T cells recognize peptide antigens presented by major histocompatibility complexes (MHC) on apposing cell surfaces as a central step in the initiation of adaptive immune responses (Rossjohn et al., 2015; Smith-Garvin et al., 2009; Dustin, 2014; Pettmann et al., 2018; Belardi et al., 2020). The antigen recognition is performed by the T-cell receptor (TCR) complex, a complex of four dimeric transmembrane proteins. In this complex, the heterodimeric TCRαβ contains the binding site for recognizing peptide antigens, and the associated CD3εδ and CD3εγ heterodimers and the CD3ζζ homodimer contain the intracellular signaling motifs that transmit antigen binding to T cell activation (Wucherpfennig et al., 2010). While this stoichiometry of the complex has been known for nearly two decades (Call et al., 2002), the structure of the TCR – CD3 complex remained a puzzling problem (Fernandes et al., 2012; Birnbaum et al., 2014; Natarajan et al., 2016) that has only been recently solved by Dong et al., 2019 with cryogenic electron microscopy (cryo-EM). To determine the structure, Dong et al. expressed all proteins of the complex in cultured cells, replaced the cell membrane around the assembled TCR – CD3 complex by the detergent digitonin, and stabilized the interactions between the extracellular (EC) domains of TCRαβ, CD3εδ and CD3εγ by chemical crosslinking. In the cryo-EM structure, the EC domains of CD3εδ and CD3εγ are both in contact with TCRαβ and with each other (see Figure 1), which explains the cooperative binding of CD3εδ and CD3εγ to TCRαβ observed in chain assembly (Call et al., 2002), mutational (Kuhns and Davis, 2007; Kuhns and Davis, 2012), and NMR experiments (He et al., 2015). As indicated by mutational experiments (Kuhns and Davis, 2007; Kuhns and Davis, 2012), the DE loop of the membrane-proximal constant domain Cα of TCRα is in contact with the CD3εδ EC domain, and the CC’ loop of the constant domain Cβ of TCRβ is in contact with both the CD3εγ and CD3εδ EC domains in the assembled TCR – CD3 complex (see Figure 1). Outstanding questions concern the orientational variability of the TCRαβ EC domain relative to the membrane, in which the TCR – CD3 complex is embedded in its native environment, and the structural variability of the overall TCR – CD3 complex, which is constrained by the chemical crosslinking of the protein chains in the approach of Dong et al., 2019; Reinherz, 2019. The Cβ FG loop, for example, has been suggested to play a key role in T cell activation (Kim et al., 2010; Touma et al., 2006), but exhibits only rather limited contacts with CD3εγ in the cryo-EM structure (see Figure 1).

Figure 1

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In this article, we investigate the structural and orientational variability of the membrane-embedded TCR – CD3 complex in extensive, atomistic molecular dynamics (MD) simulations with a cumulative simulation length of 120 μs. Compared to the cryo-EM structure, significantly more residues of TCRαβ are involved in EC domain contacts along our simulation trajectories, in particular in the Cβ FG loop, and notably also in the variable domain Vα of the TCRα chain. We find that the TCRαβ EC domain is rather variable in its orientation, with tilt angles relative to the membrane normal that range from 15° to 55°. The tilt of the TCRαβ EC domain is both coupled to a rotation of the domain and to characteristic changes in the overall structure of the TCR – CD3 complex. These structural changes include a clear decrease of contacts in the Cβ FG loop and an increase of contacts in the Vα domain with increasing tilt angle of the TCRαβ EC domain, as well as changes in the orientation of the transmembrane (TM) helices of the TCRα and CD3γ chain. The concerted motions of the membrane-embedded TCR – CD3 complex revealed in our simulations provide atomistic insights for force-based models of TCR signaling, which involve structural changes, in particular in the Cβ FG loop, that are induced by transversal, tilt-inducing forces on bound TCRs (Brazin et al., 2015; Feng et al., 2018).

Our computational analysis of the structural and orientational variability of the membrane-embedded TCR – CD3 complex is based on 120 atomistic, explicit-water MD simulation trajectories with a length of 1 μs and, thus, on simulation data with a total length of 120 μs. We have conducted these simulations with the Amber99SB-ILDN protein force field (Lindorff-Larsen et al., 2010) and the Amber Lipid14 membrane force field (Dickson et al., 2014) at a simulation temperature of 30°C on graphics processing units (GPUs). The simulation trajectories start from initial system conformations in which the cryo-EM structure of the TCR – CD3 protein complex is embedded in a membrane composed of 456 POPC lipids and 114 cholesterol molecules. We find that the orientational and conformational ensembles sampled by the 120 trajectories equilibrate within the first 0.5 μs of the simulation trajectories (see Materials and methods) and, therefore, focus on the second 0.5 μs of the MD simulation trajectories in our analysis.

Compared to the cryo-EM structure, a much larger set of residues is involved in contacts between the protein dimers of the TCR – CD3 complex in our MD simulations. Figure 2 illustrates the time-averaged contacts between residues of the TCRαβ, CD3εγ, and CD3εδ EC domains along the equilibrated second halves of the MD simulation trajectories. The fourth protein dimer in the complex, CD3ζζ, has no EC domain. The contact maps of Figure 2 include all residue-residue contacts that occur in the simulations with a probability larger than 0.5%. The probabilities of the contacts are calculated from 6000 simulation structures extracted at intervals of 10 ns from the second 0.5 μs of the 120 simulations, and indicated in grayscale in Figure 2. As in the contact maps for the cryo-EM structure shown in Figure 1, two residues are taken to be in contact in a simulation structure if the minimum distance between non-hydrogen atoms of the residues is smaller than 0.45 nm. The contacts are grouped in clusters (blue numbers) that correspond to interactions between loops and strands of the EC domains, which are labeled according to the standard convention for immunoglobulin(Ig)-like domains (Garcia et al., 1996; Wang et al., 1998; Sun et al., 2004). The EC domains of the proteins TCRα and TCRβ consist of the membrane-proximal constant domains Cα and Cβ and the variable domains Vα and Vβ, which are all Ig-like domains, as are the EC domains of the proteins CD3ε, CD3γ, and CD3δ. In our MD simulations, significantly more loops and strands, and more residues of the protein dimers TCRαβ, CD3εγ, and CD3εδ participate in EC domain interactions, compared to the cryo-EM structure. The Cβ FG loop, for example, exhibits only a single contact with an N-terminal residue of CD3γ in the cryo-EM structure (see Figure 1). In our MD simulations, in contrast, the Cβ FG loop is involved in a large number of contacts with the N-terminus of CD3γ and with several loops and strand in the $\mathrm{ϵ}$ chain of the CD3εγ EC domain. Besides the Cα DE loop, Cβ CC’ loop, Cβ EF loop, Cβ FG loop, and Cβ G strand with contacts in the cryo-EM structure, the MD contacts maps of Figure 2 include also the Cα AB loop and the Cβ A and B strand in the constant domains of TCRαβ and, remarkably, the three loops A’B, C”D, and EF in the variable region Vα of TCRα. Residue-residue contacts between Vα and the δ chain of CD3εδ have probabilities smaller than 3%, but occur in 75 of the 120 trajectories and are, thus, a robust feature of our simulations. These contacts are grouped in four small, correlated contact clusters (see cluster-cluster correlation coefficients in Figure 2—figure supplement 1).

