Assembly Reactions of Hepatitis B Capsid Protein into Capsid Nanoparticles Follow a Narrow Path through a Complex Reaction Landscape

Abstract

For many viruses, capsids (biological nanoparticles) assemble to protect genetic material and dissociate to release their cargo. To understand these contradictory properties, we analyzed capsid assembly for Hepatitis B virus; an endemic pathogen with an icosahedral, 120-homodimer capsid. We used solution X-ray scattering to examine trapped and equilibrated assembly reactions. To fit experimental results, we generated a library of unique intermediates, selected by umbrella sampling of Monte Carlo simulations. The number of possible capsid intermediates is immense, ~ 10 30 , yet assembly reactions are rapid and completed with high fidelity. If the huge number of possible intermediates were actually present, maximum entropy analysis shows that assembly reactions would be blocked by an entropic barrier, resulting in incomplete nanoparticles. When an energetic term was applied to select the stable species that dominated the reaction mixture, we found that only a few hundred intermediates, mapping out a narrow path through the immense reaction landscape. This is a solution to a viral application of the Levinthal paradox. With the correct energetic term, the match between predicted intermediates and scattering data was striking. The grand canonical free energy landscape for assembly, calibrated by our experimental results, supports a detailed analysis of this complex reaction. There is a narrow range of energies that supports on-path assembly. If association energy is too weak or too strong progressively more intermediates will be entropically blocked, spilling into paths leading to dissociation or trapped incomplete nanoparticles, respectively. These results are relevant to many viruses, provide a basis for simplifying assembly models and identifying new targets for antiviral intervention. They provide a basis for understanding and designing biological and abiological self-assembly reactions.

Complete and cooperative in vitro assembly of computationally designed self-assembling protein nanomaterials

“…Because equimolar assemblies proceed at similar apparent rates for both nanomaterials, it is possible that partial I53-40 structures transiently form in some non-stoichiometric regimes, but then (unlike I53-50) self-cure via disassembly and error correction prior to analysis. These results are consistent with previous analyses of in vitro virus capsid assembly, which suggest that relatively weak interfaces are required for cooperativity 23 , 33 , 50 , 54 . Furthermore, for HBV, a virus capsid architecture with thermodynamic properties similar to I53-40 and I53-50, contact energies and kinetic parameters which lead to cooperative assembly are constrained by the dual requirements of efficiency and fidelity 33 , 55 .…”

“…5a). Percent error minimization converged on ΔG con values of about 3.6 kcal/mol for I53-40 and 4.1 kcal/mol for I53-50, which, intriguingly, are similar to values previously observed for cooperatively assembling virus capsids 23,33,50,52 . Overlaying the experimental data onto the model shows that while the I53-40 data globally matches the model well, the I53-50 data deviate from the model in the regime where pentamer is super-stoichiometric ( Fig.…”

“…The combination of two features in particular appears to largely account for the observed cooperativity: (i) a hierarchical assembly process in which protein subunits first form oligomeric building blocks which then further assemble [19][20][21] and (ii) specific, yet weak, protein-protein interactions between the building blocks 22,23 . This conclusion is supported both by experiment [24][25][26][27][28][29] and by multiple theoretical models of assembly [30][31][32][33] . For example, a simple equilibrium model 21 comprising a cascade of low-order reactions predicts that weak association energies are sufficient to drive the assembly of modest concentrations of oligomeric building blocks to completion, with very low levels of intermediate structures present at equilibrium.…”

Expression of quasi-equivalence and capsid dimorphism in the Hepadnaviridae

“…90 dimers [65]. What occurs between these two states, including the point(s) where the paths leading to T = 3 and T = 4 capsids diverge, has been obscure though progress is being made [66]. It has been reported that T = 3 capsids form early and briefly (seconds) whereas T = 4 capsids continue to be assembled for extended periods (hours), eventually becoming the majority species [67].…”

Physics of viral dynamics

“…Mutations that alter the assembly pathway can cause deep kinetic traps to reappear. Kinetic assembly pathways have been identified in HBV, by a combination of time-dependent small-angle X-ray scattering (SAXS) and umbrella Monte Carlo simulation with maximum entropy optimization 37 . Importantly, these kinetic assembly pathways appear only over narrow intervals of parameter space.…”