Kinetic theory of virus capsid assembly

A phenomenological theory is presented for the kinetics of the in vitro assembly and disassembly of icosahedral virus capsids in solutions of coat proteins. The focus is on conditions where nucleation-type processes can be ignored. We find that the kinetics of assembly is strongly concentration dependent and that the late-stage relaxation time varies as the inverse of the square of the concentration. These findings are corroborated by experimental observations on a number of viruses. Further, our theory shows that hysteresis observed in some experiments could be a direct effect of the kinetics of a high-order mass action law, not necessarily the result of a free energy barrier between assembled and disassembled states.