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In our MD simulations, the TCRαβ EC domain is rather variable in its orientation relative to the membrane. The orientation can be quantified by two angles, a tilt angle and a rotation angle. To determine these angles, we choose two axes A and B in the TCRαβ EC domain: Axis A connects the centres of mass of Cαβ and Vαβ, where Cαβ is the dimer of the constant domains Cα and Cβ, and Vαβ is the dimer of the variable domains Vα and Vβ. Axis B connects the centres of mass of the variable domains Vα and Vβ. The tilt angle of the TCRαβ EC domain then is the angle between axis A and the membrane normal, and the rotation angle is the angle between axis B and the normal of the plane spanned by axis A and the membrane normal. The rotation angle describes the rotation of the TCRαβ EC domain around axis A (see Figure 3(a) and (b)). In our MD simulations, the tilt angle of TCRαβ EC domain roughly varies between 15° and 55°, while the rotation angle varies between 0° and 55°. A rotation angle of 0° indicates a TCRαβ EC domain orientation in which the centres of mass of the variable domains Vα and Vβ are equally close to the membrane, and the rotation angle is larger than 0° in conformations in which the variable domain Vα is closer to the membrane than the variable domain Vβ (see Figure 3(a) and (b)).

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The two-dimensional probability distribution of the angles in Figure 3(c) indicates that the rotation of the TCRαβ EC domain is coupled to its tilt: For tilt angles between 15° and 35°, the rotation angle predominantly adopts values between about 5° and 25°. For a tilt angle of 40°, the most probable value of the rotation angle is about 32°, and further increases to 40° for a tilt angle of 50°. The coupling between the tilt and rotation of the TCRαβ EC domain is also illustrated in Figure 3(a) and (b). In the structure of the membrane-embedded TCR – CD3 complex of Figure 3(a), the TCRαβ EC domain has a tilt angle of 32.8° and a rotation angle of 12.8°. In the structure of Figure 3(b) with a larger tilt angle of 50.8°, the rotation angle of the TCRαβ EC domain is 42.9°. The rotation and tilt angle for the TCRαβ EC domain in the cryo-EM structure of the TCR – CD3 complex can be determined by aligning the TM domain of this structure to our simulation conformations. This structural alignment embeds and orients the cryo-EM structure in our simulated membranes. From TM domain alignment to the 120 final simulation conformations of our trajectories, we obtain the tilt angle 31.2±0.4° and the rotation angle 14.7±0.7° for the TCRαβ EC domain of the cryo-EM structure. The errors here have been estimated as the error of the mean of the 120 values obtained after structural alignment to these simulation conformations.

The tilt angle of the TCRαβ EC domain is associated with characteristic changes in the overall structure of the TCR – CD3 complex, in particular with changes in the number of residue-residue contacts of the Vα domain and of the Cβ FG loop (see Figure 3(d)) and in the orientations of the transmembrane (TM) helices of the TCRα and CD3γ chains (see Figure 3(e)). Residue-residue contacts of the A’B, C”D, and EF loops of the variable domain Vα with the protein CD3δ only occur for tilt angles of the TCRαβ EC domain larger than about 30° (see Figure 3(d)). The average number of these residues-residue contacts increases to values around two for tilt angles of 50° and larger. For the Cβ FG loop, in contrast, the average number of residues-residue contacts decreases from a value around 30 at the tilt angle 15° to values close 0 for tilt angles of 50° and larger. A decrease in the average number of contacts with increasing tilt angle can also be observed for the Cα AB loop and the Cβ A strand, CC’ loop, and G strand (see Figure 3—figure supplement 1). Only for the Cα DE loop and Cβ EF loop, the average number of contacts is rather independent of the tilt angle. The tilt of the TCRαβ EC domain also affects the orientation of TM helices. The average inclination of the TCRα TM helix relative to the membrane normal decreases from about 11.5° to values around 8.5° with increasing tilt angle of the TCRαβ EC domain, while the average inclination of the CD3γ TM helix increases from about 15.5° to values around 24° (see Figure 3(e)). An increase from about 19° to values around 22° with increasing tilt angle of the TCRαβ EC domain also occurs for the average inclination angle of the TM helix of the ε chain of CD3εγ (see Figure 3—figure supplement 2). The average orientation of the other five TM helices relative to the membrane normal exhibits only small variations with the tilt angle of the TCRαβ EC domain.

The coupling of the tilt angle of the TCRαβ EC domain to overall conformational changes in the TCR – CD3 complex, which we observe in our MD simulations, provides insights on conformational changes induced by transversal, tilt-inducing forces. Transversal forces acting on the TCRαβ EC domain after binding to MHC-peptide-antigen complexes arise during the scanning of antigen-presenting cells by T cells (Göhring et al., 2020; Cai et al., 2017; Huse, 2017; Rushdi et al., 2020). While experiments indicate that the TCR – CD3 complex responds to mechanical force (Kim et al., 2009; Feng et al., 2017) and that the Cβ FG loop plays a key role in this response (Das et al., 2015), an outstanding question is how this force alters the conformation of the TCR – CD3 complex (Courtney et al., 2018). Our MD simulations show that an increased tilt of the TCRαβ EC domain leads to a marked decrease in the contacts between the Cβ FG loop and the CD3εγ EC domain (see Figure 3(d)), and also to changes in the inclination of TM helices relative to the membrane normal (see Figure 3(e)). Such structural changes in the TM domain of the TCR – CD3 have been suggested to be involved in the transmission of forces from the EC domain to the signaling motifs on the intracellular segments of the CD3 chains (Brazin et al., 2015; Brazin et al., 2018), which are not resolved in the cryo-EM structure. Similar to the Cβ FG loop, we also find a decrease of contacts between the Cα AB loop, which has been implicated in TCR triggering (Beddoe et al., 2009), and the ε chain of the CD3εγ EC domain with increasing tilt angle of the TCRαβ EC domain (see Figure 3—figure supplement 1).

