ=2Rcη(1η) : 12<η<1.
(iii) Pearled intermediate

A pearled intermediate corresponds to carriers form by an incomplete bud with opening angle 0<θ<π, connected via a narrow connection with n complete buds (Appendix 2—figure 1B (iii)). Here, we can write that Ac=2πRc2 2n+(1-cosθ), where 0<θ<π and n1. In addition, Am=πRc2 4n+1+1-cosθ2; Ap=πRc2; and zmax=Rc2n+1-cosθ. Expressing these quantities as a function of the shape parameter, η, we obtain

(B16) Ac=4πRc2η : η>1,
(B17) Am=πRc2(1+4n+4(ηn)2) : η>1,
(B18) Ap=πRc2 : η>1,
(B19) ρ=2Rc(ηn)(ηn)2 : η>1.

Putting together Equations B9-19, we get:

(B20) Ac=4πRc2η
(B21) Am={4πRc2η,η<1/2πRc2[1+4n+4(ηn)2],η>1/2
(B22) Ap={4πRc2η(1η),η<1/2πRc2,η>1/2
(B23) ρ=2Rc(ηn)(1η+n),
(B24) zmax=2Rcη.

where n=η is the number of complete pearls, the brackets denoting the integer part operator. This allows us to express Equation 1 in the main text as

(B25) Δfc=σημ1η+λ(ω)η(1η)4ω κTc0Rcη(1η)+ω κT[η(1η)]3/2, η<1/2,
(B26) Δfc=4σ[n+(ηn)2]4μη +4λ(ω)(ηn)(1η+n)+4ωκT[1(ηn)(1η+n)4 c0Rc], η>1/2,

where μ~=μc0-2κbRc2+N2πRc, λ~ω=λ0- ω ΔλRc+4ωκ~Tc0Rc2, and κ~T=κT8Rc3 (Equation 2 in the main text).

Parameter estimation

The free energy per unit area, Equation (1) depends on a number of structural, biochemical, and mechanical parameters, which we can split in three groups: (i) membrane-associated parameters, (ii) coat-associated parameters, and (iii) TANGO1-associated parameters (Appendix 2—table 1). As for the membrane-associated parameters, we have the lateral tension, σ, and the bending rigidity, κb.

Regarding membrane-associated parameters, we use the experimentally measured values of the standard membrane tension of the ER, σER=0.003 kBT/nm2 (Upadhyaya and Sheetz, 2004); and of the membrane bending rigidity, κb=20 kBT (Niggemann et al., 1995; Appendix 2—table 1).

Regarding coat-associated parameters, we use the size of the standard spherical COPII vesicle, Rc=37.5 nm (Miller and Schekman, 2013). The line tension and the binding free energy of the polymerizing COPII coat, λ0 and μc0, respectively, have not been, to the best of our knowledge, experimentally measured. Nevertheless, for clathrin coats, which lead to the formation of vesicles of a size comparable to the standard COPII vesicles, these values have been recently measured, yielding a value of λclathrin=0.05 pN for the line tension and of μclathrin0=0.024±0.012 kBT/nm2 for the binding free energy (Saleem et al., 2015). We use these values as starting estimations for COPII coats, which we will then vary within a certain range (Appendix 2—table 1). It is also informative to estimate the binding energy of COPII polymerization per molecule. To obtain this energy in units of kBT for the polymerization of a single COPII unit, we use the characteristic size of the Sec13-31 heterotetramers, ~30 nm (Stagg et al., 2008; Zanetti et al., 2013), which gives a characteristic area of a COPII unit, aCOPII~(30 nm)2. This gives that μc0 aCOPII~22 kBT, very similar to the estimated lateral interaction energy per triskelion of the clathrin coat (Saleem et al., 2015).

Finally, regarding the TANGO1-associated parameters, which are associated to different protein-protein interactions, we have the bending rigidity of the TANGO1 filament, κT; the preferred curvature of the filament, c0; and the TANGO1-COPII binding energy/linactant strength of TANGO1, Δλ. The elastic parameters of the TANGO1 filament, κT and c0, depend on the chemistry of the bonds between the different proteins within a TANGO1 filament. As we lack experimental data on the value of these parameters, we consider them within a wide range of reasonable values. Typical values of the bending rigidity of intracellular filaments formed by protein-protein interactions, such as intermediate filaments, are of the order of κIF=2000 pNnm2 (Fletcher and Mullins, 2010), which we consider as an upper limit for the rigidity of a TANGO1 filament. In addition, by taking κT=0, we can exploit our model to study the case where TANGO1 proteins do not form a cohesive filament by attractive lateral protein-protein interactions, but individual proteins can still bind COPII subunits and hence act as monomeric linactants. For our analytical analysis, we will start by taking a zero spontaneous curvature of the TANGO1 filament, c0=0, and later study it within a range given by twice the radius of experimentally measured TANGO1 rings, -0.02 nm1<c0<0.02 nm1. For the value of Δλ, we can make an upper limit estimate, by considering that the TANGO1-COPII binding energy should be lower than the corresponding binding energy between polymerizing COPII components, that is, Δλ l1<μc0 l1l2, where l116 nm and l210 nm are the lateral dimensions of the inner COPII coat components Sec23/24 (Matsuoka et al., 2001). Hence, our estimation gives that Δλ <0.24 kBT/nm, and therefore we use as the initial value for our analysis half of the upper limit value, Δλ=0.12 kBT/nm, which is 10-fold larger than the bare line tension of the coat (Appendix 2—table 1).

Appendix 2—figure 1
Geometry and physical forces in the transport intermediate generation model.

(A) TANGO1 rings assembling on the ER membrane are depicted in light blue, accounting for a line tension reduction of the COPII coat, Δλ. The ER membrane is shown in black, associated with a tension, σ0. The COPII coat polymerizing on the membrane is depicted in orange, and accounts for a coat binding free energy (or chemical potential), μc, and a COPII coat line tension, λ0. Packaged procollagen rods are shown in magenta, which can (but not necessarily) contribute with a pushing normal force, N, and sterically prevent membrane fission. Finally, ERGIC53-containing membranes tethered to the export site through the NRZ complex (dark blue) are shown, which can be a source of membrane tension reduction, Δσ. (B) Schematics of the different surface areas used in the model for both shallow (i) and deep (ii) buds: the projected area, Ap, shown in light blue; the membrane area, Am, shown in black; and the coat area, Ac, shown in orange. (C) Scheme of the carrier geometry used for shallow buds (i), deep buds (ii); and pearled carriers (iii).

Appendix 2—table 1
Parameters used in the large transport intermediate formation model.

The free energy Equation (2) depends on a number of different parameters, which are described in this table.

ParameterDescriptionValueNotesReference
σMembrane tension0.003 kBT/nm2 (ER);
0.0012 kBT/nm2 (Golgi membranes)
Upadhyaya and Sheetz, 2004
κbMembrane bending rigidity20 kBTNiggemann et al., 1995
RcRadius of curvature of the COPII coat37.5 nmMiller and Schekman, 2013
λ0Bare coat line tension0.012 kBT/nmNot measured for COPII. Used the clathrin value as a referenceSaleem et al., 2015
μc0COPII coat polymerization energy0.024 ± 0.012 kBT/nm2Not measured for COPII. Used the clathrin values as a referenceSaleem et al., 2015
κTTANGO1 filament bending rigidity120 kBT nmNot measured. Range based on standard filament rigidities (see text)
c0TANGO1 filament spontaneous curvature(−0.02, 0.02) nm−1Not measured. Range based on observed TANGO1 ring sizesRaote et al., 2017
λTANGO1 linactant strength0.12 kBT/nmNot measured. Range based on protein-protein affinity (see text)-
NOutwards-directed force0 – 5kBT/nmNot measured. Range based on known intracellular forcesKovar and Pollard, 2004 (Actin); Block et al., 2003 (Molecular motors)

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Decision letter

  1. Jure Derganc
    Reviewing Editor; University of Ljubljana, Slovenia
  2. Suzanne R Pfeffer
    Senior Editor; Stanford University School of Medicine, United States

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Thank you for submitting your article "A physical mechanism of TANGO1-mediated bulky cargo export" for consideration by eLife. Your article has been reviewed by three peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Suzanne Pfeffer as the Senior Editor. The reviewers have opted to remain anonymous.

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

As the editors have judged that your manuscript is of interest, but as described below that additional work is required before it is published, we would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). First, because many researchers have temporarily lost access to the labs, we will give authors as much time as they need to submit revised manuscripts. We are also offering, if you choose, to post the manuscript to bioRxiv (if it is not already there) along with this decision letter and a formal designation that the manuscript is "in revision at eLife". Please let us know if you would like to pursue this option. (If your work is more suitable for medRxiv, you will need to post the preprint yourself, as the mechanisms for us to do so are still in development.)

The paper presents an elaborate theoretical analysis of TANGO1-mediated transport of large procollagen cargo from endoplasmic reticulum exit sites (ERES). The paper addresses a very exciting topic since the mechanisms of cellular transport of large cargo are still poorly understood. The central hypothesis of the paper is that TANGO1 binds to the boundary of a growing COPII bud, where it (a) acts as linactant and modulates COPII assembly; (b) tethers ERGIC53-containing membranes that subsequently fuse with ERES and promote the growth of the transport carrier; (c) binds to procollagen in ER lumen and directs it into the carrier. Compared to the previous submission, the paper has been, without any doubt, substantially improved. However, as the topic is complex, it is no surprise that there are still some open questions.

