A parameter estimation technique for stochastic self-assembly systems and its application to human papillomavirus self-assembly

Virus capsid assembly has been a key model system for studies of complex self-assembly but it does pose some significant challenges for modeling studies. One important limitation is the difficulty of determining accurate rate parameters. The large size and rapid assembly of typical viruses make it infeasible to directly measure coat protein binding rates or deduce them from the relatively indirect experimental measures available. In this work, we develop a computational strategy to deduce coat-coat binding rate parameters for viral capsid assembly systems by fitting stochastic simulation trajectories to experimental measures of assembly progress. Our method combines quadratic response surface and quasi-gradient descent approximations to deal with the high computational cost of simulations, stochastic noise in simulation trajectories and limitations of the available experimental data. The approach is demonstrated on a light scattering trajectory for a human papillomavirus (HPV) in vitro assembly system, showing that the method can provide rate parameters that produce accurate curve fits and are in good concordance with prior analysis of the data. These fits provide an insight into potential assembly mechanisms of the in vitro system and give a basis for exploring how these mechanisms might vary between in vitro and in vivo assembly conditions.