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Biophys. J. BioFAST: First Published February 10, 2006. doi:10.1529/biophysj.105.076737
© 2006 by the Biophysical Society.

A more recent version of this article appeared on May 1, 2006.
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BIOPHYSICAL THEORY AND MODELING

Stochastic kinetics of viral capsid assembly based on detailed protein structures

Martin Hemberg 1, Sophia N Yaliraki 2 and Mauricio Barahona 1*

1 Dept of Bioengineering, Imperial College London
2 Dept of Chemistry, Imperial College London

* To whom correspondence should be addressed. E-mail: m.barahona{at}imperial.ac.uk.

Submitted on October 27, 2005
Revised on November 21, 2005
Accepted on 28 December 2005


  Abstract
We present a generic computational framework for the simulation of viral capsid assembly which is quantitative and specific. Starting from PDB files containing atomic coordinates, the algorithm builds a coarse grained description of protein oligomers based on graph rigidity. These reduced protein descriptions are used in an extended Gillespie algorithm to investigate the stochastic kinetics of the assembly process. The association rates are obtained from a diffusive Smoluchowski equation for rapid coagulation, modified to account for water shielding and protein structure. The dissociation rates are derived by interpreting the splitting of oligomers as a process of graph partitioning akin to the escape from a multidimensional well. This modular framework is quantitative yet computationally tractable, with a small number of physically motivated parameters. The methodology is illustrated using two different viruses which are shown to follow quantitatively different assembly pathways. We also show how in this model the quasi-stationary kinetics of assembly can be described as a Markovian cascading process in which only a few intermediates and a small proportion of pathways are present. The observed pathways and intermediates can be related a posteriori to structural and energetic properties of the capsid oligomers.

Key Words: Biophysical modelling, Gillespie algorithm, Protein models, Stochastic processes, Virus self-assembly




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Copyright © 2006 by the Biophysical Society.