What became evident during the review process is a sense that what must seem clear to the authors was not clear to the reviewers, and the authors are strongly encouraged to respond with great care in the revised text to address each of the comments/concerns raised. Because of the extensive reviewer comments, we include them in full to guide you as you revise the manuscript.

Reviewer #1:

The paper presents an elaborate theoretical analysis of TANGO1-mediated transport of large procollagen cargo from endoplasmic reticulum exit sites (ERES). The paper addresses a very exciting topic since the mechanisms of cellular transport of large cargo are still poorly understood. The central hypothesis of the paper is that TANGO1 binds to the boundary of a growing COPII bud, where it (a) acts as linactant and modulates COPII assembly; (b) tethers ERGIC53-containing membranes that subsequently fuse with ERES and promote the growth of the transport carrier; (c) binds to procollagen in ER lumen and directs it into the carrier. The analysis presented in the paper comprises two distinct theoretical models:

A) within the first model, the transport carrier shape is approximated by a string of spherical pearls and parametrized by a shape parameter eta. The equilibrium configuration of the carrier is determined by analytical minimization of the system's free energy in a quasi-static approximation.

B) the second model is a dynamic computational model, where the shape of the transport carrier is constrained only by axial symmetry, and the time-evolution of the carrier configuration is determined by using Onsager's variational approach applied to a membrane with freely diffusing and interacting COPII and TANGO1 proteins. The solution is calculated numerically.

If compared to previous submissions, the paper has been, without any doubt, substantially improved. However, as the topic is complex, it is no surprise that there are still some open questions.

1) The paper could be more clear on why TANGO1 has to act as a linactant stabilizing a growing COPII coat. Is it because the linactant effect is needed to slow down the growing COPII bud and thus give the time that is needed to recruit procollagen? If so, this should be additionally emphasized in the paper and corroborated by the model results. As it stands now, model A focuses mostly on the quasi-equilibrium shapes of the carrier and not on kinetics (the kinetics of the growth is described only briefly in L706-L733). Within equilibrium mechanics "stabilizing" can have a slightly different meaning than "slowing down". Consequently, the reader could wonder if the linactant effect is needed at all? The role of TANGO1 could as well be just to recruit the procollagen. The carrier would grow by itself, driven by COPII polymerization (see also point 2). In this regime, the closure of COPII bud would be prevented simply by the presence of procollagen on the luminal side, as described in model B. Why is this option not possible? Within the same lines: are the authors aware of any data on the kinetics of procollagen recruitment?

2) The region in the parameter space, where the proposed model can describe the transport carrier growth, is relatively small, i.e., having other parameters fixed, it spans approximately within 0.026 kT/nm2 < muc0 < 0.032 kT/nm2 and 0.001 < σ < 0.003 kT/nm2 (Figure 4A). This raises concerns that the proposed mechanism is not very robust, e.g., if one parameter from the Table 1 changes for ~10% the proposed mechanism could break down completely. E.g. if muc0 is 0.034, the carrier could grow spontaneously, without the need for a linactant effect or tension regulation. I would encourage the authors to discuss this aspect of their model.

3) While the analysis carried out with model B (dynamic computational model) is very comprehensive and sophisticated (kudos to its authors!), it is not clear if it can be applied to TANGO1/COPII transport carrier growth as presented in this paper. How to compare the results of both models presented? Namely, while the first model assumes that the whole carrier is covered with COPII, and that COPII coat is surrounded by a TANGO1 ring, the second model in intrinsically continuous and its results do not show any phase separation (or capping/no-capping transitions). Also, it is not clear how to compare the (values of) parameters muc0 and chic, which are not defined in the same way. Even if these parameters were conceptually similar, can one be sure that the model B is being solved in the same parameter region as Model A (as we saw earlier, model A is very sensitive to the values of muc0)? Unsurprisingly, Tozzi, Walani and Arroyo, 2019, show growth of protrusions that are very similar to the ones presented in Figure 7D, but with only one protein species and different parameter values. In addition, the time scales within both models are quite different, Model A assumes average budding transition times in the region of 0.1 min, while Model B shows that this time can be less than 100 ms.

Reviewer #2:

The authors present a theoretical study of how TANGO1 protein controls the transport of large cargo (procollagen) from the endoplasmic reticulum exit sites (ERES) to the Golgi apparatus. This is an interesting problem and has been dealt with experimentally from various angles by the authors (several published in eLife). This work builds on the 2018 eLife paper that revealed how TANGO1 organizes to corral COPII coats, and recruits ERGIC (ER-Golgi intermediate compartment) membranes for procollagen export. Here the authors develop an analytical model that considers COPII assembly into a spherical shell on the membrane and TANGO1 polymerization into a filament that caps the COPII lattice. They then study how various physical parameters (TANGO1 self-interaction, COPII self-interaction, TANGO-COPII interaction, membrane tension, external force) influence the resulting equilibrium membrane shape. In the end they discuss the dynamic growth of the protrusion.

The problem is interesting, and the Abstract seems exciting, however, in my opinion the data presented fails to support the main claims of the paper.

Main concerns:

i) The first claim by the authors is that by capping the COPII lattice TANGO1 prevents premature carrier scission and enables packing the bulky cargo into the carrier. This claim is repeated many times throughout the paper, without any data to support it, since the model does not consider carrier scission or cargo loading. This claim appears mainly speculative.

The authors do indeed show that TANGO1 capping stabilizes incomplete buds, but they do not show the relationship between this stabilization and cargo-loading or carrier scission. In fact, in their dynamic model they prevent carrier scission "by hand", by not allowing radii below certain size. They also do not present any experimental evidence that the procollagen transport is necessarily carried by incomplete buds or pearled tubes.

Hence the result that the capping stabilizes incomplete buds can also be interpreted in other ways, for instance as inhibitory to the carrier growth since the capping imposes a free energy barrier for the growth (Figure 2). In summary: there is no evidence in the paper that the capping indeed enables packing the bulky cargo.

ii) Related to the previous comment, the main assumption of the paper is that the procollagen transport is facilitated by incomplete COPII buds. However, the authors do not really present any evidence for that. For instance, if the carrier has a spherocylindrical shape (which has been reported for COPII in vitro) the whole conclusions on the role of capping would be different.

iii) The second main claim of the paper is that TANGO1 enables the carrier growth by reducing the membrane tension, by recruiting ERGIC. The authors model this effect "by hand", by decreasing the tension in their model and showing that the free energy minimum is shifted to long carrier shapes. In their dynamic model they impose sudden decrease and increase in tension and show that this enables and prevents the carrier growth, respectively. This result is nice, but not unexpected. The authors also do not really show that TANGO1 enables the carrier growth, but rather that the decrease of the membrane tension enables it, be it mediated by TANGO1 or otherwise. The role of membrane tension on the protrusion growth has been studied extensively before (see eg the body of work by Nassoy and Bassereau, for instance EPL 2005), and agrees with the findings presented here. In that sense the physical result that the decrease in the membrane tension enables the protrusion growth is not novel, although it has been put in a context of a different system.

iv) The paper feels unnecessarily long and repetitive, where the same claims are repeated many times.

Overall, this is a nice exploratory paper that makes bold claims that appear not to be supported by data, it is my impression that the authors somewhat try to fit the results into a preconceived mechanism of how TANGO1 enables procollagen transport, as opposed to the mechanism arising from their data. The physical result that the decrease in the membrane tension enables protrusion growth is not surprising (or novel). In my opinion the work does not present a substantial development with respect to the 2018 eLife paper by the same authors.

Reviewer #3:

In this manuscript, the authors develop a theoretical model to analyse a scenario for the formation of large membrane carrier able to export procollagen fibres from ERES. COPII coat components polymerise into a spherical cap, which is prevented from maturation and budding by TANGO1 proteins assembling into a ring at the coat edge. TANGO1 also promotes the fusion of ERGIC vesicles which lower membrane tension locally and allow for the longer COPII-covered carriers able to incorporate procollagen.

I appreciate some aspect of the model, primarily the analysis of the self-organisation of two types of membrane proteins into non-trivial structure. The fairly thorough study of the different possible range of behaviour, including a careful account of the relevance of different parameters, is valuable.

On the other hand, other aspects of the manuscript seem dubious to me and rely on what I believe to be incompatible assumptions. This is true for the tension regulation aspect, which is unfortunately a point that is strongly emphasise in the manuscript. Another weak point is the way the interaction with the procollagen fibres is treated.

Another problem I have with the manuscript is the constant mixing between rigorous results obtained from the model and speculations which are not supported by the model. Therefore, I think that this paper present interesting results regarding the self-organisation of coatomers and ring-forming proteins, which are certainly relevant for the situation under study, but that it requires important rewriting to put the result in their proper context and to separate facts from conjectures.

1) The deformation of membrane by aggregation of proteins inducing membrane curvature has been studied in great details, and the role of the different physical parameters in the process, including membrane tension, is well documented. The originality of the present model is the involvement of a second class of proteins that stabilise the coat (e.g. disfavor the formation of a full spherical coat) due to attractive interaction with coat proteins AND the fact that these proteins tend to form semi-flexible filaments. The problem is treated at thermodynamic equilibrium, through energy minimisation. As such, it assumes ergodicity; that the entire space of configuration can be explored, and cannot investigate situations where the system is kinetically trapped into a particular state. This limitation is insufficiently discuss in the text, especially in the Introduction. Furthermore, the possibility for kinetic trapping is often explicitly mentioned without a word of caution, which could confused an uninformed reader that this possibility is accounted for by the model. It is not, and this must be stated explicitly.

