Dynamic metastable long-living droplets formed by sticker-spacer proteins
- Department of Chemistry and Chemical Biology, Harvard University, United States
Figures
Figure 1
Model.
Schematic of the polymer model for studying phase-separation by multivalent biopolymers.
Figure 2 with 1 supplement
Cluster Sizes in Langevin Dynamics simulations.
(A) Black Curve – The single largest cluster as a function of free monomer concentration (in μM) for irreversible functional interactions. The largest cluster size is shown as a fraction of the …
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Figure 2—source data 1
Compressed zip file containing the source data for cluster sizes and cluster size distributions (along with raw unprocessed data) plotted in Figure 2.
- https://cdn.elifesciences.org/articles/56159/elife-56159-fig2-data1-v2.zip
Figure 2—figure supplement 1
Cluster Sizes in Langevin Dynamics simulations.
(A) The single largest cluster as a function of free monomer concentration (in μM). The largest cluster size is shown as a fraction of the total number of monomers in the simulation box. The smooth …
Figure 3 with 1 supplement
Tracking cluster formation at early timescales.
A and B show the temporal evolution of specific contacts for a free monomer concentration of 10, and 50 μM, respectively. For a low concentration of 10 μM, there is an initial decrease in the …
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Figure 3—source data 1
Compressed zip file containing the source data for temporal evolution of different species (dimer,trimer,monomer etc) for different concentrations plotted in Figure 3.
- https://cdn.elifesciences.org/articles/56159/elife-56159-fig3-data1-v2.zip
Figure 3—figure supplement 1
The size of the largest cluster, for different values of bond formation probability, .
A lower results in a slower arrest of the clusters, and thereby results in increased cluster sizes for smaller free monomer concentration, .
Figure 4
Factors influencing the key timescales.
(A) The mean first passage time for the first specific interaction between a pair of polymer chains as a function of the bulk density, , (see Table 1 for definition). (B) The mean first passage …
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Figure 4—source data 1
Compressed zip file containing the source data for Figure 4.
- https://cdn.elifesciences.org/articles/56159/elife-56159-fig4-data1-v2.zip
Figure 5 with 3 supplements
Linkers as modulators of self-assembly propensity.
(A) The size of the largest cluster for flexible linker regions(=2 kcal/mol) with varying inter-linker interaction strength (black curve, 0.1 kcal/mol and purple curve, 0.5 kcal/mol). Sticky …
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Figure 5—source data 1
Compressed zip file containing the source data for largest cluster size, density of the cluster and radius of gyration of constituent chains, for different values of plotted in Figure 5.
- https://cdn.elifesciences.org/articles/56159/elife-56159-fig5-data1-v2.zip
Figure 5—figure supplement 1
Fraction of valencies utilized as a function of increasing inter-linker interaction strength, for (A) 10 μM and (B) 50 μM free monomer concentration.
Figure 5—figure supplement 2
The probability of finding clusters with varying densities (normalized by the bulk densities) for different values of inter-linker interactions.
As the inter-linker interactions increase, the degree of enrichment can go from 10-fold to 100-fold.
Figure 5—figure supplement 3
Comparision between the size distributions of the largest cluster, for flexible (=2 kcal/mol) versus stiff (=5 kcal/mol) linker regions.
The free monomer concentration used for this plot was 50 μM and a weak interlinker interaction strength of = 0.1 kcal/mol was used.
Figure 6
A schematic figure detailing the different rates in our phenomenological kinetic model simulated using the Gillespie algorithm.
The particles on the lattice can diffuse freely (when there are no neighboring particles) with a rate . In the presence of a neighboring particle, a non-specifically interacting monomer can …
Figure 7 with 6 supplements
Kinetic Monte Carlo Simulations.
(A) Phase diagram highlighting the different phases (metastable microphase (μ1) or system-spanning macrophase (μ2), and the non-phase separated state (No PS) ) encountered upon increasing (between …
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Figure 7—source data 1
Compressed zip file containing the source data for kinetic phase diagrams in Figure 7.
- https://cdn.elifesciences.org/articles/56159/elife-56159-fig7-data1-v2.zip
Figure 7—figure supplement 1
Detailed phase diagrams for (A) and (B) -, (C) - as the phase parameters.
The cluster sizes were computed at the end of a simulation run of 2 hr (actual time), setting the rate of diffusion to 1 . (D) The bonding rate was varied to identify the relationship …
Figure 7—figure supplement 2
Intra-cluster densities of largest cluster (solid curves) and the corresponding sizes of the single largest cluster (dashed curves) as a function of bulk density, for three different values of .
In the regime where cluster sizes approach the total number of monomers, the density of the cluster is at its lowest.
Figure 7—figure supplement 3
Cluster size distributions for varying densities for λ=3 (A), and λ=5 (B).
