Kinetics versus Thermodynamics in Virus Capsid Polymorphism

Guanidine Hydrochloride-Induced Hepatitis B Virus Capsid Disassembly Hysteresis

Hepatitis B virus (HBV) displays remarkable self-assembly capabilities that interest the scientific community and biotechnological industries as HBV is leading to an annual mortality of up to 1 million people worldwide (especially in Africa and Southeast Asia). When the ionic strength is increased, hepatitis B virus-like particles (VLPs) can assemble from dimers of the first 149 residues of the HBV capsid protein core assembly domain (Cp149). Using solution small-angle X-ray scattering, we investigated the disassembly of the VLPs by titrating guanidine hydrochloride (GuHCl). Measurements were performed with and without 1 M NaCl, added either before or after titrating GuHCl. Fitting the scattering curves to a linear combination of atomic models of Cp149 dimer (the subunit) and T = 3 and T = 4 icosahedral capsids revealed the mass fraction of the dimer in each structure in all the titration points. Based on the mass fractions, the variation in the dimer-dimer association standard free energy was calculated as a function of added GuHCl, showing a linear relation between the interaction strength and GuHCl concentration. Using the data, we estimated the energy barriers for assembly and disassembly and the critical nucleus size for all of the assembly reactions. Extrapolating the standard free energy to [GuHCl] = 0 showed an evident hysteresis in the assembly process, manifested by differences in the dimer-dimer association standard free energy obtained for the disassembly reactions compared with the equivalent assembly reactions. Similar hysteresis was observed in the energy barriers for assembly and disassembly and the critical nucleus size. The results suggest that above 1.5 M, GuHCl disassembled the capsids by attaching to the protein and adding steric repulsion, thereby weakening the hydrophobic attraction.

Relaxational dynamics of the T-number conversion of virus capsids

We extend a recently proposed kinetic theory of virus capsid assembly based on Model A kinetics and study the dynamics of the interconversion of virus capsids of different sizes triggered by a quench, that is, by sudden changes in the solution conditions. The work is inspired by in vitro experiments on functionalized coat proteins of the plant virus cowpea chlorotic mottle virus, which undergo a reversible transition between two different shell sizes (T = 1 and T = 3) upon changing the acidity and salinity of the solution. We find that the relaxation dynamics are governed by two time scales that, in almost all cases, can be identified as two distinct processes. Initially, the monomers and one of the two types of capsids respond to the quench. Subsequently, the monomer concentration remains essentially constant, and the conversion between the two capsid species completes. In the intermediate stages, a long-lived metastable steady state may present itself, where the thermodynamically less stable species predominate. We conclude that a Model A based relaxational model can reasonably describe the early and intermediate stages of the conversion experiments. However, it fails to provide a good representation of the time evolution of the state of assembly of the coat proteins in the very late stages of equilibration when one of the two species disappears from the solution. It appears that explicitly incorporating the nucleation barriers to assembly and disassembly is crucial for an accurate description of the experimental findings, at least under conditions where these barriers are sufficiently large.

Molecular Dynamics Simulations of Deformable Viral Capsomers

Most coarse-grained models of individual capsomers associated with viruses employ rigid building blocks that do not exhibit shape adaptation during self-assembly. We develop a coarse-grained general model of viral capsomers that incorporates their stretching and bending energies while retaining many features of the rigid-body models, including an overall trapezoidal shape with attractive interaction sites embedded in the lateral walls to favor icosahedral capsid assembly. Molecular dynamics simulations of deformable capsomers reproduce the rich self-assembly behavior associated with a general T=1 icosahedral virus system in the absence of a genome. Transitions from non-assembled configurations to icosahedral capsids to kinetically-trapped malformed structures are observed as the steric attraction between capsomers is increased. An assembly diagram in the space of capsomer-capsomer steric attraction and capsomer deformability reveals that assembling capsomers of higher deformability into capsids requires increasingly large steric attraction between capsomers. Increasing capsomer deformability can reverse incorrect capsomer-capsomer binding, facilitating transitions from malformed structures to symmetric capsids; however, making capsomers too soft inhibits assembly and yields fluid-like structures.

Beyond COVID-19: Do biothermodynamic properties allow predicting the future evolution of SARS-CoV-2 variants?

During the COVID-19 pandemic, many statistical and epidemiological studies have been published, trying to predict the future development of the SARS-CoV-2 pandemic. However, it would be beneficial to have a specific, mechanistic biophysical model, based on the driving forces of processes performed during virus-host interactions and fundamental laws of nature, allowing prediction of future evolution of SARS-CoV-2 and other viruses. In this paper, an attempt was made to predict the development of the pandemic, based on biothermodynamic parameters: Gibbs energy of binding and Gibbs energy of growth. Based on analysis of biothermodynamic parameters of various variants of SARS-CoV-2, SARS-CoV and MERS-CoV that appeared during evolution, an attempt was made to predict the future directions of evolution of SARS-CoV-2 and potential occurrence of new strains that could lead to new pandemic waves. Possible new mutations that could appear in the future could lead to changes in chemical composition, biothermodynamic properties (driving forces of new virus strains) and biological properties of SARS CoV-2 that represent a risk for humanity.