2) Thermodynamic equilibrium implies that proteins in the coat and in the ring can freely exchange with a reservoir, or that the time scales associated with this exchange are much faster than other time scales, such as the one for tension variation. The chemical potential of COPII monomer is assumed fixed, regardless of the coat size. This means that there exists a reservoir of monomer at fixed chemical potential with which the coat can freely exchange component. I see two possibilities. The reservoir is the flat membrane, which is itself in equilibrium with coat component in the cytosol, or the reservoir is the cytosol itself, which requires that coat component bind directly from the cytosol onto the growing coat. The chemical potential \muc is said to include binding energy, without specifying if it is the binding of one monomer to the membrane or the binding between two monomers. I assume it is the latter which suggests that the reservoir is indeed the rest of the membrane. This makes sense to me, but it should be clearly discussed, including the fact that this model only makes sense if coatomers can be freely exchange between the growing coat and the rest of the membrane. By the way, the binding energy \muc0 is expressed as an energy per unit area. This is not optimal. It should be expressed as an energy, so it can be compared with the thermal energy kT.

3) The equilibrium treatment becomes particularly problematic when the situation involves diffusion barrier, which is the main argument put forward by the author in support of their claim that TANGO1 is a regulator of membrane tension, allowing to the elongation of membrane carrier. For this two happen, at least three conditions must be satisfied: i) lipids must be prevented from diffusing across the TANGO1 ring, ii) ERGIC vesicles must be allowed to fuse within the area delimited by the TANGO1 ring, and iii) coatomers must be able to freely exchange with their reservoir, i.e. to cross the diffusion barrier. It seems rather unlikely that condition 1 is strictly satisfied. the TANGO1 ring could slow down lipid diffusion, but probably not abolish it. This is indeed the conclusion of Raote et al., 2020, so the question of tension regulation becomes a competition between time scales; the time scale of tension equilibration vs. the time scale of coat formation. It is not discussed as such but it should.

There is an even bigger problem. There is a clear conflict between conditions (i) and (iii). It is not reasonable to claim that lipids are trapped but not coatomers. Furthermore, the fusion of ERGIC vesicles, even if one assumes that it occurs inside the TANGO1 ring, which seems very unlikely considering that this part of the membrane is crowded with COPII presumptuous, would locally and transiently reduce tension because membrane area of a completely different composition than the initial coat would be added to the region inside the ring. None of this is discussed. Probably because it is a difficult problem, but the way it is handled here is not at all satisfactory. The bottom line is that the claim of tension regulation is presumptuous and not acceptable in the current form.

4) As far as I can see, procollagen is entirely absent from the model equations. Nevertheless it is present in the Discussion in mostly two ways; as a way to sterically hinder neck closure or as responsible for a normal force that helps elongate the membrane carrier. The first aspect is entirely conjectural and is not included in any way in the model. It should be presented as such in the Discussion. The second is somewhat introduced phenomenologically in the model, but is not properly discussed. For polymerising procollagen fibres to push on the coat, it would need to exert an opposite force on something else. What would that be? The ER membrane opposite to the ERES presumably, but expect if the fiber is perfectly perpendicular to that membrane, the force would also result in a torque that would made the fibre tilt. It is said repeatedly in the text that this force is dispensable, but we are still lacking an argument to explain how the fibre would properly orientate along the carrier axis of symmetry to be properly incorporated. Since this is a model for how to build membrane carrier for bulky cargo, the interaction between the cargo and the carrier must be discussed more thoroughly.

5) Regarding the energy minimisation procedure. It is unclear why all energies are expressed in unit of Ap (Equations.1-4 etc…). Ap is the projected area of the carrier, which changes non-linearly with the number of coatomers as the coat grows. It is unclear to me why this area is important, except if one wishes to discuss steric interaction between buds. I would think that the proper thing to do is to compare the energy per coatomer for different coat geometry, rather than to minimise the energy divided by Ac. As such, I don't think that the minimisation procedure is correct. For instance, looking at Figure 2B, we can see that the "free" energy of the double bud is smaller than that of the single bud so that the former is said to be "globally stable". What should be compared is the chemical potential (energy per COPII monomer) is both situations, which could very well favour single buds for the parameters of Figure 1B, in particular due to the favorable interaction between TANGO1 and COPII monomers.

Related to this, I could not figure out what is the difference between Am and Ac. Ac is supposed to be the coat area and Am the membrane area, but in this simplified geometry using spherical caps, I imagine that the entire curved part of the membrane is covered by coat, so why is Am not equal to Ac?

6) TANGO1 is repeatedly described as a linactant, but it is not clear that the stabilisation of incomplete buds is due to the linactant effect. The TANGO1 ring is rigid and its caping of the coat edges involve an elastic energy penalty. Isn't this the dominant effect of coat stabilisation, rather than the linactant effect?

7) The section proposal of experimental approaches to test the model is not very useful. It does not really provide experimental test of the model based on the quantitative findings of the model. The section .…“ TANGO1 as a regulator of membrane tension homeostasis” in largely speculative and not supported by the model. It is rather presents hypothesis that are a starting point of the model, several of which are dubious (in particular the fact that tension is reduced while membrane composition is not changed, as discussed above). It should be presented as speculation.

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Thank you for submitting your article "A physical mechanism of TANGO1-mediated bulky cargo export" for consideration by eLife. Your article has been reviewed by three peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Suzanne Pfeffer as the Senior Editor.

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

We would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). Specifically, when editors judge that a submitted work as a whole belongs in eLife but that some conclusions require a modest amount of additional new data, as they do with your paper, we are asking that the manuscript be revised to either limit claims to those supported by data in hand, or to explicitly state that the relevant conclusions require additional supporting data.

Summary:

The paper entitled "A physical mechanism of TANGO1-mediated bulky cargo export" by Raote et al. has been re-submitted to eLife as a research advance to their prior research paper entitled "TANGO1 builds a machine for collagen export by recruiting and spatially organizing COPII, tethers and membranes" (Raote et al., 2018).

The paper addresses cellular transport of large cargo from endoplasmic reticulum exit sites (ERES), which is a very important open question in cell biology. Based on their previous experimental paper (Raote et al., 2018), the authors put forward a hypothesis that TANGO1 binds to the boundary of a growing COPII bud in the ERES, where it (a) acts as linactant and modulates COPII assembly; (b) tethers ERGIC53-containing membranes that subsequently fuse with ERES, decreases the ERES membrane tension and thus promote the growth of the transport carrier; (c) binds to procollagen in the ER lumen and directs it into the carrier. The present paper introduces an elaborate and interesting theoretical analysis showing that the TANGO1 hypothesis is compatible with the current understanding of physical mechanisms that guide membrane remodeling. Thus, the results present an essential and invaluable step towards a thorough understanding of cellular trafficking of large cargo.

The reviewers agree that the paper is suitable for publication in eLife after the authors address the following two concerns:

1) The narrative of the paper has been much improved and the complex modeling is now presented clearly and concisely. However, the reviewers judge that the link between the modeling and the biological situation remains rather speculative. The reviewers therefore suggest that the authors add a paragraph of open and honest discussion on the speculative link between the model and biology.

2) The authors should address the inconsistent use of high / low tension values in the two models. (0.006 / 0.003 kBT/nm2 in the continuous model, and 0.003 / 0.0012 kBT/nm2 in the equilibrium model).

https://doi.org/10.7554/eLife.59426.sa1

Author response

Reviewer #1:

The paper presents an elaborate theoretical analysis of TANGO1-mediated transport of large procollagen cargo from endoplasmic reticulum exit sites (ERES). The paper addresses a very exciting topic since the mechanisms of cellular transport of large cargo are still poorly understood. The central hypothesis of the paper is that TANGO1 binds to the boundary of a growing COPII bud, where it (a) acts as linactant and modulates COPII assembly; (b) tethers ERGIC53-containing membranes that subsequently fuse with ERES and promote the growth of the transport carrier; (c) binds to procollagen in ER lumen and directs it into the carrier. The analysis presented in the paper comprises two distinct theoretical models:

A) within the first model, the transport carrier shape is approximated by a string of spherical pearls and parametrized by a shape parameter eta. The equilibrium configuration of the carrier is determined by analytical minimization of the system's free energy in a quasi-static approximation.

B) the second model is a dynamic computational model, where the shape of the transport carrier is constrained only by axial symmetry, and the time-evolution of the carrier configuration is determined by using Onsager's variational approach applied to a membrane with freely diffusing and interacting COPII and TANGO1 proteins. The solution is calculated numerically.

If compared to previous submissions, the paper has been, without any doubt, substantially improved. However, as the topic is complex, it is no surprise that there are still some open questions.

1) The paper could be more clear on why TANGO1 has to act as a linactant stabilizing a growing COPII coat. Is it because the linactant effect is needed to slow down the growing COPII bud and thus give the time that is needed to recruit procollagen? If so, this should be additionally emphasized in the paper and corroborated by the model results. As it stands now, model A focuses mostly on the quasi-equilibrium shapes of the carrier and not on kinetics (the kinetics of the growth is described only briefly in L706-L733). Within equilibrium mechanics "stabilizing" can have a slightly different meaning than "slowing down". Consequently, the reader could wonder if the linactant effect is needed at all? The role of TANGO1 could as well be just to recruit the procollagen. The carrier would grow by itself, driven by COPII polymerization (see also point 2). In this regime, the closure of COPII bud would be prevented simply by the presence of procollagen on the luminal side, as described in model B. Why is this option not possible? Within the same lines: are the authors aware of any data on the kinetics of procollagen recruitment?

