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1 Department of Mathematics and Statistics, University of Central Oklahoma, Edmond, Oklahoma 73034, USA
2 Department of Biochemistry and Molecular Biology, University of Oklahoma Health Sciences Center, Oklahoma City, Oklahoma 73190, USA
(RECEIVED December 24, 2004; FINAL REVISION December 24, 2004; ACCEPTED March 24, 2005)
The capsids of spherical viruses may contain from tens to hundreds of copies of the capsid protein(s). Despite their complexity, these particles assemble rapidly and with high fidelity. Subunit and capsid represent unique end states. However, the number of intermediate states in these reactions can be enormous—a situation analogous to the protein folding problem. Approaches to accurately model capsid assembly are still in their infancy. In this paper, we describe a sailshaped reaction landscape, defined by the number of subunits in each species, the predicted prevalence of each species, and species stability. Prevalence can be calculated from the probability of synthesis of a given intermediate and correlates well with the appearance of intermediates in kinetics simulations. In these landscapes, we find that only those intermediates along the leading edge make a significant contribution to assembly. Although the total number of intermediates grows exponentially with capsid size, the number of leading-edge intermediates grows at a much slower rate. This result suggests that only a minute fraction of intermediates needs to be considered when describing capsid assembly.
Keywords: capsid assembly; virus assembly; protein polymerization; protein folding; energy landscape
Abbreviations: N, number of subunits in a complete capsid • n, number of subunits in an intermediate • stat, the statistical factor reflecting assembly degeneracy over a whole capsid • 
Gcontact, pairwise association energy between subunits • Gn,j, the overall association energy for the j-th intermediate of n subunits • P, probability of the specified intermediate • µ, a weighting factor for reaction chemistry • s, the statistical factor reflecting assembly degeneracy for a specific reaction • f, the forward reaction rate for a specified reaction, a function of s and a microscopic rate • b, the backward rate for a specified reaction, a function of f and Gn,j • t, time.
Article and publication are at http://www.proteinscience.org/cgi/doi/10.1110/ps.041314405.
Reprint requests to: Adam Zlotnick, Department of Biochemistry and Molecular Biology, University of Oklahoma Health Sciences Center, P.O. Box 26901, BRC464, Oklahoma City, OK 73190, USA; e-mail: adam-zlotnick{at}ouhsc.edu; fax: (405) 271-3910.
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