Relaxational dynamics of the T-number conversion of virus capsids

We extend a kinetic theory of virus capsid assembly and disassembly, based on Model A kinetics, to study the dynamics of the size interconversion of virus capsids triggered by a quench—sudden changes in solution conditions. This work is inspired by in vitro experiments on functionalized coat proteins of the plant virus CCMV, which reversibly transition between two shell sizes (T = 1 and T = 3) upon changing acidity and salinity of the solution. Our findings reveal that relaxation dynamics occurs on two timescales, generally attributed to two distinct processes: an initial response from monomers and one of the two capsid species, quickly followed by a stabilization of the monomer concentration, allowing conversion between capsid species to complete. During intermediate stages, a long-lived metastable state may arise, where the thermodynamically less stable species predominate. While a Model A based relaxational model approach accurately captures early and intermediate stages of conversion experiments, it does not effectively model late-stage equilibration, where one capsid species vanishes from the solution. Incorporating nucleation barriers may be essential for accurately describing these experimental findings, particularly under conditions with significant barriers.