We apologize for not explaining this point clearly in the previous version of the manuscript. The results obtained by using our equilibrium model indicate that capping of the TANGO1 ring to growing COPII patches modulates the energetically stable shapes of the transport intermediates (see e.g. Figure 4A). The increase in the linactant strength of the filament (and/or the reduction of its bending rigidity) triggers the formation of TANGO1 ring capping COPII coats. Importantly, these changes also lead to expansion of the parameter space in which incomplete, open budded structures are predicted (see Figure 6B,C).

To better illustrate this point, we include a new figure panel, Figure 6—figure supplement 1B. In there, we show the plots of two cross-section lines of Figure 6B, corresponding to a situation where TANGO1 is not a linactant (∆𝜆 = 0) and where it is a linactant (∆𝜆 = 0.12 𝑘*𝑇/𝑛𝑚), respectively. In these cross-section plots, we can readily observe how TANGO1 linactant strength modulates the stable bud shapes and the capping state. First, it expands the range of values of the parameter 𝜇01 where the stable shape is a shallow open bud with a finite sized neck radius, 𝜌 (see Figure 6—figure supplement 1B); and second, it increases the radius of the opening neck, 𝜌. In summary, TANGO1 as a linactant (in capping conditions) implies that (i) there is a larger range of parameters that lead to stable open buds; and (ii) the radius of the neck opening is larger.

In our dynamic model, the linactant effect of TANGO1 is included by an interaction parameter (𝜒05, see Appendix 1—table 1). We have not tested the entire parameter space of the dynamic model, because it is more complex and elaborated that our equilibrium model (in the revised manuscript we emphasize the fact that we use the equilibrium model to obtain simple semi-quantitative and analytical estimations of the effects of the different model parameters). In spite of this, our results show that the effect of a functional TANGO1 (which forms a ring capping the COPII patch), as compared to an inert TANGO1 (no interactions), is to increase the region of the parameter space where incomplete, open-necked structures are found (Figure 5B). This is qualitatively similar to our predictions from the equilibrium model (Figure 5A), which we believe further supports our view that a possible function of the TANGO1-COPII interaction is in “stabilizing” structures with wide-open necks. This, we speculate, is used by TANGO1 to facilitate the packaging of procollagens into the nascent transport intermediate.

In summary, our data shows that although not strictly necessary, the linactancy of TANGO plays an important role in large carrier formation by creating wider necks and making the carrier growth mechanisms more robust. Importantly, in our previous manuscript (Raote et al., 2018), we experimentally showed that the mutant of TANGO1 with a reduced affinity for COPII components (TANGO1-∆PRD mutant), which can still bind and recruit procollagen to ERES, is defective in procollagen export. This observation suggests that a strong affinity of TANGO1 for COPII molecules (which corresponds in our models as the linactant strength of the filament) is indeed required for efficient procollagen export.

Unfortunately, we are not aware of any in vivo data on the kinetics of procollagen recruitment to export sites. It is known that the overall time spent from synthesis to secretion to the ECM of procollagen I is about 10-30 minutes (see e.g. Weinstock M, Leblond CP. (1974) J. Cell Biol. 60(1):92–127), and that a synchronizable procollagen I takes about 15 minutes from completion of triple helical formation in the ER to arrival at early Golgi cisternae (McCaughey et al., 2018). Moreover, the half-lives of COPII components on the ER membrane are in the order of a few seconds (Forster et al., 2006). It is therefore plausible to suggest that a mechanism to stabilize open nascent carriers exists, and that such mechanism could facilitate the efficient packing of complex cargoes. Taking into consideration our theoretical results on the role of TANGO1 in stabilizing incomplete transporters (Figure 2, Figure 5A,B), we propose that TANGO1 rings can fulfill such a task of arresting the growth of standard COPII carriers and stabilizing open shallow buds for the efficient packaging of procollagens (Figure 8A,B).

We concur with the reviewer on the difference between stabilization and slow-down of the dynamics. With our equilibrium model, we can only obtain the stable and metastable membrane shapes for each set of parameters. We refer to “stabilization of open shallow buds” to the formation of such stable (or metastable) shapes. If one of the parameters (e.g. membrane tension) changes, then the free energy profile of the system is concomitantly altered and new stable/metastable states appear (see e.g. Figure 4A). Depending on the initial state of the system (e.g. globally stable state before changing the parameters), the new stable state could be separated by an energy barrier, which we calculated and is presented in Figure 4C. We simplified the estimation of the transition times based on Arrhenius kinetics and added a cautionary note in the text that our equilibrium model cannot provide dynamic information about the actual transition times between metastable shape. We have also removed any reference to “slowing down” the transitions between local equilibrium states.

All these points above have been clarified and explained in more detail in the revised version of the manuscript.

2) The region in the parameter space, where the proposed model can describe the transport carrier growth, is relatively small, i.e., having other parameters fixed, it spans approximately within 0.026 kT/nm2 < muc0 < 0.032 kT/nm2 and 0.001 < σ < 0.003 kT/nm2 (Figure 4A). This raises concerns that the proposed mechanism is not very robust, e.g., if one parameter from the Table 1 changes for ~10% the proposed mechanism could break down completely. E.g. if muc0 is 0.034, the carrier could grow spontaneously, without the need for a linactant effect or tension regulation. I would encourage the authors to discuss this aspect of their model.

We agree that the region of the parameter space that allows for a tension regulation-mediated carrier growth seems relatively small. However, similar narrow ranges of parameters have been shown to regulate clathrin-coated vesicle formation (Saleem et al., 2015; Hassinger et al., 2017). Moreover, the shape diagram is much more robust with respect to other parameters, in particular to those related to the TANGO1 filaments (see Figure 6B,C). Indeed, if 𝜇01 is too large, growth of a procollagen-containing carrier could grow spontaneously without the requirement of other mechanisms (tension regulation, linactant effect, etc.). However, we know that different modular aspects of TANGO1 interactions with its effectors are individually required for efficient procollagen export from the ER (e.g. PRD domain, which controls linactant strength; cytosolic coiled-coiled domains, which control TANGO1 filament formation and recruitment and fusion of ERGIC membranes) (Raote et al., 2018). We believe these experimental evidences provide context to the relatively narrow range of parameters obtained by our theoretical approach. Finally, although in some parameter regions TANGO1 is not required for bud growth, its presence (or absence) allows for a richer range of COPII-mediated budding behavior, influencing cargo selectivity and export efficiency. We discuss these points in the revised version of the manuscript.

3) While the analysis carried out with model B (dynamic computational model) is very comprehensive and sophisticated (kudos to its authors!), it is not clear if it can be applied to TANGO1/COPII transport carrier growth as presented in this paper. How to compare the results of both models presented? Namely, while the first model assumes that the whole carrier is covered with COPII, and that COPII coat is surrounded by a TANGO1 ring, the second model in intrinsically continuous and its results do not show any phase separation (or capping/no-capping transitions). Also, it is not clear how to compare the (values of) parameters muc0 and chic, which are not defined in the same way. Even if these parameters were conceptually similar, can one be sure that the model B is being solved in the same parameter region as Model A (as we saw earlier, model A is very sensitive to the values of muc0)? Unsurprisingly, Tozzi, Walani and Arroyo, 2019, show growth of protrusions that are very similar to the ones presented in Figure 7D, but with only one protein species and different parameter values. In addition, the time scales within both models are quite different, Model A assumes average budding transition times in the region of 0.1 min, while Model B shows that this time can be less than 100 ms.

In our dynamic model, which we have renamed in the revised version as model “A” due to the re-ordering of the manuscript, we have not directly observed dissolution of TANGO1 rings after they are initially formed. Although we might find such a behavior through a thorough exploration of the parameter space, we believe this would be too overwhelming in the context of the present study, and is beyond the scope of this paper. However, we did observe that there is nucleation of TANGO1 ring-like structures at the base of COPII coats (phase separation) (see e.g. Figure 2B). The reviewer is right that this model is continuous in the sense that the TANGO1 ring is not a two-dimensional line but more like a diffuse interface with a certain thickness (somehow analogous to the way phase-field or level-set methods deal with interfaces). In spite of this fundamental difference, the results of this model (formation of a narrow ring-like TANGO1 structure around COPII patches) qualitatively agree with the results obtained using the equilibrium model (renamed as model B).

Moreover, it is true that it is not straightforward to quantitatively compare 𝜇01 (equilibrium model) with 𝜒0 (dynamic model), but given the similarity of behaviors between the two models, we consider that we are qualitatively in the right range. Indeed, since the two models are fundamentally different, we do not think that a quantitative comparison would be more informative. However, we argue that the qualitative match between the two models (see e.g. Figure 5A,B), despite their different implementation of the underlying hypotheses, suggest that the proposed mechanism is robust and possibly more general than any of the two specific models.

In Tozzi et al., 2019, similar pearled shapes are indeed obtained with a single (curvature-inducing) protein component. It is important to note, their explanation required imposition of a cut-off neck radius to obtain such shape, exactly the same way we impose a minimum radius representing the procollagen molecules in the bud. Importantly, the question we ask is completely different. Here we ask what possible mechanism compatible with known TANGO1 characteristics can regulate COPII-mediated procollagen export. Our answer is that in a system with curvature-inducing proteins (here COPII) such as the one considered in Tozzi et al., adding a second species (TANGO1) finely controls the budding mechanism. And that when the neck size is sterically constrained, such as in the presence of procollagen, long transport intermediates can grow. This later point was not rationalized in biological context by Tozzi et al., but rather used as a practical way to obtain a variety of shapes.