Based on our simulation results for the orientational variations of the unbound TCR EC domain, the tilt of the bound TCR-MHC complex induced by a transversal force $f$ parallel to the membrane can be estimated under the assumption that the membrane anchoring of the MHC EC domain is more flexible than the membrane anchoring of the TCR EC domain within the TCR - CD3 complex. This assumption appears reasonable because MHC class I and MHC class II EC domains are anchored by one and two peptide linkers, respectively, to a pair of transmembrane helices, whereas the three EC domains of the TCR - CD3 complex are jointly anchored by six linkers to a bundle of eight transmembrane helices. The anchoring flexibility of MHC class I molecules is also illustrated by a presumably binding-incompetent, supine conformation observed in two-dimensional crystals in which the MHC EC domains are positioned with their 'sides’ on the membrane, rather than 'standing up' (Mitra et al., 2004). In the absence of transversal forces, the tilt-angle distribution of the TCR-MHC EC domain then can be approximated by the distribution of the TCR EC domain tilt angle observed in our simulations of the TCR – CD3 complex. From the energy contribution $-f\beta h\beta \sin [\tau ]$ associated with a transversal force $f$ on the TCR-MHC EC complex with extension $h\simeq 13$ nm (Wang et al., 2009) along the tilt axis and tilt angle $\tau$ in units of rad, the maximum of the tilt-angle distribution can be estimated to be shifted from 34° for zero force to 41° for a transversal force $f=2$ pN and to 49° for a transversal force $f=5$ pN acting on the EC domain of the TCR-MHC complex (see Figure 3—figure supplement 3(a) and Materials and methods). Such transversal forces on TCR-MHC complexes up to 5 pN are within the range measured with force sensors (Göhring et al., 2020).

An increased tilt of the TCR-MHC complex due to transversal forces also affects the membrane separation at the site of the complex and, thus, the size-based segregation of large surface molecules such as CD45 or of other receptor-ligand complexes from TCR-MHC complexes. In the kinetic segregation mechanism, a key step in T cell activation is the size-based segregation of the inhibitory tyrosine phosphatase CD45 from TCR-MHC complexes (Davis and van der Merwe, 2006; Choudhuri and van der Merwe, 2007; Chang et al., 2016). A change of the tilt angle of the EC domain of the TCR-MHC complex with length $h\simeq 13$ nm from 34° to 49° leads to a decrease of about 2.2 nm in the separation $h\beta \cos [\tau ]$ between the membrane surfaces and, thus, to an increased segregation of large surface molecules. Such force-induced decreases of the membrane separation at the site of TCR-MHC complexes may also be relevant for the the recently observed segregation of CD2-CD58 complexes from TCR-MHC complexes, which both have EC domain lengths of about 13 nm (Demetriou et al., 2019).

The orientations of the TCRαβ EC domain within the TCR – CD3 complex are affected by the low-affinity interactions with the CD3εγ and CD3εδ EC domains (He et al., 2015). Because of the inherent limitations of coarse-grained models to describe such low-affinity interactions (Javanainen et al., 2017), we chose state-of-the-art atomistic force fields for our simulations of the TCR – CD3 complex. Our 120 simulation trajectories with a length of 1 μs provide a cumulative sampling on timescales that exceed the length of the individual trajectories (Pande et al., 2003; Noé et al., 2009) and lead to equilibrated conformational and orientational distributions of the EC domains (see Figure 4). The rather large orientational variations of the TCRαβ EC domain observed in our simulations make it plausible that processes on longer timescales do not contribute significantly to the overall EC domain conformations. Our sampling of the TM domain, in contrast, may be limited to conformations close to the cryo-EM structure of the TM domain, which is embedded in the detergent digitonin in the experiments. Larger conformational rearrangements of the TM helices such as the bending of the TCRα TM helix at a helix hinge observed in NMR experiments (Brazin et al., 2018) may occur on longer timescales, and may also depend on the composition of the lipid membrane. The TCRα TM helix remains intact on the microsecond timescales of our simulations and does not break into two helix halves connected by a hinge. Overall, our simulation result for the TM domain illustrate that the tilt of the TCRαβ EC domain is associated with statistically significant changes in the orientation of TM helices. How these orientational changes are affected by the membrane composition, and whether they can be related to conformational changes in the largely disordered intracellular signaling domains requires further simulations, likely with atomistic resolution because of limitations in modeling secondary structure propensities and disordered protein segments with coarse-grained force fields (Monticelli et al., 2008; Robustelli et al., 2018). In recent modeling based on the cryo-EM structure of the TCR – CD3 complex, the intracellular signaling domains have been included in coarse-grained simulations of the entire complex with a cumulative simulation time of 25 μs (Prakaash et al., 2021), and the conformations of the TM domain in a complex, asymmetric membrane have been explored in atomistic simulations with a cumulative simulation time of about 4 μs (Lanz et al., 2021). Future atomistic simulations of the TCR – CD3 complex bound to the MHC-peptide EC domain may provide insights on the role of binding-induced conformational changes in TCR activation (Hwang et al., 2020; Ayres et al., 2016). The orientational distributions of the TCRαβ EC domain complex obtained from our simulations also provide a basis for the coarse-grained or multiscale modeling of the TCR-MHC complex anchored to apposing membranes (Steinkühler et al., 2019).

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The concerted conformational changes of the TCR – CD3 complex in our simulations are reflected in the correlations of contact clusters in the EC domain interactions. The largest positive correlations of clusters in the TCRαβ/CD3εδ contact map of Figure 2 occur between the contact clusters 1 to 4 (see Figure 2—figure supplement 1, top left), which correspond to interactions of the variable domain Vα of TCRα and the δ chain of CD3εδ. The large positive correlations of these four contact clusters can be understood from the coupling to the tilt of the TCRαβ EC domain, because the contacts of the Vα domain reported by the four contact clusters are only possible at high tilt angles of the TCRαβ EC domain (see Figure 3(d)). Relatively large positive correlations occur also between the clusters 13 to 21 of the TCRαβ/CD3εγ contact map (see Figure 2—figure supplement 1, bottom left). These clusters reflect interactions of the Cβ FG loop and G strand with the $\mathrm{ϵ}$ chain and the N-terminus of the γ chain of CD3εγ, which decrease with increasing tilt angle of the TCRαβ EC domain (see Figure 3(d) and Figure 3—figure supplement 1). Besides these positive correlations that result from the concerted conformational changes coupled to the tilt angle of the TCRαβ EC domain, the overall weak correlations between the majority of the other contact clusters in Figure 2 indicate independent motions of the loops and strands involved in these EC domain contacts. In addition, relatively strongly negative correlations of several pairs of contact clusters point to alternative EC domain contacts. For example, the overall rather negative correlations between the clusters 13 to 21 and the cluster 22 of the TCRαβ/CD3εγ contact map show that the interaction of the Cβ G strand and the γ AB loop reported by cluster 22 is not compatible with the interactions of the Cβ FG loop and G strand to the ε chain and the N-terminus of the γ chain of CD3εγ, which are reflected by the clusters 13 to 21.

