(593ae) 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