Computational and Mathematical Methods in Medicine
Volume 9 (2008), Issue 3-4, Pages 277-293
Original Article

Pathway Complexity of Model Virus Capsid Assembly Systems

1Department of Physics, Carnegie Mellon University, Pittsburgh, PA, USA
2Department of Computer Science, Amherst University, Amherst, MA, USA
3Department of Biological Sciences, Carnegie Mellon University, Pittsburgh, PA, USA

Received 21 January 2008; Accepted 29 April 2008

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


As computational and mathematical studies become increasingly central to studies of complicated reaction systems, it will become ever more important to identify the assumptions our models must make and determine when those assumptions are valid. Here, we examine that question with respect to viral capsid assembly by studying the ‘pathway complexity’ of model capsid assembly systems, which we informally define as the number of reaction pathways and intermediates one must consider to accurately describe a given system. We use two model types for this study: ordinary differential equation models, which allow us to precisely and deterministically compare the accuracy of capsid models under different degrees of simplification, and stochastic discrete event simulations, which allow us to sample use of reaction intermediates across a wide parameter space allowing for an extremely large number of possible reaction pathways. The models provide complementary information in support of a common conclusion that the ability of simple pathway models to adequately explain capsid assembly kinetics varies considerably across the space of biologically meaningful assembly parameters. These studies provide grounds for caution regarding our ability to reliably represent real systems with simple models and to extrapolate results from one set of assembly conditions to another. In addition, the analysis tools developed for this study are likely to have broader use in the analysis and efficient simulation of large reaction systems.