Overall, our simulations reveal that the orientation of the TCR EC domain relative to the membrane is coupled to structural changes throughout the TCR – CD3 complex. Besides this concerted structural motion, the overall weak correlations of the majority of EC domain interactions indicate additional independent motions of the loops and strands that are involved in these interactions.

All 6000 molecular dynamics structures of the membrane-embedded TCR-CD3 complex used in the analysis have been deposited in the Edmond Open Research Data Repository under https://doi.org/10.17617/3.5m.

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Acceptance summary:

Your work shows, based on Molecular Dynamics simulations, the structural variability of the T cell receptor complex. Changes in the tilt angles of the extracellular antigen binding domains were observed to correlate with changes in the orientation of transmembrane helices, which may well impact signal transduction during antigen recognition. Your responses to the reviewers have improved the clarity of the approach and interpretations are well supported by experimental observations where available.

Decision letter after peer review:

Thank you for submitting your article "Structural variability and concerted motions of the T cell receptor – CD3 complex" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, including Michael L Dustin as the Reviewing Editor and Reviewer #1, and the evaluation has been overseen by Tadatsugu Taniguchi as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Brian Baker (Reviewer #2).

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

Essential revisions:

All the reviewers found the early results on MD simulations of full TCR to be of great interest and potential value. The paper currently doesn't provide sufficient insight for publication in eLife, but it was felt that additional discussion could address this in different directions that might be best selected by the authors. The reviewers didn't reach a consensus, but hope that with the individual reviews below the authors can revise the manuscript to increase the value for immunology and signalling audiences along one or two of the lines suggested.

1) There was some consensus regarding discussion of the limitations of the short simulations with implications for stability of the system and the ability to establish correlations. Is there potential to use the results from these simulations to develop coarser simulations over longer time that might get into the time frame of pMHC interaction and force application. A discussion of these future directions could be helpful in addition to pointing out current limitations.

2) A video showing the TCR fluctuations would be nice.

Reviewer #1:

It would be important to determine if this atomistic simulation lasting 1 µs could be used to seed a coarse grained simulation that could operate in time frames relevant to natural ligand binding and capture the major movements documented here, for example the 4 clusters, to enable MD simulations of sufficient duration to ask questions about TCR signalling in a realistic time frame.

Reviewer #2:

While the strengths of the paper are in the testable hypotheses that are generated, there are weaknesses that should be considered:

– The simulations give a window into thermal fluctuations around the 'average' cryoEM structure. The extent these rapid motions give insight into signaling mechanisms is limited. For example, there is no comparison of how the motions of a pMHC bound structure might differ, or how fluctuations might be altered under load.

– The authors do a limited analysis of equilibration, which is always needed in complex simulation papers to ensure the robustness of the data and conclusions.

– There is a limited analysis of structural variance or correlated motion. Overall, the authors give very limited attention to the high level of detail that MD simulations are capable of and arguably best known for.

Comments for the authors:

There are major weaknesses that should be considered:

1) The authors perform a total of 120 microseconds of simulation in explicit solvent, performed by compositing many shorter simulations. This is a considerable amount of simulation time. However, the authors are still looking at motions that would be comparable to experiments on the nanosecond timescale. It is highly unlikely that these simulations would capture what occurs upon binding or applied force, which would occur with higher barriers and over longer timescales. Instead, we are looking at thermal fluctuations around an equilibrium structure. While still providing testable hypotheses regarding how a TCR/CD3 might be 'poised' for signaling, the immediate insight into signaling mechanisms and thus impact is very limited. The authors need to consider this throughout their manuscript.

2) The authors do not do a complete analysis of equilibration, using domain angles and contacts as a window into equilibration. There are none of the analyses that are traditionally performed with long simulations to ensure equilibration of the structure (e.g., is domain assembly maintained, how is secondary or tertiary structure maintained, what about membrane stability, etc.).

3) Similar to the point above, the analysis is limited to contacts and angles. One might expect various higher frequency motions to be insightful – for example, what does the structure of the FG loop do over the course of the simulation? That about the β chain AB loop, which has been implicated in triggering? The overall analysis is very high level and lacking in the kind of rich detail that extensive MD simulations are capable of.

4) There are no direct connections to experiments here. Experimental data do not need to be included, but over the years there have been many mutation, perturbations, etc. performed that the authors could look at. Similarly, there are no pMHC bound or force experiments included that could give insight into actual signaling mechanisms as opposed to the ligand-free and force-free fluctuations that presumably occur as the molecule is waiting for something to happen.

5) Related to the point above, there is data suggesting dynamic allostery as a mechanism contributing to TCR triggering. Dynamic allostery requires correlated motion – none of that is considered here.

Reviewer #3:

Weikl and colleagues used the structure of the T cell receptor complex, which has recently been determined via cryo-electron microscopy, as basis for an atomistic modelling approach. This method offers the advantage to overcome a central limitation of cryo-EM, which is the choice of the membrane lipid environment: while experiments have been based on embedding the protein in detergent, Weikl et al. used here glycerophospholipids and cholesterol, which reflects the natural situation in the plasma membrane more appropriately. In addition, cryo-EM required the addition of fixatives, which is not necessary in the MD simulation approach.

The paper reveals interesting new dynamical information about the TCR complex. It would be informative, if the authors would include a discussion on the following points:

Figure 2: How is contact between residues defined? Would an isolated 10ns encounter already qualify as contact? What about analyzing the contact duration? What is distance between two sites to qualify as contact?

Figure 3a/b:

• It would be helpful to indicate rotation angle 0; maybe by adding an en face view onto the axis A?

• The tilting of the TM helices appears to be accompanied by slight local thinning of the membrane. Is that correct? Do lipids adjacent to the transmembrane helices follow the tilt, and/or is there different ordering of the fatty acids? Is the cholesterol distribution affected by the tilt? How would different lipids with different length or compressibility affect the helix tilting?

• What would generally happen if different lipids were tested, particularly asymmetric lipid distributions across the membrane? In the natural plasma membrane environment lipids are distributed asymmetrically across the leaflets, with saturated and unsaturated lipids of different chain length being enriched in the extracellular and cytoplasmic leaflet, respectively. It would be interesting, whether this compensates or probably even amplifies the observed mechanism. Maybe the authors could add a discussion on this aspect.

Figure 3 c and e: It would be informative to add the results of the cryo-EM study here.

Figure 3: For better comparison, it would be nice to scale the y-axes with identical increments.