(C) Effect of valency on size distributions at a fixed of 0.09. These distributions were computed at the end of 100-independent simulation runs of 2 hr (actual time) each. μ1 and μ2, in these …
Figure 7—figure supplement 4
Inter-protein interaction strengths.
(A) The mean pair-wise interaction energy for 100 different dimeric structures (from the LD simulations), for an inter-linker interaction strength of 0.1 kcal/mol, for different values of linker …
Figure 7—figure supplement 5
Convergence of phase diagrams.
(A and B) The fraction of monomers in the largest cluster for 2 and 10 hr of actual time, for of 3 and 5, respecively. (C and D). The - phase diagram at the end of 2 and 10 hr of simulation …
Figure 7—figure supplement 6
Detailed phase diagrams for (A) and (B) - as the phase parameters.
The was set to 0.04, an intermediate density identified from the previous phase diagrams with density as a phase parameter. The cluster sizes were computed at the end of a simulation run of 2 hr …
Figure 8 with 1 supplement
Effect of model parameters on the exchange times between monomers and the aggregates.
The parameter values used in panels A and B are =0.04, / = 1. (A) Mean first passage time for the monomers to go from the buried state (with four neighbors) to the free state (with no …
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Figure 8—source data 1
Compressed zip file containing the source data for kinetic phase diagrams in Figure 8.
- https://cdn.elifesciences.org/articles/56159/elife-56159-fig8-data1-v2.zip
Figure 8—figure supplement 1
<> for varying values of and , for a of 0.04, and a ratio of 1.
(B) Mean first passage times for a particle to exchange between a cluster and the bulk. The parameter values are same as in panel A.
Figure 9 with 1 supplement
Effect of solvent viscosity.
Langevin Dynamics Simulations. (A and B) Cluster size distributions from Langevin dynamics simulations for different values of solvent viscosity and different free monomer concentrations. The shaded …
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Figure 9—source data 1
Compressed zip file containing the source data for mean largest cluster sizes (and size distributions) from LD and MC simulations studying the effect of solvent viscosity.
- https://cdn.elifesciences.org/articles/56159/elife-56159-fig9-data1-v2.zip
Figure 9—figure supplement 1
as a function of free monomer concentrations in LD simulations performed with various solvent viscosities.
Figure 10
Graphical Summary.
Muli-valent proteins can exist in two Flory-like equilibrium states, the fully mixed solvated state and a single large macro-phase separated state (when free monomer concentration () exceeds the …
Tables
Table 1
Important simulation variables and order parameters.
| Notation/Terminology | Physical Interpretation | Definition |
|---|---|---|
| Ntot | Total number of polymer chains in the system. Ntot = 400 in our simulations. | – |
| Lclus | Size of the single largest cluster | represented as fraction of Ntot |
| Sclus | Size of the cluster | represented as fraction of Ntot |
| Cmono | Concentration of polymer chains in the simulation box | In units of μM |
| φ | Bulk density of proteins (in their monomeric state) when the individual chains are randomly placed in the simulation box at the start of the simulation. | is the the radius of gyration of proteins when they are randomly positioned in simulation box at the start of the simulation. |
| φclus | Intra-cluster density of polymer chains. | is the radius of gyration of the system of proteins within the cluster. |
| φclus /φ | Normalized intracluster density describing the degree of enrichment of polymer chains within the cluster. | For system-spanning networks, φclus /φ→1. For dense clusters, φclus /φ >> 1. |
| εns | Interaction strength for isotropic, non-specific interactions between linker regions. εns in LD simulations is a pairwise interaction strength between individual beads In kMC simulations, εns is the net non-specific interaction strength between two lattice particles. | – . |
| εsp | Strength of attractive interaction between functional domains (specific interactions). | – |
| φlattice | Bulk density of monomers in the 2D-lattice in kMC simulations. This quantity is analogous to the concentration of monomers on the lattice. | φlattice = Ntot/L2, where L is the size of the 2D square-lattice. |
| λ | Valency of the polymer chain, that is the number of adhesive functional domains per interacting polymer chain. | – |
| Κ | Bending stiffness of the linker regions in LD simulations. A higher value of K is used to model stiffer linkers that prefer a more open configuration. | Κ = 2 kcal/mol, in LD simulations with flexible linkers. |
| η | The viscosity of the medium in LD simulations | η = 10−3Pa.s in LD simulations, unless mentioned otherwise. |
| kdiff | Diffusion rate of free monomers in the 2D-lattice kMC simulations. | – |
| kbond | Rate of formation of specific interactions between neighboring particles in 2D-lattice kMC simulations. | – |
Additional files
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Source code 1
Langevin Dynamics Simulation LAMMPS Script.
Langevin dynamics simulation script.
- https://cdn.elifesciences.org/articles/56159/elife-56159-code1-v2.zip
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Transparent reporting form
- https://cdn.elifesciences.org/articles/56159/elife-56159-transrepform-v2.docx
