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.

For a three-dimensional structure to spontaneously self-assemble from many identical components, the steps on the pathway must be kinetically accessible. Many virus capsids are icosahedral and assembled from hundreds of identical proteins, but how they navigate the assembly process is poorly understood. Capsid assembly is thought to involve stepwise addition of subunits to a growing capsid fragment. Coarse-grained models suggest that the reaction occurs on a downhill energy landscape, so intermediates are expected to be fleeting. In this work, charge detection mass spectrometry (CDMS) has been used to track assembly of the hepatitis B virus (HBV) capsid in real time. The icosahedral T = 4 capsid of HBV is assembled from 120 capsid protein dimers. Our results indicate that there are multiple pathways for assembly. Under conditions that favor a modest association energy there is no accumulation of large intermediates, which indicates that available pathways include ones on a downhill energy surface. Under higher salt conditions, where subunit interactions are strengthened, around half of the products of the initial assembly reaction have masses close to the T = 4 capsid and the other half are stalled intermediates which emerge abruptly at around 90 dimers, indicating a bifurcation in the ensemble of assembly paths. When incubated at room temperature, the 90-dimer intermediates accumulate dimers and gradually shift to higher mass and merge with the capsid peak. Though free subunits are present in solution, the stalled intermediates indicate the presence of a local minima on the energy landscape. Some intermediates may result from hole closure, where the growing capsid distorts to close the hole due to the missing capsid proteins or from a species where subsequent additions are particularly labile.

Understanding capsid assembly is important because of its role in virus lifecycles and in applications to drug discovery and nanomaterial development. Many virus capsids are icosahedral, and assembly is thought to occur by the sequential addition of capsid protein subunits to a nucleus, with the final step completing the icosahedron. Almost nothing is known about the final (completion) step because the techniques usually used to study capsid assembly lack the resolution. In this work, charge detection mass spectrometry (CDMS) has been used to track the assembly of the T = 4 hepatitis B virus (HBV) capsid in real time. The initial assembly reaction occurs rapidly, on the time scale expected from low resolution measurements. However, CDMS shows that many of the particles generated in this process are defective and overgrown, containing more than the 120 capsid protein dimers needed to form a perfect T = 4 icosahedron. The defective and overgrown capsids self-correct over time to the mass expected for a perfect T = 4 capsid. Thus, completion is a distinct phase in the assembly reaction. Capsid completion does not necessarily occur by inserting the last building block into an incomplete, but otherwise perfect icosahedron. The initial assembly reaction can be predominently imperfect, and completion involves the slow correction of the accumulated errors.

Plant viral nanoparticle CPMV outperforms other icosahedral viruses as an in situ vaccine for cancer immunotherapy.

There are ∼ 10 30 possible intermediates on the assembly path from hepatitis B capsid protein dimers to the 120-dimer capsid. If every intermediate was tested, assembly would often get stuck in an entropic trap and essentially every capsid would follow a unique assembly path. Yet, capsids assemble rapidly with minimal trapped intermediates, a realization of the Levinthal paradox. To understand the fundamental mechanisms of capsid assembly it is critical to resolve the early stages of the reaction. We have used Time-Resolved Small Angle X-ray Scattering, which is sensitive to solute size and shape and has millisecond temporal resolution. Scattering curves were fit to a thermodynamically curated library of assembly intermediates, using the principle of maximum entropy. Maximum entropy also provides a physical rationale for the selection of species. We found that the capsid assembly pathway was exquisitely sensitive to 1 initial assembly conditions. With the mildest conditions tested, the reaction appeared two-state from dimer to 120-dimer capsid with some dimers-of-dimers and trimers-ofdimers. In slightly more aggressive conditions, we observed transient accumulation of a decamer-of-dimers and appearance of 90-dimer capsids. In conditions where there is measurable kinetic trapping, we found that a highly diverse early intermediates accumulated within a fraction of a second and propagated into long-lived kinetically trapped states (≥ 90-mer). In all cases, intermediates between 35 and 90 subunits did not accumulate. These results are consistent with the presence of low barrier paths that connect early and late intermediates and direct the ultimate assembly path to late intermediates where assembly can be paused.