If fluctuations of the TCR α/β would be similar in reality as it was revealed in the simulation, I would expect continuous fluctuations of helix tilt angles. If helix tilt angle was indeed a cause for signaling, wouldn't that lead to continuous aberrant activation of the TCR?

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

Thank you for submitting your article "Structural variability and concerted motions of the T cell receptor – CD3 complex" for consideration by eLife. Your article has been reviewed by 2 peer reviewers, including Michael L Dustin as the Reviewing Editor and Reviewer #1, and the evaluation has been overseen by Tadatsugu Taniguchi as the Senior Editor.

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

The paper is significantly improved by the inclusion of the videos and discussion of some biological implications.

1) Is it correct that the rotation angle 0 is defined by the origination in the published cry-EM structure? Regardless, this should be defined more clearly in the text and figure.

2) The authors should address the points raised by reviewer 3 regarding force induced tilt through clarification of the text and explanatory schematics if helpful. It may also be interesting in addressing the last comment to determine if the observation of supine orientation of MHC class I at a membrane surface is relevant to the discussion. see Mitra AK, Celia H, Ren G, Luz JG, Wilson IA, Teyton L. Supine orientation of a murine MHC class I molecule on the membrane bilayer. Curr Biol. 2004;14(8):718-24. Epub 2004/04/16. doi: 10.1016/j.cub.2004.04.004. PubMed PMID: 15084288. Is this natural orientation of MHC class I aligned with the tilt of the TCR when the interface is formed? Does the tilt angle of the TCR create a natural rudder to orient the TCR and would it matter which of the CD3 or zeta-zeta tails are pulled.

Reviewer #3:

In principle, all of my previous questions were adequately addressed. There was a misunderstanding concerning my previous comment on the specification of the rotational angle in Figure 3: My problem was to understand, which TCR conformation corresponds to a rotation angle 0. The authors may still consider to add this information.

Concerning the new data on force-induced tilt, however, I have a few questions:

– First, the authors mention on multiple locations in their paper a force-induced tilt of the TCR-MHC complex. The MHC, however, was not included in their simulations. I suggest being more precise in this aspect.

– Second, if I understand correctly, force was not included in the simulations, but instead the effect was added a posteriori. I had difficulties to understand the rationale behind it. What is the justification for the equation given in line 346? What was actually multiplied by the exponential function?

– Third, wouldn't one expect a directionality of the effect? In other words, if force acted, say, in the opposite direction to the naturally occurring tilt, is the idea that the TCR would align with the external force field?

– Fourth, I would be more careful with speculations concerning CD45 segregation. The authors argue in the discussion (line 175 and following) that TCR tilt brings the two membranes in closer juxtaposition. But that would only be true if MHC would also be sufficiently flexible to compensate for the TCR tilt, keeping the two membranes parallel.

Essential revisions:

All the reviewers found the early results on MD simulations of full TCR to be of great interest and potential value. The paper currently doesn't provide sufficient insight for publication in eLife, but it was felt that additional discussion could address this in different directions that might be best selected by the authors. The reviewers didn't reach a consensus, but hope that with the individual reviews below the authors can revise the manuscript to increase the value for immunology and signalling audiences along one or two of the lines suggested.

We first would like to thank all reviewers for their constructive and helpful comments and suggestions. To address these comments, we have added 3 new page-wide figures with subfigures and 3 videos and have substantially extended the text, in particular in the Discussions and Methods sections. To increase the value for immunology and signalling audiences:

– We have modelled the tilt of the TCR EC domain under a transversal force acting on the TCR – MHC complex, based on the force-free tilt-angle distribution TCR EC domain obtained from our simulations (see Figure 3 – supplement 3 (a)), and

– We discuss implications for size-based segregation that result from a decreased membrane separation due to a force-induced tilt of the TCR – MHC complex (see new paragraph starting on line 175 of the Discussions section).

1) There was some consensus regarding discussion of the limitations of the short simulations with implications for stability of the system and the ability to establish correlations. Is there potential to use the results from these simulations to develop coarser simulations over longer time that might get into the time frame of pMHC interaction and force application. A discussion of these future directions could be helpful in addition to pointing out current limitations.

We discuss simulation lengths, coarse-grained versus atomistic simulations, and future directions now in a new paragraph starting on line 187 in the Discussions section. In the last years, advances in computing on graphics processing units (GPUs) have made it possible to investigate protein association with atomistic models. We see it as a main contribution of our manuscript to make use of these advances in our atomistic simulations of the TCR – CD3 complex. As emphasized in the new paragraph of the Discussions section, we think that our simulations provide equilibrated conformational ensembles of the EC domain arrangements of the TCR – CD3 complex. We also use popular coarse-grained models such as the MARTINI model in simulations of other, larger systems in our group, but think that these coarse-grained models are not reliable for weak-affinity complexes or disordered segments because of inherent limitations regarding binding affinities and secondary structure propensities. In the MARTINI model, for example, secondary structure needs to be predefined and constrained, and also tertiary structure stability typically requires further artificial constraints. But we also mention that the orientational distributions of the TCR – CD3 complex obtained from our atomistic simulations can be used for multiscale modeling of TCR – MHC complexes anchored to apposing membranes, as in our recent multiscale modeling of CD47 – SIRPa complexes in Steinkühler et al., 2019. We also show now that the EC domains are stable in our simulations (see Figure 4 – supplement 1 and new text paragraph starting on line 327 of Methods section), which confirms that the main structural variations of the TCR – CD3 complex discussed in the Results section arise from the orientational variations of TCRab EC domain and the changes in the quaternary interactions between the EC domains associated with these orientational variations.

2) A video showing the TCR fluctuations would be nice.

We agree, and have added three videos of trajectory segments along which the tilt angle increases from around 20° to values above 50°, together with the new Figure 3 – supplement 4 showing the values of the tilt and rotation angle along these trajectory segments.

Reviewer #1:

It would be important to determine if this atomistic simulation lasting 1 µs could be used to seed a coarse grained simulation that could operate in time frames relevant to natural ligand binding and capture the major movements documented here, for example the 4 clusters, to enable MD simulations of sufficient duration to ask questions about TCR signalling in a realistic time frame.

Please see our response to the essential point (1) above. We think that we have “solved the sampling problem” in our atomistic simulations, at least for the EC domain arrangements of the TCR – CD3 complex. In other words, we think that our results for the orientation and quaternary interactions of the TCR EC domain within the TCR – CD3 complex are not limited by the (cumulative) simulation times. And we think that the accuracy of atomistic models is necessary here, because only state-of-the-art atomistic models are sufficiently reliable in reproducing stable, folded tertiary structures of proteins and quaternary interactions of proteins. Overall, we think that a main remaining challenge for TCR signalling is to include the largely disordered intracellular signaling domains in atomistic simulations. These signaling domains are not included in the cryo-EM structure, and therefore beyond the scope of this manuscript.

