The stoichiometric interaction model for mesoscopic MD simulations of liquid-liquid phase separation

Abstract

Liquid-liquid phase separation (LLPS) has received considerable attention in recent years for explaining the formation of cellular biomolecular condensates. The fluidity and the complexity of their components make molecular simulation approaches indispensable for gaining structural insights. Domain-resolution mesoscopic model simulations have been explored for cases in which condensates are formed by multivalent proteins with tandem domains. One problem with this approach is that interdomain pairwise interactions cannot regulate the valency of the binding domains. To overcome this problem, we propose a new potential, the stoichiometric interaction (SI) potential. First, we verified that the SI potential maintained the valency of the interacting domains for the test systems. We then examined a well-studied LLPS model system containing tandem repeats of SH3 domains and proline-rich motifs. We found that the SI potential alone cannot reproduce the phase diagram of LLPS quantitatively. We had to combine the SI and a pairwise interaction; the former and the latter represent the specific and nonspecific interactions, respectively. Biomolecular condensates with the mixed SI and pairwise interaction exhibited fluidity, whereas those with the pairwise interaction alone showed no detectable diffusion. We also compared the phase diagrams of the systems containing different numbers of tandem domains with those obtained from the experiments and found quantitative agreement in all but one case.

Figure 1

Pairwise interaction cannot reproduce appropriate dilute phase concentration. (A) A schematic representation of the SH3₄-PRM₄ system. SH3 domain and PRM motif are connected in tandem by flexible linkers. (B) The relation between ε_attr and the contact probability in 712 μM condition of SH3 and PRM. The 50% contact probability corresponds to the case K_D = 356 μM. (C) The snapshots of the SH3₄-PRM₄ system simulation with pairwise attractive interaction in the DC protocol. Blue particles represent SH3 domains, and gray particles represent PRM domains. To see this figure in color, go online.

Figure 2

Stoichiometric interactions can repress overstabilization. (A) Schematic view of the pairwise attractive interaction and the one-to-one stoichiometric interaction. Top panel: with one SH3 and two PRMs in contact, the pairwise interactions are doubled, but the number of actual one-to-one contacts is one. Bottom panel: with three SH3s and two PRMs, there are six pairwise attractive interactions, whereas actual one-to-one contacts are only two. (B) Distributions of the number of contacts per one SH3 (or PRM) in the stoichiometry assay for the SI model (left), the pairwise interaction (center), and with no attractive interaction (right). The error bar shows standard deviation. (C) Distribution of the number of contacts per A or B molecules in the case of non-1:1 valency. In this assay, the attractive interaction is only the SI model. The error bar shows standard deviation. To see this figure in color, go online.

Figure 3

The system with both stoichiometric and pairwise interaction can reproduce appropriate dilute phase concentration of SH3₄-PRM₄ mixed system. (A) The strength of pairwise attractive interaction versus critical concentration. SI interaction strength corresponds to K_D = 356 μM. Error bar shows standard deviation. The ε_attr = 0.5 kcal/mol matches the experiment. (B) The snapshot of a part of the dilute phase molecules. One of the SH3₄ molecules and PRM₄ molecules around that SH3₄ are visualized. (C) The snapshot of a part of the condensed phase molecules. One of the SH3₄ molecules and PRM₄ molecules around that SH3₄ are visualized. PRM₄ molecules in different colors have different nearest domains of SH3₄ molecules. (D) The snapshot of three types of systems. In the top system, only pairwise interactions are included. The middle system shows inclusion of both pairwise interactions and SI (Video S1). Bottom system depicts a system with only SI. Blue spheres represent SH3 domains, and gray spheres represent the PRM motives. The linker between each domain and motif is not displayed for visibility. To see this figure in color, go online.

Figure 4

The system with both stoichiometric and pairwise interactions can reproduce phase diagram of SH3₄-PRM₄ mixed system. (A) The phase diagram for the phase separation of the SH3₄-PRM₄ system using experiments and simulations. Diamonds are critical concentrations in the simulation. The color of the diamonds indicates the ratio of SH3 and PRM domains. Circles show the result obtained from previously reported experiments (41). Orange indicates phase separation, while green indicates the no phase separation. (B) Tie lines (dashed lines) of simulated SH3₄-PRM₄ systems. The dilute phase concentrations, same as those in diamond points in (A), are all aggregated to the bottom left points near the origin. Circles represent the condensed phase concentrations. (C) Snapshots of the cases with the ratios of SH3 domains being 40% (top), 50% (center), and 60% (bottom). Blue particles indicate SH3 domains, and gray particles indicate PRM motives. The linker between domains is not shown for visibility. To see this figure in color, go online.

Figure 5

The system with both stoichiometric and pairwise interactions shows the liquid activity of condensed phase. (A) The MSD curves of SH3 molecule with respect to the MD step. The asymptotic regions of the curves were fitted via the linear regression. Orange and blue indicate the dilute and condensed phases with the balanced SI and pairwise interactions, respectively. Green indicates the condensed phase with only pairwise interactions. The error bar shows standard error. (B) The diffusion coefficient of SH3 molecule along the strength of the pairwise attractive interaction. The snapshots in the graph are of corresponding fluorescence recovery after photobleaching-like simulation, tracking 10,000 MD step cases. The error bar shows standard error. (C) In silico fluorescence recovery after photobleaching-like simulation (Videos S2 and S3). Gray area shows the condensed phase. At a time, all the particles in a cubic box are labeled. These particles were tracked after 5,000 MD steps and 10,000 steps. Top: with only the pairwise interaction; bottom: with the balanced SI and pairwise interaction. To see this figure in color, go online.

Figure 6

The simulation from the configuration with uniformly distributed molecules to equilibrated phase-separated system. (A) Time series of the maximum cluster size of the simulation start from a uniform distribution. Cluster size represents the number of SH3 and PRM molecules in the cluster. (B) Snapshots of the trajectory start from a uniform distribution (Video S4). Blue particles represent SH3 domain, and gray particles represent PRM motives. The linker between domains is not shown for visibility. To see this figure in color, go online.

Figure 7

Phase diagrams depicting phase separation for various valences of SH3 and PRM. The valences of SH3 are 3, 4, and 5 for the top, middle, and bottom rows, respectively. The valences of PRM are 3, 4, and 5 for the left, middle, and right columns, respectively. In each panel, the vertical axis of each graph represents the SH3 domain concentration, and the horizontal axis represents the PRM concentration. Blue diamonds represent critical concentrations in the simulation. Circles show the results obtained from previously reported experiments (41). Orange, the phase separated; green, the uniform phase. To see this figure in color, go online.