Model-based analysis of assembly kinetics for virus capsids or other spherical polymers

The assembly of virus capsids or other spherical polymers-empty, closed structures composed of hundreds of protein subunits-is poorly understood. Assembly of a closed spherical polymer is unlike polymerization of a filament or crystal, examples of open-ended polymers. This must be considered to develop physically meaningful analyses. We have developed a model of capsid assembly, based on a cascade of low-order reactions, that allows us to calculate kinetic simulations. The behavior of this model resembles assembly kinetics observed in solution (Zlotnick, A., J. M. Johnson, P. W. Wingfield, S. J. Stahl, and D. Endres. 1999. Biochemistry. 38:14644-14652). We exhibit two examples of this general model describing assembly of dodecahedral and icosahedral capsids. Using simulations based on these examples, we demonstrate how to extract robust estimates of assembly parameters from accessible experimental data. These parameters, nucleus size, average nucleation rate, and average free energy of association can be determined from measurement of subunit and capsid as time and concentration vary. Mathematical derivations of the analyses, carried out for a general model, are provided in an Appendix. The understanding of capsid assembly developed in this paper is general; the examples provided can be readily modified to reflect different biological systems. This enhanced understanding of virus assembly will allow a more quantitative analysis of virus stability and biological or antiviral factors that affect assembly.