Exploring the Paths of (Virus) Assembly

Abstract

Assembly of viruses that have hundreds of subunits or folding of proteins that have hundreds of amino acids-complex biological reactions-are often spontaneous and rapid. Here, we examine the complete set of intermediates available for the assembly of a hypothetical viruslike particle and the connectivity between these intermediates in a graph-theory-inspired study. Using a build-up procedure, assuming ideal geometry, we enumerated the complete set of 2,423,313 species for formation of an icosahedron from 30 dimeric subunits. Stability of each n-subunit intermediate was defined by the number of contacts between subunits. The probability of forming an intermediate was based on the number of paths to it from its precedecessors. When defining population subsets predicted to have the greatest impact on assembly, both stability- and probability-based criteria select a small group of compact and degenerate species; ergo, only a few hundred intermediates make a measurable contribution to assembly. Though the number of possible intermediates grows combinatorially with the number of subunits in the capsid, the number of intermediates that make a significant contribution to the reaction grows by a much smaller function, a result that may contribute to our understanding of assembly and folding reactions.

Modeling Viral Capsid Assembly

“…3). Although the assumption that there is one dominant intermediate per partial capsid size is an oversimplification, simulations [106, 208] and theory [79, 184] indicate that under many conditions assembly pathways predominantly pass through only a few nucleus structures which correspond to completion of small polygons. Measured critical nucleus sizes under simulated conditions have ranged from 3-10 subunits [75, 76, 141, 208].…”

The Bacteriophage Lambda gpNu3 Scaffolding Protein Is an Intrinsically Disordered and Biologically Functional Procapsid Assembly Catalyst

“…It is generally accepted that an appropriate distribution of dimer and monomer is required to balance nucleation and shell growth, respectively. 9,10,35 Indeed, an excess of scaffolding protein affords partially formed shells in many viral systems including phage P22 56 and phage T7. 23 It has been proposed that excess scaffolding protein “overdrives” a nucleation event, ostensibly mediated by the scaffolding protein dimer.…”

“…9,10 Yet, the capsid assembly pathways are strongly conserved in all of the complex dsDNA viruses. To prevent the formation of aberrant procapsids, bacteriophages such as λ, φ29, P22, and SPP1 and the eukaryotic herpesviruses use internal scaffolding proteins to “chaperone” the major capsid protein into an icosahedral shell.…”

Using Markov state models to study self-assembly

“…While the number of possible graphs for a given model is exponential in the number of subunits N in the target structure, productive assembly reactions only visit a relatively small subset of possible structures. 73,140 Since the MSM state space includes only those states which are visited during estimation of the transition rate matrix, we expect only polynomial scaling. Although additional degrees of freedom, such as the number of subunits interacting with the scaffold (n s ), increases the size The number of unique transitions between states as a function of N. Both plots are from MSMs built using either (n s , n) or (n s , graphIso).…”