Understanding the Concentration Dependence of Viral Capsid Assembly Kinetics—the Origin of the Lag Time and Identifying the Critical Nucleus Size

Abstract

The kinetics for the assembly of viral proteins into a population of capsids can be measured in vitro with size exclusion chromatography or dynamic light scattering, but extracting mechanistic information from these studies is challenging. For example, it is not straightforward to determine the critical nucleus size or the elongation time (the time required for a nucleus to grow to completion). In this work, we study theoretical and computational models for capsid assembly to show that the critical nucleus size can be determined from the concentration dependence of the assembly half-life and that the elongation time is revealed by the length of the lag phase. Furthermore, we find that the system becomes kinetically trapped when nucleation becomes fast compared to elongation. Implications of this constraint for determining elongation mechanisms from experimental assembly data are discussed.

Using Markov state models to study self-assembly

“…3 and 4). In the patchy sphere model, assembly for the weakest subunitnanoparticle interaction (ε S = 6.6) is heavily nucleationdominated, while for the strongest value (ε S = 9) the nucleation timescale is comparable to the elongation timescale 128 (i.e., the time required for a critical nucleus to grow to completion 129 ). These two scenarios are distinguished by the spectrum of implied timescales (Fig.…”

“…For example, while the CPU time for unbiased dynamics increases with decreasing total subunit concentration c 0 according to ∼ c n * 0 with n* the critical nucleus size, the MSM approach will scale as the minimum assembly time,∼ c −1 0 (Ref. 129). This scaling could be further improved upon using coordinates that consider positions of free subunits (e.g., w described in Sec.…”

“…133 This situation occurs in empty capsid assembly when nucleation barriers are sufficiently large that nucleation timescales are slow in comparison to growth times. 128,129 While this condition might seem limiting, it is precisely the regime in which enhanced sampling methods can be expected to provide significant speedup, since there is a significant separation of timescales. Furthermore, most experiments are performed under these conditions, with concentrations of intermediates often so low as to be undetectable, because assembly is most robust against kinetic traps when nucleation is rate limiting.…”

“…Furthermore, most experiments are performed under these conditions, with concentrations of intermediates often so low as to be undetectable, because assembly is most robust against kinetic traps when nucleation is rate limiting. 4,99,128,129 The MSM approach described here enables simulating assembly at these experimentally relevant parameter values.…”

Probing the Early Temporal and Spatial Interaction of the Sindbis Virus Capsid and E2 Proteins with Reverse Genetics

“…In the infected cell, the K250/2D Cp and the K2502/E Cp may become kinetically trapped by this interaction, unable to continue down the NC assembly pathway. Computational studies with other RNA viruses have demonstrated, counterintuitively, that increasing the affinity of a viral Cp for its cognate RNA leads to an aberrant and incorrect NC assembly pathway by altering the rate of nucleation (8,21).…”