Finally, about the different time scales, we would like to highlight that they represent different physical processes. The equilibrium model, by definition, cannot provide any dynamic information on the shape changes, but it allows us to estimate the transition time between local equilibrium states using Arrhenius kinetics (knowing the free energy barriers between those states). This time scale is determined by the height of energy barriers and temperature of the system (fluctuations allowing to overcome the energy barriers). This is in 0.1 min time scale reported for relatively low energy barriers. The dynamic model, however, provides us with the actual deformation dynamics to reach a local equilibrium state from an initial (unstable) state. This time scale is related to membrane bending and protein diffusion, and describe a totally different process compared to the equilibrium model. In this context, our computations show deformation times of the order of 0.1 s. However, our dynamic model does not explicitly incorporate thermal fluctuations, and therefore the exploration of stable shapes from metastable shapes is not possible, unless the system is taken to a different state (by e.g. membrane tension reduction), where the system can naturally evolve to its new stable shape. Bringing back the system to the initial state can show indeed the existence of those different locally stable shapes (see Figure 3, where the transient decrease in tension leads to growth of the carrier).

All these points are now discussed in the revised version of the manuscript. We also adapted the x-axes in Figure 3A,B to highlight the fact that the two time scales (shape changes and in that case, membrane tension changes) are independent to each other.

Reviewer #2:

The authors present a theoretical study of how TANGO1 protein controls the transport of large cargo (procollagen) from the endoplasmic reticulum exit sites (ERES) to the Golgi apparatus. This is an interesting problem and has been dealt with experimentally from various angles by the authors (several published in eLife). This work builds on the 2018 eLife paper that revealed how TANGO1 organizes to corral COPII coats, and recruits ERGIC (ER-Golgi intermediate compartment) membranes for procollagen export. Here the authors develop an analytical model that considers COPII assembly into a spherical shell on the membrane and TANGO1 polymerization into a filament that caps the COPII lattice. They then study how various physical parameters (TANGO1 self-interaction, COPII self-interaction, TANGO-COPII interaction, membrane tension, external force) influence the resulting equilibrium membrane shape. In the end they discuss the dynamic growth of the protrusion.

The problem is interesting, and the Abstract seems exciting, however, in my opinion the data presented fails to support the main claims of the paper.

Following the reviewer’s comments (see also our specific answers below), we rewrote the Abstract to be more cautious and accurate with our claims.

Main concerns:

i) The first claim by the authors is that by capping the COPII lattice TANGO1 prevents premature carrier scission and enables packing the bulky cargo into the carrier. This claim is repeated many times throughout the paper, without any data to support it, since the model does not consider carrier scission or cargo loading. This claim appears mainly speculative.

The authors do indeed show that TANGO1 capping stabilizes incomplete buds, but they do not show the relationship between this stabilization and cargo-loading or carrier scission. In fact, in their dynamic model they prevent carrier scission "by hand", by not allowing radii below certain size. They also do not present any experimental evidence that the procollagen transport is necessarily carried by incomplete buds or pearled tubes.

Hence the result that the capping stabilizes incomplete buds can also be interpreted in other ways, for instance as inhibitory to the carrier growth since the capping imposes a free energy barrier for the growth (Figure 2). In summary: there is no evidence in the paper that the capping indeed enables packing the bulky cargo.

The reviewer is right that our models do not explicitly consider carrier scission. Regarding procollagen loading, although it is not included explicitly in any of our models, it is included “effectively” as a minimal neck radius in our dynamic model (see Appendix 1).

Taking this into account, our theoretical approaches focused on understanding the growth of a transport intermediate for procollagen export beyond that of a regular COPII-coated spherical vesicle. Our results show that, under certain conditions, TANGO1 forms a ring by binding to the periphery of a COPII lattice (a situation we referred to as capping) (see e.g. Figure 6 and Figure 5A,B). Notably, our results reveal that when there is a TANGO1 ring (capping conditions), the equilibrium shape of the membrane is altered in a way that generally favors open shapes with relatively large neck openings. This prevents the formation of fully closed buds (therefore preventing fission) (Figure 2B). In contrast, in the absence of TANGO1, the buds tend to close their necks to very small radii (Figure 2A), that we interpret as a possible route toward fission, although the precise fission mechanism is not modeled here.

We suggest that stabilization of open shallow buds could possibly enable efficient recruitment of procollagen to the export site, which is mediated by TANGO1 itself. Importantly, experimental evidence indicates a role for TANGO1 in efficiently packing procollagen for export from the ERES. Hence, our interpretation of the theoretical results presented here is in full agreement with the reviewer’s comment: TANGO1 rings have an “inhibitory role to the carrier growth”, which we phrased in our initial submission as “prevent premature fission”. Further events are required (such as tension regulation or force application, together with efficient procollagen packing to sterically prevent membrane fission away from the TANGO1 ring) for the elongation of the otherwise stable shallow bud into a large transport intermediate.

We reason that a possible source for such tension regulation would be mediated by TANGO1. TANGO1 family of proteins, being multi-domain, multi-functional proteins, are required to recruit membranes (ERGIC/early Golgi cisternae) through their interaction with the NRZ tethering complex. We hypothesize, based on estimates of ER and Golgi membrane tension, that these fusion events could produce a transient decrease in the ER membrane tension, which then would alter the stable shapes of the system and as a result can induce growth of the carrier (Figure 4B). In fact, we propose that this is the reason why in the absence of the tethering factors (NRZ proteins) or in cells expressing a deletion mutant of TANGO1 that is unable to recruit ERGIC membranes, procollagen export from the ER is inhibited (Raote et al., 2018).

Moreover, in our dynamic model, we introduced a steric interaction preventing neck closure (and therefore fission) mimicking the presence of procollagen at those necks. In the absence of functional TANGO1, which is the receptor molecule that presents procollagen to COPII coats (Saito et al., 2009), this interaction does not occur, and therefore we believe that our model’s assumptions are justified based on experimental grounds. This is explained in more detail in the revised version of the manuscript.

In sum, we agree that our interpretation is based on the combination of our experimental and theoretical findings. Therefore, following the reviewer’s comment, we have reorganized the text to make these points clear at the outset. Former Figure 1 is now split into two figures, leaving the second part (new Figure 8) as a summary of our working model. We are also more careful now with our explanations to clearly distinguish between the models’ results and our interpretation of these results within the experimental context of the process. We would also like to direct the reviewer to our detailed response to reviewer 1, point 1 on similar issues.

ii) Related to the previous comment, the main assumption of the paper is that the procollagen transport is facilitated by incomplete COPII buds. However, the authors do not really present any evidence for that. For instance, if the carrier has a spherocylindrical shape (which has been reported for COPII in vitro) the whole conclusions on the role of capping would be different.

We would like to argue that one has to be cautious about this, since COPII in vitro has no clear bearing on COPII in vivo and especially to procollagen export. In addition, as to date and to the best of our knowledge, there is no clear evidence on the shape and COPII lattice coverage of the structure responsible for procollagen export out of the ER. Two papers that claim the involvement of COPII mega containers have been challenged by new data (the work of Leikin and colleagues). For these reasons, in our dynamic model we do not assume any pre-defined membrane shape (as we do in the equilibrium model). The results from our dynamic model do not show the formation of large spherocylindrical shapes.

Based on the overall comments from the reviewers, we have re-structured and revised the text to present the more general dynamic model early in the text (and hence no shape restriction). We then move to the equilibrium, analytical model (spherical geometry imposed, justified by the results from the dynamic model) to gain insight into the physics of the process.

iii) The second main claim of the paper is that TANGO1 enables the carrier growth by reducing the membrane tension, by recruiting ERGIC. The authors model this effect "by hand", by decreasing the tension in their model and showing that the free energy minimum is shifted to long carrier shapes. In their dynamic model they impose sudden decrease and increase in tension and show that this enables and prevents the carrier growth, respectively. This result is nice, but not unexpected. The authors also do not really show that TANGO1 enables the carrier growth, but rather that the decrease of the membrane tension enables it, be it mediated by TANGO1 or otherwise. The role of membrane tension on the protrusion growth has been studied extensively before (see eg the body of work by Nassoy and Bassereau, for instance EPL 2005), and agrees with the findings presented here. In that sense the physical result that the decrease in the membrane tension enables the protrusion growth is not novel, although it has been put in a context of a different system.

We fully agree with the reviewer. We do not claim that our results on tension regulation of carrier shape, from a purely mechanical perspective, are completely novel, since as the reviewer says, there is a large pool of literature on that respect. In our previous submission, we cited only a few of these earlier manuscripts (including references to Apodaca et al., Kosmalska et al., Wu et al., Hassinger et al., Niu et al., and Saleem et al.), but we agree that we had missed relevant references. We have corrected this error by explaining this point better and adding new references (e.g. Cuvelier et al., 2015; Mercier et al., 2020).

