Physics of Viral Dynamics

REVIEWS Physics of viral dynamics Robijn F. Bruinsma1, Gijs J. L. Wuite2 and Wouter H. Roos 3 ✉ Abstract | Viral capsids are often regarded as inert structural units, but in actuality they display fascinating dynamics during different stages of their life cycle. With the advent of single-particle approaches and high-resolution techniques, it is now possible to scrutinize viral dynamics during and after their assembly and during the subsequent development pathway into infectious viruses. In this Review, the focus is on the dynamical properties of viruses, the different physical virology techniques that are being used to study them, and the physical concepts that have been developed to describe viral dynamics. Capsids Humans and other animals, as well as plants, are plagued and new methods of analysis and numerical modelling. Protein shells that surround the by infections caused by viruses. These are parasites that We first review some of the dynamic methods that viral genome. cannot reproduce by themselves and that are incapable are being applied to study the assembly of empty viral of metabolic activity. Instead, after viruses infect cells, capsids, then focus on the role of genome molecules Triangulation numbers Classification system, they alter cellular molecular machinery so that it pro- (RNA/DNA) during assembly, followed by a discussion developed by Caspar and duces new viruses, which are then released into the envi- of studies of the steady-state dynamics of assembled Klug, for icosahedral viruses. ronment. This sequence of events, the viral life cycle, is viruses. BOx 2 summarizes several experimental tech- T-numbers are integers and schematically discussed in BOx 1. The aim of the tradi- niques that have been used to study viral dynamics in contain information on the tional field of structural virology is to achieve a better the past decade. In an earlier article3, we reviewed work number of protein subunits that make up a capsid. understanding of the spatial organization of the pro- on the equilibrium physics of viral assembly under static teins inside viral particles, an understanding that should conditions and their mechanical properties. Virions increase our ability to develop more effective therapies. Viral particles, composed Since the beginnings of structural virology as a field Viral self-assembly dynamics of both capsid proteins and the viral genome, that can of study, physics has made important contributions. For In 1955, Heinz Fraenkel-Conrat and Robley Williams successfully infect cells. several decades now, electron microscopy and X-ray discovered that solutions containing tobacco mosaic diffraction imaging of crystals of viruses have provided virus (TMV) capsid proteins and single-stranded (ss) high-resolution reconstructions of viral capsids with RNA molecules spontaneously produced infectious icosahedral symmetry1. The crystallographic analy- viral particles (or virions)8,9, a process now known as sis method developed by Donald Caspar and Aaron self-assembly. Many other viruses — both with rod-like Klug in the 1960s (REF.2) provided us with a systematic helical shapes (such as TMV) and with sphere-like classification of icosahedral capsids in terms of the icosahedral shapes10–12 — were found to self-assemble so-called T-numbers (triangulation numbers), a method under in vitro conditions. Thermodynamic studies that has stood the test of time3. More recently, modern led to the construction of instructive phase diagrams cryo-electron imaging methods, including tomography4,5 for viral assembly, with pH and ionic strength acting and asymmetric reconstructions6,7, have made it possible as thermodynamic control parameters. For instance, to reconstruct not only regular capsids, but also asym- for the capsid proteins of TMV without its genome metric protein distributions and the enclosed genome by molecules, increasing ionic strength and reducing pH using images of individual viruses. both serve to weaken the electrostatic repulsive interac- 1Department of Physics and Astronomy, University of These important low-temperature imaging methods tions between the amphiphilic capsid proteins, thereby California, Los Angeles, are limited to the study of static viral structures. However, allowing the competing attractive hydrophobic interac- California, USA. evidence accumulated towards the end of the twentieth tions to overcome the repulsion and drive assembly13. 