Reviewer #2:

[…] There are major weaknesses that should be considered:

1) The authors perform a total of 120 microseconds of simulation in explicit solvent, performed by compositing many shorter simulations. This is a considerable amount of simulation time. However, the authors are still looking at motions that would be comparable to experiments on the nanosecond timescale. It is highly unlikely that these simulations would capture what occurs upon binding or applied force, which would occur with higher barriers and over longer timescales. Instead, we are looking at thermal fluctuations around an equilibrium structure. While still providing testable hypotheses regarding how a TCR/CD3 might be 'poised' for signaling, the immediate insight into signaling mechanisms and thus impact is very limited. The authors need to consider this throughout their manuscript.

We argue now in the new paragraph starting on line 187 of the Discussions section that our 120 trajectories provide a cumulative sampling on timescales that exceed the length of the individual trajectories (see new references Pandey et al., 2003 and Noe et al. 2009). We further argue that this cumulative sampling on microsecond timescale leads to equilibrated conformational and orientational distributions of the EC domains, as shown in Figure 4. We comment that the rather large orientational variations of the TCRab EC domain EC domain observed in our simulations make it plausible that processes on longer timescales do not contribute significantly to the overall EC domain conformations. Based on the equilibrated tilt-angle distribution determined from our simulations, we now estimated how transversal forces of 2 or 5 pN, which are in the range of experimentally determined transversal forces on TCR – MHC complexes, shift the tilt-angle distributions (see new Figure 3 – supplement 3, and Discussions and Methods section). We now discuss also the implications of force-induced tilt for length-based segregation, which is a key element of the kinetic segregation mechanism of T cell activation (see new paragraph starting on line 175 of the Discussion section).

2) The authors do not do a complete analysis of equilibration, using domain angles and contacts as a window into equilibration. There are none of the analyses that are traditionally performed with long simulations to ensure equilibration of the structure (e.g., is domain assembly maintained, how is secondary or tertiary structure maintained, what about membrane stability, etc.).

We have added a stability analysis of the EC domains and the TM domain in Figure 4 supplement 1. The analysis shows stability on the level of tertiary structures, i.e. stability of EC domains, and that the dominant variations analysed in the main Figures 2 and 3 are variations in the quaternary structure and orientation of the TCR – CD3 complex.

3) Similar to the point above, the analysis is limited to contacts and angles. One might expect various higher frequency motions to be insightful – for example, what does the structure of the FG loop do over the course of the simulation? That about the β chain AB loop, which has been implicated in triggering? The overall analysis is very high level and lacking in the kind of rich detail that extensive MD simulations are capable of.

The contact probabilities in our main Figure 2 provide a highly detailed, but still “human readable” representation of the quaternary interactions between the CD3 domains in our equilibrated simulations. We emphasize in the manuscript that the Cb FG loop loses quaternary contacts with increasing tilt angle of the TCR EC domain. We thank the referee for pointing out the role of the Ca AB loop in triggering (assuming that this is the loop the referee refers to). We find that the Ca AB loop also clearly loses quaternary contacts with increasing tilt angle of the TCR ECab domain (see Figure 3 – supplement 1), similar to the Cb FG loop, and address this now on lines 164 to 167 in the first pagraph of the Discussions section. Based on our simulations, changes in the Ca AB loop structure thus can be expected if TCR binding and activation is associated with an increased tilt of the TCRab EC domain, because changes in quaternary contacts of a loop also affect loop structure. Because of complexity, a detailed comparison to the fluorescence-based and mutational experiments regarding the Ca AB loop in Beddoe et al., 2009, is beyond the scope of our manuscript. We agree with the referee that there may well be further details in our simulations regarding e.g. loop structure that deserve attention in other contexts. Also for this reason, we have published all 6000 simulation structures on which our analysis is based (see Pandey and Weikl, 2021) for further analysis by others.

4) There are no direct connections to experiments here. Experimental data do not need to be included, but over the years there have been many mutation, perturbations, etc. performed that the authors could look at. Similarly, there are no pMHC bound or force experiments included that could give insight into actual signaling mechanisms as opposed to the ligand-free and force-free fluctuations that presumably occur as the molecule is waiting for something to happen.

We agree with the referee that experimental data from, e.g. mutational experiments provided indirect insights on the structure of the TCR – CD3 complex. We refer to essential data of mutational and other experiments in the first paragraph of the Introduction from lines 35 on. With the publication of the cryo-EM structure of the TCR – CD3 complex as a breakthrough in 2019, this cryo-EM structure has of course become the main reference regarding the structure of the complex. We therefore focus in our analysis on a detailed comparison to the cryo-EM structure (see Figures 1 and 2). We see the main point of our manuscript in an atomistically detailed, extensive computational analysis that goes beyond unavoidable limitations of the cryo-EM structure due to the embedding in the detergent digitonin and the chemical crosslinking of the protein chains.

5) Related to the point above, there is data suggesting dynamic allostery as a mechanism contributing to TCR triggering. Dynamic allostery requires correlated motion – none of that is considered here.

We now refer to binding-induced conformational changes such as dynamic allostery as an outlook on lines 213 to 216 of the Discussion section. Correlations of quaternary interactions in our simulation of the unbound TCR – CD3 complex are analysed in detail in Figure 1 – supplement 1.

Reviewer #3:

[…] The paper reveals interesting new dynamical information about the TCR complex. It would be informative, if the authors would include a discussion on the following points:

Figure 2: How is contact between residues defined? Would an isolated 10ns encounter already qualify as contact? What about analyzing the contact duration? What is distance between two sites to qualify as contact?

We define contacts based on distances between non-hydrogen atoms in the cryoEM structure and simulation conformations, and state the contact definition now also in the main text of the Results section:

“As in the contact maps for the cryo-EM structure shown in Figure 1, two residues are taken to be in contact in a simulation structure if the minimum distance between non-hydrogen atoms of the residues is smaller than 0.45 nm.” (lines 83 to 86).

This standard, “instantaneous” definition of contacts is both applicable to the cryo-EM structure and our simulation confirmations. An isolated 10 ns encounter can lead to contacts according to this definition. But in Figure 2 and throughout our analysis, we only include contacts that occur on at least 0.5% of the 6000 simulation conformations on which our analysis is based – i.e. we only include contacts that occur on at least 30 simulation confirmations, irrespective of contact duration, and on how many trajectories the contact occur. We give as example:

“Residue-residue contacts between Va and the d chain of CD3ed have probabilities smaller than 3%, but occur in 75 of the 120 trajectories and are, thus, a robust feature of our simulations.” (lines 100 to 102).

