Simulation study of the contribution of oligomer/oligomer binding to capsid assembly kinetics

Abstract

The process by which hundreds of identical capsid proteins self-assemble into icosahedral structures is complex and poorly understood. Establishing constraints on the assembly pathways is crucial to building reliable theoretical models. For example, it is currently an open question to what degree overall assembly kinetics are dominated by one or a few most efficient pathways versus the enormous number theoretically possible. The importance of this question, however, is often overlooked due to the difficulties of addressing it in either theoretical or experimental practice. We apply a computer model based on a discrete-event simulation method to evaluate the contributions of nondominant pathways to overall assembly kinetics. This is accomplished by comparing two possible assembly models: one allowing growth to proceed only by the accretion of individual assembly subunits and the other allowing the binding of sterically compatible assembly intermediates any sizes. Simulations show that the two models perform almost identically under low binding rate conditions, where growth is strongly nucleation-limited, but sharply diverge under conditions of higher association rates or coat protein concentrations. The results suggest the importance of identifying the actual binding pattern if one is to build reliable models of capsid assembly or other complex self-assembly processes.

FIGURE 1

Screenshots of an assembly subunit, intermediates, and complete capsid in the simulation model. (a) Assembly subunit representing a pentermeric capsomer. (b) Simplified T = 1 capsid model structure consisting of 12 subunits with structure shown in a. (c–f) Possible intermediate stages in an assembly reaction and the allowed movements between them for (c) an open linear trimer and a monomer, (d) a closed trimer and a monomer, (e) two dimers, and (f) a tetramer.

FIGURE 2

Time courses of simulations with a system size N = 1000 and varied association rate constants (0.001, 0.01, 0.1, 1) and binding patterns. Error bars represent ± 1 SD derived from 30 simulation runs. (a) Complete capsid production with the unconstrained binding pattern. (b) Complete capsid production with the constrained binding pattern. (c) Capsomer concentration changes with the unconstrained binding pattern. (d) Capsomer concentration changes with constrained binding pattern. The insets in a and b are the time course with k_a = 0.001 and a longer simulation run time.

FIGURE 3

Time courses of concentrations of species of 11 sizes (from dimer to complete capsid) from simulation runs with N = 1000. a, c, and e are for the unconstrained binding pattern with k_a = 0.001, 0.01, and 0.1. b, d, and f are for the constrained binding pattern with k_a = 0.001, 0.01, and 0.1.

FIGURE 4

Screenshots of assembly products of various sizes after capsid production has reached a plateau from simulations with different binding patterns using the parameters N = 1000, ka = 0.1, and kd = 1000. (a) Unconstrained binding pattern. (b) Constrained binding pattern.

FIGURE 5

Comparison of the two binding patterns with identical initial concentrations of capsomers (N = 1000). (a) Simulations under conditions producing kinetic trapping, with capsid yields from the constrained binding pattern for k_a = 1:100, 1:90, 1:80, and 1:70 and for the unconstrained binding pattern with k_a = 1:10. (b) Simulations under conditions not producing kinetic trapping, using k_a = 0.001 for both binding patterns.

FIGURE 6

Capsid time courses with three association rate constants (0.001, 0.01, 10⁻⁹) and two system sizes (N = 500, 2000). Left panels (a, c, e): unconstrained binding pattern. Right panels (b, d, f): constrained binding pattern.