The Dynamics of Viruslike Capsid Assembly and Disassembly

Cowpea chlorotic mottle virus (CCMV) is a widely used model for virus replication studies. A major challenge lies in distinguishing between the roles of the interaction between coat proteins and that between the coat proteins and the viral RNA in assembly and disassembly processes. Here, we report on the spontaneous and reversible size conversion of the empty capsids of a CCMV capsid protein functionalized with a hydrophobic elastin-like polypeptide which occurs following a pH jump. We monitor the concentrations of T = 3 and T = 1 capsids as a function of time and show that the time evolution of the conversion from one T number to another is not symmetric: The conversion from T = 1 to T = 3 is a factor of 10 slower than that of T = 3 to T = 1. We explain our experimental findings using a simple model based on classical nucleation theory applied to virus capsids, in which we account for the change in the free protein concentration, as the different types of shells assemble and disassemble by shedding or absorbing single protein subunits. As far as we are aware, this is the first study confirming that both the assembly and disassembly of viruslike shells can be explained through classical nucleation theory, reproducing quantitatively results from time-resolved experiments

Disassembly of Single Virus Capsids Monitored in Real Time with Multicycle Resistive-Pulse Sensing

Virus assembly and disassembly are critical steps in the virus lifecycle; however, virus disassembly is much less well understood than assembly. For hepatitis B virus (HBV) capsids, disassembly of the virus capsid in the presence of guanidine hydrochloride (GuHCl) exhibits strong hysteresis that requires additional chemical energy to initiate disassembly and disrupt the capsid structure. To study disassembly of HBV capsids, we mixed T = 4 HBV capsids with 1.0-3.0 M GuHCl, monitored the reaction over time by randomly selecting particles, and measured their size with resistive-pulse sensing. Particles were cycled forward and backward multiple times to increase the observation time and likelihood of observing a disassembly event. The four-pore device used for resistive-pulse sensing produces four current pulses for each particle during translocation that improves tracking and identification of single particles and increases the precision of particle-size measurements when pulses are averaged. We studied disassembly at GuHCl concentrations below and above denaturing conditions of the dimer, the fundamental unit of HBV capsid assembly. As expected, capsids showed little disassembly at low GuHCl concentrations (e.g., 1.0 M GuHCl), whereas at higher GuHCl concentrations (≥1.5 M), capsids exhibited disassembly, sometimes as a complex series of events. In all cases, disassembly was an accelerating process, where capsids catastrophically disassembled within a few 100 ms of reaching critical stability; disassembly rates reached tens of dimers per second just before capsids fell apart. Some disassembly events exhibited metastable intermediates that appeared to lose one or more trimers of dimers in a stepwise fashion.

Molecular recognition mechanisms directing the self-assembly of biological structures

Self-assembling may be defined as the spontaneous association of material units into structures that are often capable of cyclic reorganization and functional behavior. Various molecular recognition processes stabilize assemblies of polymers and biological structures. The present article analyzes cases in which chemical, shape and other recognition mechanisms are individually or cooperatively operative. Simpler self-assembling theories reported in the literature are highlighted. Detailed processes for which chemical recognition is the prevailing, enthalpy-driven, process include the non-ideal component of miscibility, supramolecular polymerization, host-guest complexes and template polymerization. Also discussed are systems such as liquid crystalline closed polymers, ternary mesogenic systems and rigid crystalline polymers for which shape recognition is the prevailing entropy-driven process. Other recognition mechanisms include ion condensation effects, hydrophobic bonding and growth-coupled-to-orientation. Combinations of various recognition mechanisms are particularly evident in biological structures. Self-assembling mechanisms involved in the genesis of some biological systems can be scientifically identified, but much more needs to be known to describe the "engineered" assembling modes that support complex functional organs.

Computational studies of shape control of charged deformable nanocontainers

Biological matter is often compartmentalized by soft membranes that dynamically change their shape in response to chemical and mechanical cues. Deformable soft-matter-based nanoscale membranes or nanocontainers that mimic this behavior can be used as drug-delivery carriers that can adapt to evolving physiological conditions, or as dynamic building blocks for the design of novel hierarchical materials via assembly engineering. Here, we connect the intrinsic features of charged deformable nanocontainers such as their size, charge, surface tension, and elasticity with their equilibrium shapes for a wide range of solution conditions using molecular dynamics simulations. These links identify the fundamental mechanisms that establish the chemical and materials design control strategies for modulating the equilibrium shape of these nanocontainers. We show that flexible nanocontainers of radii ranging from 10-20 nm exhibit sphere-to-rod-to-disc shape transitions yielding rods and discs over a wide range of aspect ratio λ (0.3 < λ < 5). The shape transitions can be controlled by tuning salt and/or surfactant concentration as well as material elastic parameters. The shape changes are driven by reduction in the global electrostatic energy and are associated with dramatic changes in local surface elastic energy distributions. To illustrate the shape transition mechanisms, exact analytical calculations for idealized spheroidal nanocontainers in salt-free conditions are performed. Explicit counterion simulations near nanocontainers and associated Manning model calculations provide an assessment of the stability of observed shape deformations in the event of ion condensation.