However, as the reviewer also acknowledges, our aim here was to put the tension regulation mechanism for bud/tube growth in the context of procollagen export, and to rationalize the possible role(s) of TANGO1 in modulating this. So, we believe that our results convincingly show that membrane tension regulation is a possible mechanism to create a large transport intermediate for procollagen export at ERES, which, to the best of our knowledge, has not been studied before. We expect, as also has been published by other groups, that membrane tension regulation as a means to control membrane protrusion is more general, but is controlled by different players at different intra-cellular locations (e.g. a very recent manuscript by the Roux lab, Nature Cell Biology 22 (8), 947-959).

Unfortunately, we have no direct experimental evidence of membrane tension reduction/regulation at ERES for procollagen export (as described in the “Proposal for experimental approaches to test the model” section in the Discussion). However, we have a number of experimental results that, we believe, allow us to propose that TANGO1 can possibly mediate such tension reduction (such as recruitment of ERGIC membranes, binding to tethers, interaction with SNARE proteins). We have now rewritten the text to emphasize that tension reduction is the causative effect of protrusion growth, and that TANGO1 is only one of the possible means by which such tension reduction can occur (interestingly, both cells knock-downed for NRZ components and cells expressing the TANGO1 mutant that cannot recruit these tethers accumulate procollagen at the ER).

iv) The paper feels unnecessarily long and repetitive, where the same claims are repeated many times.

We thoroughly revised and streamlined the text to make the main text shorter and try to avoid any repetitive parts.

Overall, this is a nice exploratory paper that makes bold claims that appear not to be supported by data, it is my impression that the authors somewhat try to fit the results into a preconceived mechanism of how TANGO1 enables procollagen transport, as opposed to the mechanism arising from their data. The physical result that the decrease in the membrane tension enables protrusion growth is not surprising (or novel). In my opinion the work does not present a substantial development with respect to the 2018 eLife paper by the same authors.

We respectfully disagree here with the reviewer. Our previous manuscript (Raote et al., 2018) was completely experimental, and in there we proposed that “A tug-of-war between the filament bending and the effect on COPII stabilisation created by the adsorption of TANGO1 filaments around ERES would then dictate whether and how TANGO1 rings are formed. Interestingly, it has been shown that the line tension of the polymerising protein coat can play a key role in controlling the timing and size of clathrin-coated vesicles (Saleem et al., 2015). We thus propose that the stabilising effect of TANGO1 while adsorbing around ERES would serve as a physical mechanism to delay and enlarge the COPII vesicle, commensurate with cargo size”.

In the current manuscript, we now back these proposed mechanisms with rigorous physical analyses. It is the contextualization of experimental observations within a physical framework and the presentation of their rigorous physical analysis that we believe is novel and represent a substantial development in our quest to understand the mechanisms of procollagen export from the ER.

Reviewer #3:

In this manuscript, the authors develop a theoretical model to analyse a scenario for the formation of large membrane carrier able to export procollagen fibres from ERES. COPII coat components polymerise into a spherical cap, which is prevented from maturation and budding by TANGO1 proteins assembling into a ring at the coat edge. TANGO1 also promotes the fusion of ERGIC vesicles which lower membrane tension locally and allow for the longer COPII-covered carriers able to incorporate procollagen.

I appreciate some aspect of the model, primarily the analysis of the self-organisation of two types of membrane proteins into non-trivial structure. The fairly thorough study of the different possible range of behaviour, including a careful account of the relevance of different parameters, is valuable.

On the other hand, other aspects of the manuscript seem dubious to me and rely on what I believe to be incompatible assumptions. This is true for the tension regulation aspect, which is unfortunately a point that is strongly emphasise in the manuscript. Another weak point is the way the interaction with the procollagen fibres is treated.

Another problem I have with the manuscript is the constant mixing between rigorous results obtained from the model and speculations which are not supported by the model. Therefore, I think that this paper present interesting results regarding the self-organisation of coatomers and ring-forming proteins, which are certainly relevant for the situation under study, but that it requires important rewriting to put the result in their proper context and to separate facts from conjectures.

1) The deformation of membrane by aggregation of proteins inducing membrane curvature has been studied in great details, and the role of the different physical parameters in the process, including membrane tension, is well documented. The originality of the present model is the involvement of a second class of proteins that stabilise the coat (e.g. disfavor the formation of a full spherical coat) due to attractive interaction with coat proteins AND the fact that these proteins tend to form semi-flexible filaments. The problem is treated at thermodynamic equilibrium, through energy minimisation. As such, it assumes ergodicity; that the entire space of configuration can be explored, and cannot investigate situations where the system is kinetically trapped into a particular state. This limitation is insufficiently discuss in the text, especially in the Introduction. Furthermore, the possibility for kinetic trapping is often explicitly mentioned without a word of caution, which could confused an uninformed reader that this possibility is accounted for by the model. It is not, and this must be stated explicitly.

We thank the reviewer for the comment. We completely agree that our analytical model is an equilibrium model and therefore ergodicity is assumed. To study the system with this equilibrium model, we performed direct global minimization of the free energy of the system as a function of the free parameters of the model (the shape parameter, 𝜂, and the capping fraction, 𝜔). By computing the free energy of the system for a wide range of these parameters (see e.g. Figure 4A), we have access not only to the globally stable configuration of the system, but also to locally metastable states. This further allows us to estimate the free energy barriers separating the metastable states from the globally stable states. With these results we qualitatively estimate average time scales for shape transitions between locally stable states, based on Arrhenius kinetics (that is, shape changes mediated by thermal fluctuations).

We now stress that this is just an estimation based on an equilibrium model, so the actual dynamics of the membrane shape between two locally stable shapes are beyond the reach of such a model. In addition, following the reviewer’s suggestions, we now explicitly state in the revised version the limitations of our model in terms of the kinetics of shape transitions.

2) Thermodynamic equilibrium implies that proteins in the coat and in the ring can freely exchange with a reservoir, or that the time scales associated with this exchange are much faster than other time scales, such as the one for tension variation. The chemical potential of COPII monomer is assumed fixed, regardless of the coat size. This means that there exists a reservoir of monomer at fixed chemical potential with which the coat can freely exchange component. I see two possibilities. The reservoir is the flat membrane, which is itself in equilibrium with coat component in the cytosol, or the reservoir is the cytosol itself, which requires that coat component bind directly from the cytosol onto the growing coat. The chemical potential \muc is said to include binding energy, without specifying if it is the binding of one monomer to the membrane or the binding between two monomers. I assume it is the latter which suggests that the reservoir is indeed the rest of the membrane. This makes sense to me, but it should be clearly discussed, including the fact that this model only makes sense if coatomers can be freely exchange between the growing coat and the rest of the membrane. By the way, the binding energy \muc0 is expressed as an energy per unit area. This is not optimal. It should be expressed as an energy, so it can be compared with the thermal energy kT.

We thank the reviewer for pointing out that this part was not clear. COPII coat polymerization is a multi-step process that involves many reactions, including the initiation by GDP to GTP exchange in Sar1 that anchors it into the membrane, the posterior recruitment of the inner layer of the COPII coat, etc. In our models, for the sake of simplicity, we described all the subcomponents of the COPII inner and outer coats as a single effective species (a “COPII unit”). For our purposes, we think that a more detailed description would only add complexity and extra free parameters without providing relevant biophysical insights. This is explicitly stated in the revised version with a new section with the main hypotheses and limitations of our model formulations.

Following this, and regarding the nature of the COPII reservoir, the reviewer is indeed correct. In general terms, one would consider a multi-step process by which (i) free soluble cytosolic “COPII units” could bind to/unbind from the membrane; and (ii) membrane-bound (and also soluble) “COPII units” would undergo a COPII-COPII binding reaction (polymerization). However, this would add extra complexity to our modeling strategy. To simplify this, we followed the approach proposed by Saleem et al., 2015, to investigate the mechanics of clathrin-coated vesicle formation. In there, the authors defined the chemical potential of clathrin as the free energy gain of polymerization of a clathrin unit area. That polymerization energy, 𝜇01, included the contributions of the interactions between the coat and the membrane (𝜇0KG) and between the coat subunits (actual polymerization interactions, 𝜇0K0). In their experimental measurements, the authors showed that the direct coat-coat interactions are the major contributors to the assembly of the coat. Based on this information, we assumed that a similar situation is occurring for COPII polymerization: that the binding energy 𝜇01 represents the polymerization energy due to COPII-COPII binding, and therefore the reservoir of COPII is the rest of the membrane (as is the case also for our dynamic model). This is now discussed in the revised version of our manuscript.

Finally, in the revised version, we have included an estimation of the binding energy of COPII polymerization per molecule. To estimate the binding energy in units of 𝑘*𝑇 for the binding of a single COPII unit, we used the characteristic size of the Sec13-31 heterotetramers, ~30𝑛𝑚 (see e.g. Stagg et al. Cell 2008; Zanetti et al., 2013), which gives a characteristic area of a COPII unit, 𝑎1~(30 𝑛𝑚)2. This gives that 𝜇c0 𝑎0~22 𝑘B𝑇.

3) The equilibrium treatment becomes particularly problematic when the situation involves diffusion barrier, which is the main argument put forward by the author in support of their claim that TANGO1 is a regulator of membrane tension, allowing to the elongation of membrane carrier. For this two happen, at least three conditions must be satisfied: i) lipids must be prevented from diffusing across the TANGO1 ring, ii) ERGIC vesicles must be allowed to fuse within the area delimited by the TANGO1 ring, and iii) coatomers must be able to freely exchange with their reservoir, i.e. to cross the diffusion barrier. It seems rather unlikely that condition 1 is strictly satisfied. the TANGO1 ring could slow down lipid diffusion, but probably not abolish it. This is indeed the conclusion of Raote et al., 2020, so the question of of tension regulation becomes a competition between time scales; the time scale of tension equilibration vs. the time scale of coat formation. It is not discussed as such but it should.

