Minimum theoretical model of viral capsid self-assembly on a spherical scaffold

The formation of the protective shell, or capsid, of many large icosahedral viruses requires the aid of scaffold proteins to initiate nucleation, ensure correct size and shape, and facilitate interactions with the viral genome. Interestingly, SPs often preassemble into a template structure, upon which capsid proteins subsequently self-assemble. In this article, we present a minimum theoretical model, rooted in classical nucleation theory, that describes the in vitro self-assembly of a spherical capsid in the presence of a Preformed Spherical Scaffold (PSS). Within this framework, we examine the influence of the PSS on the size of the critical capsid, the nucleation barrier, and the steady-state nucleation rate. We contrast our findings with those of a recent extension of the original classical nucleation theory of viral capsids, which accounts for bending deformations. Furthermore, we present a detailed analysis of the physical conditions that lead to stable closed capsids. These are then represented in phase diagrams that highlight regions of favorable and unfavorable assembly on top of the template. Our model quantifies the necessary interactions between CPs and the PSS for optimal assembly and extends naturally to preformed scaffolds of diverse shapes.