Simulation-Based Optimization for Learning Parameters of Viral Self-Assembly Systems

Simulation-based Optimization for Learning Parameters of Viral Self-Assembly Systems

Lu Xie, Carnegie Mellon/University of Pittsburgh Joint Ph.D. Program in Computational Biology

Greg Smith, Department of Biological Sciences, Carnegie Mellon University

Xian Feng, Department of Biological Sciences, Carnegie Mellon University

Russell Schwartz, Department of Biological Sciences and Lane Center for Computational Biology, Carnegie Mellon University

The assembly of icosahedral viral capsids, or protein shells, has become a key model system for understanding complicated self-assembly processes, attracting considerable attention from various theoretical modeling communities. Simulation methods have proven a valuable tool for these studies due to the difficulty of directly experimentally observing the assembly process.  For example, simulation models have proven useful for characterizing possible mechanisms and kinetics of capsid assembly, understanding potential pitfalls to efficient assembly, and learning strategies by which viruses overcome them.  While such models have been useful in exploring the space of possible assembly models for simple icosahedral assembly systems, though, they have been of limited value to date in understanding the assembly of any specific real viruses.  This limitation arises in large part because of the difficulty of experimentally determining the physical parameters needed to instantiate a simulation, specifically sets of rate constants for possible association and dissociation reactions between coat proteins by which the capsids can assemble. We address this problem by using simulation-based optimization to determine rate parameters consistent with indirect experimental measures of bulk assembly progress.

Our methods depend on stochastic simulations of virus capsid assembly that sample possible assembly trajectories from by coarse-grained "local rule" models that describe possible binding interactions among coat proteins [1].  The structure of any given virus is described by a set of such rules, each of which specifies positions and specificities of binding sites by which coat proteins may attach to one another.  Adding association and dissociation rates to these rules allows them to implicitly specify a distribution of possible reaction pathways by which the coat proteins might assembly into viruses.  Sampled reaction trajectories can then be converted into simulations of experimental measures assembly, which can then be fit to actual measurable data on bulk assembly progress.  We specifically seek to fit viral systems to light scattering measurements, which track average assembly sizes over time in an assembly system.

We previously described a strategy for minimizing the deviation between true and simulated light scattering measurements designed to deal with particular challenges of the viral assembly system [2].  These challenges include a typically high cost of individual simulations, making large numbers of function evaluations infeasible, and a computational necessity for stochastic simulations, making it difficult to accurately estimate gradients or response surfaces.  We previously addressed these problems with a local optimizer that interpolated between gradient-based and response surface strategies to help minimize function evaluations on smooth regions of the search space while adjusting as needed to more challenging regions.  This local optimizer was then built into a heuristic global search strategy.  In the present work, we have improved on that prior method by introducing extensions to simultaneously fit multiple real curves in order to reduce redundancy in solutions and developing new strategies to better utilize parallel computation.  We have applied the new methods to three viral assembly systems ¨C human papillomavirus (HPV), hepatitis B virus (HBV), and cowpea chlorotic mottle virus (CCMV).  The results indicate distinct kinds of assembly pathways for the three viruses, showing a diversity of assembly mechanisms available in nature for seemingly similar viral structures.  This work demonstrates the value of simulation-based optimization for understanding virus assembly and suggests the potential of such methods for broader use in learning experimentally inaccessible features of complicated reaction systems.

  <>[1] T. Zhang, R. Rohls and R. Schwartz (2005), Implementation of a discrete event simulator for biological self-assembly systems, Proceedings of the 2005 Winter Simulation Conference

[2] M. S. Kumar and R. Schwartz (2010), A parameter estimation technique for stochastic self-assembly systems and its application to human papillomavirus self-assembly, Physical Biology, Volume 7:045005