There is an even bigger problem. There is a clear conflict between conditions (i) and (iii). It is not reasonable to claim that lipids are trapped but not coatomers. Furthermore, the fusion of ERGIC vesicles, even if one assumes that it occurs inside the TANGO1 ring, which seems very unlikely considering that this part of the membrane is crowded with COPII presumptuous, would locally and transiently reduce tension because membrane area of a completely different composition than the initial coat would be added to the region inside the ring. None of this is discussed. Probably because it is a difficult problem, but the way it is handled here is not at all satisfactory. The bottom line is that the claim of tension regulation is presumptuous and not acceptable in the current form.

We apologize for the lack of clarity in our previous version. TANGO1 acting as a diffusion barrier (Raote et al., 2020) is not the main argument to support the idea of TANGO1 acting as a means to regulate membrane tension. Actually, our results (both models) hold true regardless of how membrane tension is regulated (see also our detailed responses to reviewer #2). In the models presented in this paper we do not explicitly include the presence of a (partial) diffusion barrier. This is now clearly stated in the revised version, where we also discuss our current model and its results in the context of reference Raote et al., 2020.

We know from our previous experimental work that TANGO1 forms rings at the ERES around COPII coats, and that TANGO1 recruits the NRZ tethering complex (by its coiled-coil domain CC1), which then recruits ERGIC/early Golgi membranes (Raote et al., 2018). Based on these observations, here we propose that the recruited membrane fuse to the ERES, providing a possible tension regulation mechanism. Although this hypothetical mechanism relies on the presence of TANGO1 rings at the export sites, it is independent of the role of TANGO1 as a diffusion barrier (Raote et al., 2020). We do not know the exact site where these membranes would fuse, but we do know that it likely occurs in the vicinity of the export site (see e.g. Figure 6A in Raote et al., 2018). This membrane fusion event would lead to a local reduction of membrane tension due to the addition of lipid molecules (see e.g. Sens and Turner, 2006). Tension however tends to dynamically equilibrate after membrane fusion (Shi et al., 2018). Hence, the reviewer is indeed correct that the problem of tension regulation is a problem of time scales: if tension equilibrates much faster than the time the membrane needs to change its shape, then there is no effective tension reduction.

Mechanical equilibration of the membrane shape (𝜏GQ0R) can be theoretically estimated to be of the order of milliseconds (see e.g. Campelo et al., 2017; Sens and Rao, 2013) (see also our own results from the dynamic model where shape changes are found within few milliseconds (see e.g. Figure 3)). The diffusive behavior of membrane tension (at the plasma membrane of HeLa cells) has been measured to be associated with a diffusion coefficient of 𝐷T = 0.024 𝜇𝑚2/𝑠 (Shi et al., 2018), which gives a characteristic diffusion time of the order of 𝜏T~1 𝑠 (using characteristic length scales of ~100–500 𝑛𝑚), which is much larger than 𝜏GQ0R. We envision that the TANGO1-induced diffusion barrier at the base of the growing bud can slow down even further the dynamics of tension equilibration. Hence, we think it is reasonable to assume that the time scale of mechanical equilibration of the membrane shapes is much smaller than that of tension equilibration.

This argument together with a discussion on the possible roles of TANGO1 as a diffusion barrier in controlling or modulating the tension regulation mechanisms are now found in the revised version of the manuscript.

4) As far as I can see, procollagen is entirely absent from the model equations. Nevertheless it is present in the Discussion in mostly two ways; as a way to sterically hinder neck closure or as responsible for a normal force that helps elongate the membrane carrier. The first aspect is entirely conjectural and is not included in any way in the model. It should be presented as such in the Discussion. The second is somewhat introduced phenomenologically in the model, but is not properly discussed. For polymerising procollagen fibres to push on the coat, it would need to exert an opposite force on something else. What would that be? The ER membrane opposite to the ERES presumably, but expect if the fiber is perfectly perpendicular to that membrane, the force would also result in a torque that would made the fibre tilt. It is said repeatedly in the text that this force is dispensable, but we are still lacking an argument to explain how the fibre would properly orientate along the carrier axis of symmetry to be properly incorporated. Since this is a model for how to build membrane carrier for bulky cargo, the interaction between the cargo and the carrier must be discussed more thoroughly.

The proposed role of procollagen as a means to sterically prevent neck closure is now presented in the Discussion of the revised manuscript and not in Figure 1 as before.

We now also explain in more detail our hypothesis of how procollagen folding can exert a force to elongate the carrier. We suggest that TANGO1 (as a ring) indirectly anchors a soluble lumenal protein (procollagen) to the membrane. Hence, as the reviewer correctly presumed, the force would act against the membrane through TANGO1. Indeed, if such force was applied to a single TANGO1 molecule, it would induce a torque that would tilt the procollagen and tend to position it parallel to the membrane plane (in which case the normal force applied at the tip of the carrier would vanish). However, we propose that the ring-like organization of TANGO1 could allow for torque compensation because it would act as the structure to which forces are applied. Specifically, a torque would appear for each of the TANGO1 molecules in the ring. When integrating these torques out for the entire TANGO1 ring, the resultant net torques would vanish and therefore such a structure would help align procollagen molecules perpendicular to the TANGO1 ring plane. This is now discussed in the revised manuscript.

5) Regarding the energy minimisation procedure. It is unclear why all energies are expressed in unit of Ap (Equations 1-4 etc). Ap is the projected area of the carrier, which changes non-linearly with the number of coatomers as the coat grows. It is unclear to me why this area is important, except if one wishes to discuss steric interaction between buds. I would think that the proper thing to do is to compare the energy per coatomer for different coat geometry, rather than to minimise the energy divided by Ac. As such, I don't think that the minimisation procedure is correct. For instance, looking at Figure 2B, we can see that the "free" energy of the double bud is smaller than that of the single bud so that the former is said to be "globally stable". What should be compared is the chemical potential (energy per COPII monomer) is both situations, which could very well favour single buds for the parameters of Figure 1B, in particular due to the favorable interaction between TANGO1 and COPII monomers.

Related to this, I could not figure out what is the difference between Am and Ac. Ac is supposed to be the coat area and Am the membrane area, but in this simplified geometry using spherical caps, I imagine that the entire curved part of the membrane is covered by coat, so why is Am not equal to Ac?

We apologize for not being clear with this part of the model. For our equilibrium analytical model, we followed the framework proposed by Saleem et al., 2015. Indeed, we consider (as it was also done in Saleem et al.’s manuscript) that there is a densely packed assembly of TANGO1 rings, as experimentally observed in cells (Raote et al., 2017; Raote et al., 2018); and that the amount of TANGO1 and COPII subunits is large enough (non-limiting amounts).

The reason why we express the energies in unit of 𝐴X was not clearly explained in our previous manuscript. In fact, what we did was to compute the free energy per transport intermediate (per bud) and then divide it by the surface area of the initially flat, uncoated membrane. Like this, we obtain the free energy per unit area, 𝑓0 (see e.g. Equation 1 in the revised version). The surface area projected by the coat on the initially flat membrane represents the surface area of the flat, unperturbed membrane, and that is the reason why we divide our energies by 𝐴X. These explanations are now made clear in the revised text.

Also, there is a subtle difference between 𝐴G and 𝐴0, which only arises for structures with 𝜂 > 1/2 (larger than half buds). 𝐴0 is the area of the coated surface of the membrane (represented in orange in the new Appendix 2—figure 1B); whereas 𝐴G is the overall area of the membrane in the bud (black surface area in Appendix 2—figure 1B), which includes the curved surface under the coat plus the flat surface of the membrane that connects to the projected area limit (region shaded in light blue in Appendix 2—figure 1B).

6) TANGO1 is repeatedly described as a linactant, but it is not clear that the stabilisation of incomplete buds is due to the linactant effect. The TANGO1 ring is rigid and its caping of the coat edges involve an elastic energy penalty. Isn't this the dominant effect of coat stabilisation, rather than the linactant effect?

The reviewer states correctly that stabilization of incomplete buds is not solely described by the linactant effect of TANGO1, but by a combination of different factors. These include the linactant strength of TANGO1 and also, as the reviewer suggests, the filament bending rigidity and the filament preferred curvature. In fact, our results indicate that it is the capping transition that facilitates the stabilization of open shallow buds. Hence, the role that the linactant strength of TANGO1 plays is in inducing capping. For instance, if TANGO1 would not have any linactant capacity, there would be no capping transition (see also our response to reviewer 1, major comment 1). This is now further explained in the text.

7) The section proposal of experimental approaches to test the model is not very useful. It does not really provide experimental test of the model based on the quantitative findings of the model. The section “ TANGO1 as a regulator of membrane tension homeostasis” in largely speculative and not supported by the model. It is rather presents hypothesis that are a starting point of the model, several of which are dubious (in particular the fact that tension is reduced while membrane composition is not changed, as discussed above). It should be presented as speculation.

Since this manuscript is a purely theoretical paper that presents no new experiments, we thought it was of interest to include such section in the Discussion. We believe that it can present ideas for future experimental works on the topic, following eLife’s editorial suggestions on such manuscripts (Shou et al., 2015). Following the reviewer’s comment, we adapted part of the text to provide more clear testable predictions.