In general, also stable contacts typically “flicker” on MD trajectories due to structural fluctuations, which complicates temporal analyses of contact durations.

Figure 3a/b:

• It would be helpful to indicate rotation angle 0; maybe by adding an en face view onto the axis A?

The rotation angle 0 is a lower limit of rotation angles occurring in our simulation conformations. But we think that our 3 new videos, together with the new Figure 3 – supplement 4, in which the tilt and rotation angles along the videos are shown, address the point of the referee to better illustrate the rotational motion. For example, the videos 1 and 2 show that an increase of the rotation angle with the tilt angle brings the Va loops in contact with CD3ed. Such an increase of the rotation angle with increasing tilt is “typical” because of the correlation of the angles illustrated in Figure 3(c). Video 3 shows an “atypical” situation in which the rotation angle does not increase with the tilt angle.

• The tilting of the TM helices appears to be accompanied by slight local thinning of the membrane. Is that correct? Do lipids adjacent to the transmembrane helices follow the tilt, and/or is there different ordering of the fatty acids? Is the cholesterol distribution affected by the tilt? How would different lipids with different length or compressibility affect the helix tilting?

This is an interesting question that we address in the new Figure 3 – supplement 3 (b). The answer is: Within the statistical accuracy, there is no change in the thickness of the membrane annulus around the TM domain with increasing tilt angle. A definition of this membrane annulus as lipids in contact with protein chains is given on lines 350 to 357 of the Methods section. We also don’t see any changes in the composition (POPC versus cholesterol) in this membrane annulus with changing tilt (data not shown).

• What would generally happen if different lipids were tested, particularly asymmetric lipid distributions across the membrane? In the natural plasma membrane environment lipids are distributed asymmetrically across the leaflets, with saturated and unsaturated lipids of different chain length being enriched in the extracellular and cytoplasmic leaflet, respectively. It would be interesting, whether this compensates or probably even amplifies the observed mechanism. Maybe the authors could add a discussion on this aspect.

We agree that the composition of the membrane is of relevance for changes in the TM domain. We have added now on lines 202 and following in the Discussions section:

“Overall, our simulation result for the TM domain illustrate that the tilt of the TCRab EC domain is associated with statistically significant changes in the orientation of TM helices. How these orientational changes are affected by the membrane composition, and whether they can be related to conformational changes in the largely disordered intracellular signaling domains requires further simulations, likely with atomistic resolution because of limitations in modelling secondary structure propensities and disordered protein segments with coarse-grained force fields.”

Figure 3 c and e: It would be informative to add the results of the cryo-EM study here.

This is an interesting but also tricky point. Because the cryo-EM structure does not contain a lipid membrane, the orientation of this structure in a membrane is unclear. In addition, it is unclear how the chemical crosslinking in the structural experiments affects the orientation of the EC domains relative to the TM domain. We have used structural alignment (superposition) to the TM domain of our simulation structures to embed and orient the cryo-EM structure in a membrane. From alignment to a large number of simulation structures, we obtain the estimates 31.2 ± 0.4° for the tilt angle and 14.7± 0.7° for the rotation angle of the cryo-EM structure. This is described now on lines 122 and following of the Results section. Strictly speaking, these are not “pure” experimental results, because they are based on structural alignments to our simulation structures. We therefore prefer to state these results in the text with explanations. We think that inclination helices of tilt angles in the cryo-EM structure are somewhat dubious even in our structural alignments, because of the missing membrane in the structural experiments. We therefore focus on the tilt and rotation angle.

Figure 3: For better comparison, it would be nice to scale the y-axes with identical increments.

We chose different sections and increments along the y-axes because the changes in contact numbers and inclination angles occur in different ranges. In other words, we think that the chosen y-axes sections are required for a clear representation of the data.

If fluctuations of the TCR α/β would be similar in reality as it was revealed in the simulation, I would expect continuous fluctuations of helix tilt angles. If helix tilt angle was indeed a cause for signaling, wouldn't that lead to continuous aberrant activation of the TCR?

We understand the question, and think that answering this question requires further simulations, as stated now on lines 204 and following of the Discussions section, because the intracellular signaling domains are not included in the cryo-EM structure and in our simulations, which are based on this structure.

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

The paper is significantly improved by the inclusion of the videos and discussion of some biological implications.

1) Is it correct that the rotation angle 0 is defined by the origination in the published cry-EM structure? Regardless, this should be defined more clearly in the text and figure.

To clarify this point, we have added on lines 114 and 115:

“A rotation angle of 0° indicates a TCRαβ EC domain orientation in which the centres of mass of the variable domains Vα and Vβ are equally close to the membrane”.

This statement follows from the definition of the rotation angle given on lines 110 and 111. The definition is based on the membrane normal and the two axes A and B of the TCRαβ EC domain defined on lines 106 to 109 and illustrated in Figure 3(b). At a rotation angle of 0°, the axis B that connects the centres of mass of the variable domains Vα and Vβ is parallel to the membrane.

The tilt and rotation angle of the TCRαβ EC domain in the cryo-EM structure cannot be determined directly, because of the missing membrane embedding. Without membrane embedding, the membrane normal is unclear. On lines 126 to 132 added in the previous, first revision, we describe how we estimate the tilt and rotation angle of the TCRαβ EC domain in the cryo-EM structure based on an alignment of the TM domain of this structure to our simulation conformations. This alignment orients the cryo-EM structure relative to our simulated membranes, and allows to calculate the orientation angles. We obtain a rotation angle of 14.7 ± 0.7° for the cryo-EM structure from this calculation. We have added now also on lines 115 to 117 that such positive rotation angles indicate “conformations in which the variable domain Vα is closer to the membrane than the variable domain Vβ“, see also Figure 3(a) and (b) – the conformations shown in this Figure have rotation angles of 12.8° and 42.9°.

2) The authors should address the points raised by reviewer 3 regarding force induced tilt through clarification of the text and explanatory schematics if helpful.

We have substantially extended the text both in the Discussions and Methods section, see lines 172 to 189 and lines 360 to 375. We now state also in the Discussions section that our estimation of the force-induced tilt assumes “that the membrane anchoring of the MHC EC domain is more flexible than the membrane anchoring of the TCR EC domain”. The calculation is described in detail on lines 360 to 375 of the Methods section.

