Improving Inference of Rate Parameters for Viral Capsid Assembly Systems

Abstract

Computational methods have been widely used to infer properties of complex systems that one cannot directly observe experimentally. Viral capsid assembly is a key model system for complex self-assembly for which we lack direct experimental data on critical information, such as kinetic parameters, needed to build models and reveal detailed assembly pathways. We previously sought to learn such hidden parameters with a heuristic optimization approach using gradient and response surface methods applied to the light scattering measurements of three in vitro viral assembly systems: human papillomavirus (HPV), hepatitis B virus (HBV), and cowpea chlorotic mottle virus (CCMV). This method successfully learned plausible kinetic parameters for all the three viruses leading to reconstruction of detailed models of assembly pathways. Significant computational challenges, however, hinder our ability to construct more precise or detailed models and reliably quantify uncertainty in the inferences. First, there is no closed form representation for the quality of fit of models to data, which therefore must be evaluated through computationally costly simulations. Second, the problem requires stochastic simulations, and the resulting simulation trajectories must be averaged over many replicates to suppress noise. Third, optimization of parameters must account for unknown factors and imprecision of experimental measurements. We explore here improvements based on the idea of derivative free optimization (DFO), a class of optimization algorithm that can achieve faster and more accurate fitting, especially on systems characterized by costly, noisy evaluations of quality of fit. Preliminary tests show improvements over our custom gradient-based method using a DFO strategy. Work is continuing on evaluating different DFO methods and customizing them to inference of kinetic parameters in order to determine the best strategies for inferring unobservable physical parameters in complex biological self-assembly systems.