Physical, chemical, and synthetic virology: Reprogramming viruses as controllable nanodevices

The fields of physical, chemical, and synthetic virology work in partnership to reprogram viruses as controllable nanodevices. Physical virology provides the fundamental biophysical understanding of how virus capsids assemble, disassemble, display metastability, and assume various configurations. Chemical virology considers the virus capsid as a chemically addressable structure, providing chemical pathways to modify the capsid exterior, interior, and subunit interfaces. Synthetic virology takes an engineering approach, modifying the virus capsid through rational, combinatorial, and bioinformatics-driven design strategies. Advances in these three subfields of virology aim to develop virus-based materials and tools that can be applied to solve critical problems in biomedicine and biotechnology, including applications in gene therapy and drug delivery, diagnostics, and immunotherapy. Examples discussed include mammalian viruses, such as adeno-associated virus (AAV), plant viruses, such as cowpea mosaic virus (CPMV), and bacterial viruses, such as Qβ bacteriophage. Importantly, research efforts in physical, chemical, and synthetic virology have further unraveled the design principles foundational to the form and function of viruses. This article is categorized under: Diagnostic Tools > Diagnostic Nanodevices Biology-Inspired Nanomaterials > Protein and Virus-Based Structures.

The equilibrium structure of self-assembled protein nano-cages

Understanding how highly symmetric, robust, monodisperse protein nano-cages self-assemble can have major applications in various areas of bio-nanotechnology, such as drug delivery, biomedical imaging and gene therapy. We develop a model to investigate the assembly of protein subunits into the structures with different sizes and symmetries. Using Monte Carlo simulation, we obtain global minimum energy structures. Our results suggest that the physical properties including the spontaneous curvature, flexibility and bending rigidity of coat proteins are sufficient to predict the size, symmetry and shape selectivity of the assembly products. Further, on a thermodynamic basis, we discuss the polymorphism of nano-cages observed in assembly experiments.

All-Atom Molecular Dynamics Simulations of Whole Viruses

Classical molecular dynamics modeling of whole viruses or their capsids in explicit water is discussed, and known examples from the literature are analyzed. Only works on all-atom modeling in explicit water are included. Physical chemistry of the whole system is the focus, which includes the structure and dynamics of the biomolecules as well as water and ion behavior in and around the virus particle. It was demonstrated that in most investigations molecular phenomena that currently can not be studied experimentally are successfully reproduced and explained by the simulations. These include, for example, transport and distribution of ions inside viruses that ultimately connected to their stability, the hydrodynamic pressure in the capsid related to viruses' elastic properties, the role of metal ions in virus swelling, and others. Current and future tendencies in the development of all-atom virus simulations are outlined.

A dimorphism shift of hepatitis B virus capsids in response to ionic conditions

The dimorphism of HBV capsids (coexistence of T = 3 and T = 4 capsids) was found to be regulatable by controlling the rate of capsid nucleation using cations such as K+ or Ca2+: a quick addition of highly concentrated monovalent and/or multivalent counter-cations resulted in a morphism transition from a thermodynamically more stable, T = 4 capsid-dominant state (>80% of total capsids) to a new state containing ∼1 : 1 amounts of T = 3 and T = 4 capsids. These results suggested that the salts with strong charge screening ability could narrow the difference in nucleation energy barriers between the two states, which were not inter-convertible once formed. The effect of salts was more significant than other factors such as pH or protein concentration in achieving such a dimorphism shift. The general mechanism of HBV capsid dimorphism described here provides a new perspective in understanding the virus assembly during infection and directing the design of non-infectious capsids for nanotechnology applications.

The different faces of mass action in virus assembly

The spontaneous encapsulation of genomic and non-genomic polyanions by coat proteins of simple icosahedral viruses is driven, in the first instance, by electrostatic interactions with polycationic RNA binding domains on these proteins. The efficiency with which the polyanions can be encapsulated in vitro, and presumably also in vivo, must in addition be governed by the loss of translational and mixing entropy associated with co-assembly, at least if this co-assembly constitutes a reversible process. These forms of entropy counteract the impact of attractive interactions between the constituents and hence they counteract complexation. By invoking mass action-type arguments and a simple model describing electrostatic interactions, we show how these forms of entropy might settle the competition between negatively charged polymers of different molecular weights for co-assembly with the coat proteins. In direct competition, mass action turns out to strongly work against the encapsulation of RNAs that are significantly shorter, which is typically the case for non-viral (host) RNAs. We also find that coat proteins favor forming virus particles over nonspecific binding to other proteins in the cytosol even if these are present in vast excess. Our results rationalize a number of recent in vitro co-assembly experiments showing that short polyanions are less effective at attracting virus coat proteins to form virus-like particles than long ones do, even if both are present at equal weight concentrations in the assembly mixture.