2Fysica van levende century that viruses and viral capsids are in fact dynam- TMV-like capsids appear under conditions of low pH. systemen, Vrije Universiteit, ical structures that should be viewed as active ‘nano- This is not the case under physiological conditions, but Amsterdam, the Netherlands. machines’. When a virus assembles, a highly dynamical adding the viral genome molecules to the solution does 3 Moleculaire Biofysica, and disorganized state of individual capsid proteins in tilt the balance and produces infectious viruses (Fig. 1a). Zernike Instituut, Rijksuniversiteit Groningen, solution progressively turns into a more ordered, collec- In comparison, the capsid proteins of the spherical cow- Groningen, the Netherlands. tive multi-protein state of partially and eventually fully pea chlorotic mottle virus (CCMV) form empty capsids ✉e-mail: [email protected] closed shells, the viral capsid. Yet these closed capsids under conditions of low pH but higher ionic strength, https://doi.org/10.1038/ are still quite dynamic. Studying the dynamics of viruses but form concentric multi-shells at low pH and lower s42254-020-00267-1 called for a new toolbox, in terms of both new probes ionic strength14. 76 | FEBRUARY 2021 | VOLUME 3 www.nature.com/natrevphys REVIEWS Key points provided by a combined electron microscopy and atomic force microscopy (AFM) study of the assembly of the • Viruses are highly dynamic structures. minute virus of mice (MVM)22 that provided insight • Physics approaches are well suited to study the mechanisms behind the viral life cycle. into the nature of the transient assembly intermediates • New single-particle techniques provide unprecedented insight into viral assembly. that interpolate between the monomer and capsid state. These techniques include resistive-pulse sensing, high-speed atomic force These experiments demonstrated the importance of microscopy, interferometric scattering, charge-detection mass spectrometry and single-particle approaches. optical tweezers. According to the equilibrium self-assembly theory of • Assembly studies of both empty shells and genome-filled shells provide insights into viral capsids16, capsid assembly is initiated at a critical the molecular mechanism and pathways of viral self-assembly. protein aggregation concentration (the CAC). At the • Maturation is a fascinating process in which large structural changes occur in viruses. CAC, the critical nucleus is roughly half of a complete • Closed-shell dynamics includes soft modes and conformational changes. shell, which is much larger than the size of the experi- mentally observed nucleation complexes. Theoretically, When empty capsids are present in such a solu- the size of a nucleation complex should decrease in size tion, they coexist with a certain concentration of single for increasing levels of supersaturation21. So, according capsid proteins (monomers) or small protein groups to nucleation-and-growth theory, the dynamical exper- (oligomers). Light-scattering studies15,16 have shown that iments are best understood as taking place under con- the concentrations of capsid protein monomers or oli- ditions of high levels of supersaturation — that is, far gomers and of assembled capsids obey the law of mass from thermodynamic equilibrium. But if that is the case, action (LMA) of chemical thermodynamics, a direct then how can the equilibrium LMA apply? Moreover, consequence of the application of the second law of ther- when the protein concentration is reduced after capsid modynamics to multi-component solutions in thermo- formation, the capsids do not spontaneously disassemble dynamic equilibrium. This observation suggested that as would happen if the system really did obey the LMA. viral self-assembly could be understood as an equilib- Some insight in this strange interplay between equi- rium self-assembly process, similar to the formation librium and non-equilibrium properties can be obtained of micelles in surfactant-rich solutions17. Insight into from a simple model for the kinetics of capsid assembly23 the dynamics of capsid assembly was mainly achieved in which the capsid is treated as a dodecahedron com- in the past decade, typically involving more advanced posed of 12 pentamers with sticky edges. The capsids probes. We discuss some of these studies, first for the assemble in a solution of pentamers. At each assembly case of assembly of empty capsids and then for the case step, a pentamer is added to a partial capsid on a loca- of assembly of virions. tion that minimizes the energy of the partial capsid. This leads to a minimum energy assembly pathway E(n) Assembly dynamics of empty capsids where the index n runs from 1 to 12. Mathematically, the The first dynamical studies of the assembly of cap- assembly kinetics is similar to that of a one-dimensional sids used time-dependent light scattering and turbid- (1D) random walk across a non-uniform energy land- ity measurements to probe bulk solutions of capsid scape E(n). The cluster size distribution function C(n,t) proteins18. Capsid assembly was initiated by a reduction is the probability that

Load more