Regarding the section on TANGO1 as a regulator of membrane tension homeostasis, we also revised it to a large extent, to be clear about which of our statements are hypothesis, results, and speculations (also following comments from reviewer 2).

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

The reviewers agree that the paper is suitable for publication in eLife after the authors address the following two concerns:

1) The narrative of the paper has been much improved and the complex modeling is now presented clearly and concisely. However, the reviewers judge that the link between the modeling and the biological situation remains rather speculative. The reviewers therefore suggest that the authors add a paragraph of open and honest discussion on the speculative link between the model and biology.

We adapted and expanded a paragraph in the Discussion section, where we now state clearly the potential link between our physical hypotheses and the available biological data:

“We have proposed and analyzed a theory by which TANGO1 assembles into a ring at the ERES to facilitate cargo export. […] The new experimental data will undoubtedly improve our understanding of how cells engage to export cargoes based on their size, volume, and the overall cellular needs.”

2) The authors should address the inconsistent use of high / low tension values in the two models. (0.006 / 0.003 kBT/nm2 in the continuous model, and 0.003 / 0.0012 kBT/nm2 in the equilibrium model).

This is now discussed in the revised manuscript:

“It is worth noting that, despite the different modeling and implementation choices taken in these two approaches, the values of the membrane tension at which the predictions agree only differ by a factor two. This difference could certainly be further reduced by undergoing a thorough analysis of the computational model's parameter space. However, given the computational cost of such study and the uncertainty of the experimental estimates for the ER and Golgi membrane tensions, seeking such a quantitative match between two qualitative models would only bring very limited insights.”

https://doi.org/10.7554/eLife.59426.sa2

Article and author information

Author details

  1. Ishier Raote

    Centre for Genomic Regulation (CRG), The Barcelona Institute of Science and Technology, Barcelona, Spain
    Contribution
    Conceptualization, Formal analysis, Investigation, Writing - original draft, Writing - review and editing
    Contributed equally with
    Morgan Chabanon
    For correspondence
    ishier.raote@crg.eu
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-5898-4896
  2. Morgan Chabanon

    1. ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Barcelona, Spain
    2. Universitat Politècnica de Catalunya-BarcelonaTech, Barcelona, Spain
    Contribution
    Conceptualization, Software, Formal analysis, Investigation, Methodology, Writing - original draft, Writing - review and editing
    Contributed equally with
    Ishier Raote
    Competing interests
    No competing interests declared
  3. Nikhil Walani

    Universitat Politècnica de Catalunya-BarcelonaTech, Barcelona, Spain
    Contribution
    Software, Formal analysis, Investigation, Methodology, Writing - review and editing
    Competing interests
    No competing interests declared
  4. Marino Arroyo

    1. Universitat Politècnica de Catalunya-BarcelonaTech, Barcelona, Spain
    2. Institute for Bioengineering of Catalonia, The Barcelona Institute of Science and Technology, Barcelona, Spain
    3. Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Barcelona, Spain
    Contribution
    Conceptualization, Software, Supervision, Funding acquisition, Methodology, Project administration, Writing - review and editing
    Competing interests
    No competing interests declared
  5. Maria F Garcia-Parajo

    1. ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Barcelona, Spain
    2. ICREA, Barcelona, Spain
    Contribution
    Conceptualization, Supervision, Funding acquisition, Methodology, Project administration, Writing - review and editing
    Competing interests
    No competing interests declared
  6. Vivek Malhotra

    1. Centre for Genomic Regulation (CRG), The Barcelona Institute of Science and Technology, Barcelona, Spain
    2. ICREA, Barcelona, Spain
    3. Universitat Pompeu Fabra (UPF), Barcelona, Spain
    Contribution
    Conceptualization, Supervision, Funding acquisition, Writing - original draft, Project administration, Writing - review and editing
    For correspondence
    vivek.malhotra@crg.eu
    Competing interests
    Senior editor, eLife
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-6198-7943
  7. Felix Campelo

    ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Barcelona, Spain
    Contribution
    Conceptualization, Formal analysis, Supervision, Funding acquisition, Investigation, Methodology, Writing - original draft, Project administration, Writing - review and editing
    For correspondence
    felix.campelo@icfo.eu
    Competing interests
    Reviewing editor, eLife
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-0786-9548

Funding

Government of Spain ("Severo Ochoa" Programme (CEX2019-000910-S))

  • Morgan Chabanon
  • Maria F Garcia-Parajo
  • Felix Campelo

Government of Spain (BFU2015-73288-JIN)

  • Maria F Garcia-Parajo
  • Felix Campelo

Government of Spain (FIS2015-63550-R)

  • Maria F Garcia-Parajo
  • Felix Campelo

Government of Spain (FIS2017-89560-R)

  • Morgan Chabanon
  • Maria F Garcia-Parajo
  • Felix Campelo

Fundacio Privada Cellex

  • Morgan Chabanon
  • Maria F Garcia-Parajo
  • Felix Campelo

Fundacio Privada Mir-Puig

  • Morgan Chabanon
  • Maria F Garcia-Parajo
  • Felix Campelo

Generalitat de Catalunya (CERCA program)

  • Ishier Raote
  • Morgan Chabanon
  • Maria F Garcia-Parajo
  • Vivek Malhotra
  • Felix Campelo

European Research Council (ERC Advanced Grant (GA 788546))

  • Morgan Chabanon
  • Maria F Garcia-Parajo
  • Felix Campelo

European Research Council (LaserLab 4 Europe GA 654148)

  • Morgan Chabanon
  • Maria F Garcia-Parajo
  • Felix Campelo

Spanish Government (BFU2013-44188-P)

  • Ishier Raote
  • Vivek Malhotra

Spanish Government (Consolider CSD2009-00016)

  • Ishier Raote
  • Vivek Malhotra

Spanish Government (Severo Ochoa Program SEV-2012-0208)

  • Ishier Raote
  • Vivek Malhotra

Spanish Government (Maria de Maeztu MDM-2015-0502)

  • Vivek Malhotra

BIST (Ignite grant eTANGO)

  • Ishier Raote
  • Maria F Garcia-Parajo
  • Vivek Malhotra
  • Felix Campelo

Spanish Ministry of Science and Innovation (IJCI-2017-34751)

  • Ishier Raote

Spanish Ministry of Science and Innovation (RYC-2017-22227)

  • Felix Campelo

European Research Council (CoG-681434)

  • Nikhil Walani
  • Marino Arroyo

Generalitat de Catalunya (2017-SGR-1278)

  • Marino Arroyo

ICREA (ICREA academia)

  • Marino Arroyo

Ministerio de Economía y Competitividad (Severo Ochoa Program CEX2018-000797- S)

  • Marino Arroyo

State Research Agency (PID2019-106232RB-I00/ 10.13039/501100011033)

  • Morgan Chabanon
  • Felix Campelo

Ministerio de Economía y Competitividad (Severo Ochoa Program SEV-2012–0208)

  • Ishier Raote
  • Vivek Malhotra

María de Maeztu Unit of Excellence (MDM-2015–0502)

  • Ishier Raote
  • Vivek Malhotra

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We thank Javier Diego Íñiguez, Iván López-Montero, and members of the Garcia-Parajo lab for valuable discussions. MF Garcia-Parajo and V Malhotra are Institució Catalana de Recerca i Estudis Avançats professors at ICFO-Institut de Ciencies Fotoniques and the Centre for Genomic Regulation (CRG), respectively. M Chabanon, MF Garcia-Parajo and F Campelo acknowledge support from the Government of Spain (FIS2015-63550-R, FIS2017-89560-R, BFU2015-73288-JIN, RYC-2017–22227, and PID2019-106232RB-I00/10.13039/501100011033; Severo Ochoa CEX2019-000910-S), Fundació Cellex, Fundació Mir-Puig, and Generalitat de Catalunya (CERCA, AGAUR), ERC Advanced Grant NANO-MEMEC (GA 788546) and LaserLab 4 Europe (GA 654148). I Raote and V Malhotra acknowledge funding by grants from the Ministerio de Economía, Industria y Competitividad Plan Nacional (BFU2013-44188-P) and Consolider (CSD2009-00016); support of the Spanish Ministry of Economy and Competitiveness, through the Programmes ‘Centro de Excelencia Severo Ochoa 2013–2017’ (SEV-2012–0208) and Maria de Maeztu Units of Excellence in R and D (MDM-2015–0502); and support of the CERCA Programme/Generalitat de Catalunya. I Raote, MF Garcia-Parajo, V Malhotra., and F Campelo acknowledge initial support by a BIST Ignite Grant (eTANGO). I Raote acknowledges support from the Spanish Ministry of Science, Innovation and Universities (IJCI-2017–34751). This work reflects only the authors’ views, and the EU Community is not liable for any use that may be made of the information contained therein. M Arroyo and N Walani acknowledge the support of the European Research Council (CoG-681434), and M Arroyo that of the Generalitat de Catalunya (2017-SGR-1278 and ICREA Academia prize for excellence in research) and of the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme (CEX2018-000797- S).

Senior Editor

  1. Suzanne R Pfeffer, Stanford University School of Medicine, United States

Reviewing Editor

  1. Jure Derganc, University of Ljubljana, Slovenia

Publication history

  1. Received: June 1, 2020
  2. Accepted: November 9, 2020
  3. Accepted Manuscript published: November 10, 2020 (version 1)
  4. Version of Record published: November 30, 2020 (version 2)

Copyright

© 2020, Raote et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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