Polyomaviridae assembly polymorphism from an energy landscape perspective

Polyomaviridae assemble in vitro into different aggregates depending on experimental conditions. We use an energy landscape approach using empirical energy calculations to quantify how the formation of these different aggregates depends on pH, the presence of bound calcium ions and disulfide linkages. Computations are carried out for SV40, a member of the Polyomaviridae family and are based on the binding free energy landscape of three distinct trimers of pentamers that correspond to the different bonding configurations between the capsid proteins observed in its crystal structure. Our computational analysis shows that the energetics of one of these environments is pivotal for the polymorphic assembly behaviour of SV40, whilst the binding energy landscapes of the other two environments are broadly funnelshaped and thus contribute little to the formation of particles other than virus-like particles (VLP). We have quantified how the existence of bound calcium ions in the absence of disulfide linkages enhances the binding free energies of all three environments and hence, favours the assembly of VLPs. Moreover, estimation of the relative binding free energies of the three environments at pH 5 and pH 8 reveals that they are destabilized at pH 5 relative to pH 8. The extent of this destabilization is dependent on the presence of disulfide linkages and bound calcium ions and accounts for the experimentally observed polymorphic behaviour of VP1 proteins at pH 5. Interestingly, concurrent existence of bound calcium ions and disulfide linkages is found to be destabilizing and thus may disrupt the assembly of VLPs at pH 8.