The capsids of most spherical viruses are icosahedral, an arrangement of multiples of 60 subunits. Though it is a salient point in the life cycle of any virus, the physical chemistry of virus capsid assembly is poorly understood. We have developed general models of capsid assembly that describe the process in terms of a cascade of low order association reactions. The models predict sigmoidal assembly kinetics, where intermediates approach a low steady state concentration for the greater part of the reaction. Features of the overall reaction can be identified on the basis of the concentration dependence of assembly. In simulations, and on the basis of our understanding of the models, we find that nucleus size and the order of subsequent "elongation" reactions are reflected in the concentration dependence of the extent of the reaction and the rate of the fast phase, respectively. The reaction kinetics deduced for our models of virus assembly can be related to the assembly of any "spherical" polymer. Using light scattering and size exclusion chromatography, we observed polymerization of assembly domain dimers of hepatitis B virus (HBV) capsid protein. Empty capsids assemble at a rate that is a function of protein concentration and ionic strength. The kinetics of capsid formation were sigmoidal, where the rate of the fast phase had second-power concentration dependence. The extent of assembly had third-power concentration dependence. Simulations based on the models recapitulated the concentration dependences observed for HBV capsid assembly. These results strongly suggest that in vitro HBV assembly is nucleated by a trimer of dimers and proceeds by the addition of individual dimeric subunits. On the basis of this mechanism, we suggest that HBV capsid assembly could be an important target for antiviral therapeutics.

The assembly of virus capsids or other spherical polymers--empty, closed structures composed of hundreds of protein subunits--is poorly understood. Assembly of a closed spherical polymer is unlike polymerization of a filament or crystal, examples of open-ended polymers. This must be considered to develop physically meaningful analyses. We have developed a model of capsid assembly, based on a cascade of low-order reactions, that allows us to calculate kinetic simulations. The behavior of this model resembles assembly kinetics observed in solution (Zlotnick, A., J. M. Johnson, P. W. Wingfield, S. J. Stahl, and D. Endres. 1999. Biochemistry. 38:14644-14652). We exhibit two examples of this general model describing assembly of dodecahedral and icosahedral capsids. Using simulations based on these examples, we demonstrate how to extract robust estimates of assembly parameters from accessible experimental data. These parameters, nucleus size, average nucleation rate, and average free energy of association can be determined from measurement of subunit and capsid as time and concentration vary. Mathematical derivations of the analyses, carried out for a general model, are provided in an Appendix. The understanding of capsid assembly developed in this paper is general; the examples provided can be readily modified to reflect different biological systems. This enhanced understanding of virus assembly will allow a more quantitative analysis of virus stability and biological or antiviral factors that affect assembly.

Objective: Friedreich's ataxia patients are homozygous for expanded alleles of a GAA triplet-repeat sequence in the FXN gene. Patients develop progressive ataxia due to primary neurodegeneration involving the dorsal root ganglia (DRGs). The selective neurodegeneration is due to the sensitivity of DRGs to frataxin deficiency; however, the progressive nature of the disease remains unexplained. Our objective was to test whether the expanded GAA triplet-repeat sequence undergoes further expansion in DRGs as a possible mechanism underlying the progressive pathology seen in patients. Methods: Small-pool polymerase chain reaction analysis, a sensitive technique that allows the measurement of repeat length in individual FXN genes, was used to analyze somatic instability of the expanded GAA triplet-repeat sequence in multiple tissues obtained from six autopsies of Friedreich's ataxia patients. Results: DRGs showed a significantly greater frequency of large expansions ( p Ͻ 0.001) and a relative paucity of large contractions compared with all other tissues. There was a significant age-dependent increase in the frequency of large expansions in DRGs, which ranged from 0.5% at 17 years to 13.9% at 47 years (r ϭ 0.78; p ϭ 0.028). Interpretation: Progressive pathology involving the DRGs is likely due to age-dependent accumulation of large expansions of the GAA triplet-repeat sequence. Thus, somatic instability of the expanded GAA triplet-repeat sequence may contribute directly to disease pathogenesis and progression. Progressive repeat expansion in specific tissues is a common theme in the pathogenesis of triplet-repeat diseases.Ann Neurol 2007;61: [55][56][57][58][59][60] Friedreich's ataxia (FRDA) is characterized by progressive sensory ataxia with onset before 25 years of age, areflexia, loss of position and vibration senses, dysarthria, and extensor plantar responses. 1 Patients have primary degeneration of dorsal root ganglia (DRGs), associated with axonal degeneration of the posterior columns, spinocerebellar tracts, and corticospinal tracts, and large myelinated fibers in peripheral nerves. 2 In later stages, the cerebellum may be affected; however, other regions of the nervous system remain unaffected. Two-thirds of patients have cardiomyopathy. Although the rate of progression is variable, the mean age of loss of ambulation is 25 years, and patients often die prematurely. 1 FRDA is an autosomal recessive disease, and most patients are homozygous for expanded GAA tripletrepeat sequences (E alleles) in intron 1 of the FXN gene. 3 E alleles interfere with transcription in a lengthdependent manner, 4 resulting in deficiency of the mitochondrial protein frataxin. 5 E alleles contain 66 to 1,700 triplets, and the severity of disease and rate of progression correlate with repeat length. 6 -8 DRG neurons are hypersensitive to frataxin deficiency as seen in neuronal-specific, conditional, frataxin knock-out mice. 9 However, this mouse model did not accurately mimic the situation in FRDA, because the mice had normal levels th...