Relaxational dynamics of the size interconversion of virus capsids

Recent experiments show that a modified coat protein of a simple icosahedral plant virus forms capsids of different sizes, or T-numbers, under different solution conditions, and that by changing the solution conditions one T-number can be converted into the other albeit that the kinetics of the process is rather slow. We apply a simple relaxational model that ignores the impact of any nucleation barriers, and finds a reasonable agreement between theory and experiment with a minimal number of adjustable parameters. We conclude that following a sudden change in pH or salinity, and starting off from a solution dominated by one of the T-numbers, the initial response must be driven by an increase in mixing entropy giving rise to a mixture of sizes. In the late stages, the impact of minimizing the binding free energy kicks in and the solution relaxes to thermodynamic equilibrium. We find that the concentration of free protein subunits, or dimers, relaxes very swiftly and that their concentration remains virtually constant for most of the T-number conversion.