Should Virus Capsids Assemble Perfectly? A Simple Equilibrium Model for Defects

Abstract

Although published structural models of virus capsids generally exhibit perfect symmetry, defects might be expected for several reasons including the finite-temperature, fluctuating environment in which capsids assemble and, in some cases, the requirement for disassembly during the infection cycle. Different lines of evidence also suggest the presence of defects: the observation of defective structures in computer simulations, and the presence of imperfect capsids in single-particle cryo-EM studies. To begin to quantify the conditions under which defects might be expected, we develop a simple equilibrium theory for capsids based on a lattice model allowing for both ideal and defective sites. Both analytical and numerical calculations with the model show that a significant population of defects appears below a fairly sharp threshold value of a key parameter: the difference in effective pair-binding affinities between ideally oriented and mixed ideal/defective pairs of interacting sites. The generality of the model enables us to estimate threshold values for a wide range of virus capsids, providing potential guidance for future experimental studies. Beyond furthering our understanding of potential structural heterogeneity in virus capsids, the findings suggest a novel strategy for assembly inhibition by enhancing ‘off-lattice’ interactions among capsid proteins via adaptor molecules.