In essence, the calculation makes use of the standard statistical-physical Boltzmann factor to relate tilt-angle distributions to effective free energies for the tilt. We now also state on lines 371 to 372:

“We assume that the TCR-MHC complex rotates and aligns its tilt direction to the direction of the force.“

It may also be interesting in addressing the last comment to determine if the observation of supine orientation of MHC class I at a membrane surface is relevant to the discussion. see Mitra AK, Celia H, Ren G, Luz JG, Wilson IA, Teyton L. Supine orientation of a murine MHC class I molecule on the membrane bilayer. Curr Biol. 2004;14(8):718-24. Epub 2004/04/16. doi: 10.1016/j.cub.2004.04.004. PubMed PMID: 15084288. Is this natural orientation of MHC class I aligned with the tilt of the TCR when the interface is formed?

Strictly speaking, addressing this question requires to model the TCR-MHC complex, which is beyond the scope of our manuscript. However, Mitra et al. state that the supine orientation of the MHC class places “the peptide binding groove approximately perpendicular to the membrane surface.” We therefore find it plausible to say to that this conformation is “presumably binding-incompetent”, as we state now on line 180. The supine conformation may be stabilized by the two-dimensional crystal of the experiments. We think that the supine conformation can be seen to indicate high anchoring flexibility. We now state on lines 179 to 182:

“The anchoring flexibility of MHC class I molecules is also illustrated by a presumably binding-incompetent, supine conformation observed in two-dimensional crystals in which the MHC EC domains are positioned with their "sides" on the membrane, rather than "standing up" (Mitra et al., 2004).”

Does the tilt angle of the TCR create a natural rudder to orient the TCR and would it matter which of the CD3 or zeta-zeta tails are pulled.

This is an interesting question, which leads to the follow-up question: What controls the rudder? We tend to think that there is no “hand on the rudder”. So, without force, there are just (thermal) fluctuations of the orientation and tilt of the TCR EC domain. And with force on the bound TCR-CD3 complex, the rudder follows the drag – this is also implied by our assumption that the tilt direction aligns with the force direction, which is now stated on lines 371/72.

We also tend to think that it should not matter which intracellular CD3 segments are coupled to the T cell cytoskeleton. We think that a transversal, membrane-parallel force on any of these segments should lead to a dragging of the TM domain of 8 helices along the membrane – and a dragging and transport of the whole complex. This view is largely influenced by the experiments of DeMond et al., 2008 and Mossman et al., 2005, which indicate a “frictional coupling” between T cell cytoskeleton and TCR – CD3 complex, as included now on lines 369 to 371.

Reviewer #3:

In principle, all of my previous questions were adequately addressed. There was a misunderstanding concerning my previous comment on the specification of the rotational angle in Figure 3: My problem was to understand, which TCR conformation corresponds to a rotation angle 0. The authors may still consider to add this information.

We indeed misunderstood this point. As indicated already above in our response to the suggestions of the reviewing editor, we have added on lines 114 and 115:

“A rotation angle of 0° indicates a TCRαβ EC domain orientation in which the centres of mass of the variable domains Vα and Vβ are equally close to the membrane”.

This statement follows from the definition of the rotation angle given on lines 110 and 111. The definition is based on the membrane normal and the two axes A and B of the TCRαβ EC domain defined on lines 106 to 109 and illustrated in Figure 3(b). At a rotation angle of 0°, the axis B that connects the centres of mass of the variable domains Vα and Vβ is parallel to the membrane.

Concerning the new data on force-induced tilt, however, I have a few questions:

– First, the authors mention on multiple locations in their paper a force-induced tilt of the TCR-MHC complex. The MHC, however, was not included in their simulations. I suggest being more precise in this aspect.

We have extended and clarified the description of our modelling of force-induced tilt, both in the Discussions section (lines 172 to 189) and the Methods section (lines 360 to 375). In the first sentence on lines 172 to 175 that mentions this modelling, we state that the modelling is “based on our simulation results for the orientational variations of the unbound TCR EC domain”.

– Second, if I understand correctly, force was not included in the simulations, but instead the effect was added a posteriori. I had difficulties to understand the rationale behind it. What is the justification for the equation given in line 346? What was actually multiplied by the exponential function?

This is correct. We now provide a detailed description of the calculation on lines 360 to 375 of the Methods section. We agree that this description was too short in the previous version of the manuscript. The two main and now clearly stated assumptions of our calculations are (1) that the MHC complex is more flexibly anchored than the TCR EC domain, and (2) that the tilt direction of the TCR-MHC complex aligns with the direction of the transversal, membrane-parallel force. Our calculation then is largely based on the standard exponential Boltzmann factor to relate probability distributions to energies.

– Third, wouldn't one expect a directionality of the effect? In other words, if force acted, say, in the opposite direction to the naturally occurring tilt, is the idea that the TCR would align with the external force field?

Yes, this is correct. We now state on lines 371/72:

“We assume that the TCR-MHC complex rotates and aligns its tilt direction to the direction of the force.”

We think that this assumption is plausible also because of the experiments of DeMond et al., 2008 and Mossman et al. 2005 mentioned now on lines 369 to 371, which indicate a frictional coupling that “allows slip” (DeMond et al. 2008). In other words, we think that these experiments indicate that the coupling between T cell cytoskeleton and TCR – CD3 complex does not block or preclude a rotation of the TCR – CD3 complex. A rotation leading to alignment then is a consequence of the exerted force.

– Fourth, I would be more careful with speculations concerning CD45 segregation. The authors argue in the discussion (line 175 and following) that TCR tilt brings the two membranes in closer juxtaposition. But that would only be true if MHC would also be sufficiently flexible to compensate for the TCR tilt, keeping the two membranes parallel.

We agree – the assumption that the MHC complex is more flexibly anchored than the TCR EC domain withing the TCR – CD3 complex is a central assumption of our calculation and now clearly stated and discussed both in the Results and Methods section.

Author details

1. Prithvi R Pandey

   Max Planck Institute of Colloids and Interfaces, Department of Theory and Bio-Systems, Potsdam, Germany

   Contribution

   Software, Formal analysis, Validation, Investigation, Methodology, Writing - original draft

   Competing interests

   No competing interests declared

2. Bartosz Różycki

   Institute of Physics, Polish Academy of Sciences, Warsaw, Poland

   Contribution

   Formal analysis, Methodology

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-5938-7308

3. Reinhard Lipowsky

   Max Planck Institute of Colloids and Interfaces, Department of Theory and Bio-Systems, Potsdam, Germany

   Contribution

   Conceptualization, Supervision, Funding acquisition

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8417-8567

4. Thomas R Weikl

   Max Planck Institute of Colloids and Interfaces, Department of Theory and Bio-Systems, Potsdam, Germany

   Contribution

   Conceptualization, Formal analysis, Supervision, Investigation, Visualization, Methodology, Writing - original draft

   For correspondence

   thomas.weikl@mpikg.mpg.de

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-0911-5328

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