Modeling Viral Capsid Assembly

I present a review of the theoretical and computational methodologies that have been used to model the assembly of viral capsids. I discuss the capabilities and limitations of approaches ranging from equilibrium continuum theories to molecular dynamics simulations, and I give an overview of some of the important conclusions about virus assembly that have resulted from these modeling efforts. Topics include the assembly of empty viral shells, assembly around single-stranded nucleic acids to form viral particles, and assembly around synthetic polymers or charged nanoparticles for nanotechnology or biomedical applications. I present some examples in which modeling efforts have promoted experimental breakthroughs, as well as directions in which the connection between modeling and experiment can be strengthened.Comment: 42 pages (single column), 24 figures. Will appear in: Advances in Chemical Physics, vol. 155 (2013

Emergent Self-organization in Active Materials

Biological systems exhibit large-scale self-organized dynamics and structures which enable organisms to perform the functions of life. The field of active matter strives to develop and understand microscopically-driven nonequilibrium materials, with emergent properties comparable to those of living systems. This review will describe two recently developed classes of active matter systems, in which simple building blocks --- self-propelled colloidal particles or extensile rod-like particles --- self-organize to form macroscopic structures with features not possible in equilibrium systems. We summarize the recent experimental and theoretical progress on each of these systems, and we present simple descriptions of the physics underlying their emergent behaviors.Comment: Submitted to Current Opinion in Cell Biology. 9 pages (including references) and 3 figure

Diffusion-limited rates on low-dimensional manifolds with extreme aspect ratios

We consider a single-species diffusion-limited annihilation reaction with reactants confined to a two-dimensional surface with one arbitrarily large dimension and the other comparable in size to interparticle distances. This situation could describe reactants which undergo both longitudinal and transverse diffusion on long filamentous molecules (such as microtubules), or molecules that undergo truly one-dimensional translational diffusion (e.g. a transcription factor on DNA) but simultaneously exhibit diffusive behavior in a second dimension corresponding to a rotational or conformational degree of freedom. We combine simple analytical arguments and Monte Carlo simulations to show that the reaction rate law exhibits a crossover from one-dimensional to two-dimensional diffusion as a function of particle concentration and the size of the smaller dimension. In the case of a reversible binding reaction, the diffusion-limited reaction rate is given by the Smoluchowski expression, but the crossover is revealed in the statistics of particle collision histories. The results can also be applied to a particle-antiparticle annihilation reaction.Comment: 6 pages, 4 figures, submitted to Phys. Rev.

Recent advances in coarse-grained modeling of virus assembly

In many virus families, tens to thousands of proteins assemble spontaneously into a capsid (protein shell) while packaging the genomic nucleic acid. This review summarizes recent advances in computational modeling of these dynamical processes. We present an overview of recent technological and algorithmic developments, which are enabling simulations to describe the large ranges of length-and time-scales relevant to assembly, under conditions more closely matched to experiments than in earlier work. We then describe two examples in which computational modeling has recently provided an important complement to experiments.Comment: 9 pages, 3 figure

Allosteric control in icosahedral capsid assembly

During the lifecycle of a virus, viral proteins and other components self-assemble to form a symmetric protein shell called a capsid. This assembly process is subject to multiple competing constraints, including the need to form a thermostable shell while avoiding kinetic traps. It has been proposed that viral assembly satisfies these constraints through allosteric regulation, including the interconversion of capsid proteins among conformations with different propensities for assembly. In this article we use computational and theoretical modeling to explore how such allostery affects the assembly of icosahedral shells. We simulate assembly under a wide range of protein concentrations, protein binding affinities, and two different mechanisms of allosteric control. We find that, above a threshold strength of allosteric control, assembly becomes robust over a broad range of subunit binding affinities and concentrations, allowing the formation of highly thermostable capsids. Our results suggest that allostery can significantly shift the range of protein binding affinities that lead to successful assembly, and thus should be accounted for in models that are used to estimate interaction parameters from experimental data.Comment: Bill Gelbart's Festschrif

Encapsulation of a polymer by an icosahedral virus

The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication and enable use of capsids in nanomaterials applications. To this end, we perform Brownian dynamics on a coarse-grained model that describes the dynamics of icosahedral capsid assembly around a flexible polymer. We identify several mechanisms by which the polymer plays an active role in its encapsulation, including cooperative polymer-protein motions. These mechanisms are related to experimentally controllable parameters such as polymer length, protein concentration, and solution conditions. Furthermore, the simulations demonstrate that assembly mechanisms are correlated to encapsulation efficiency, and we present a phase diagram that predicts assembly outcomes as a function of experimental parameters. We anticipate that our simulation results will provide a framework for designing in vitro assembly experiments on single-stranded RNA virus capsids.Comment: This is an author-created, un-copyedited version of an article accepted for publication in Physical Biology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is expected to be published online in November 201

Mechanisms of virus assembly

Viruses are nanoscale entities containing a nucleic acid genome encased in a protein shell called a capsid, and in some cases surrounded by a lipid bilayer membrane. This review summarizes the physics that govern the processes by which capsids assembles within their host cells and in vitro. We describe the thermodynamics and kinetics for assembly of protein subunits into icosahedral capsid shells, and how these are modified in cases where the capsid assembles around a nucleic acid or on a lipid bilayer. We present experimental and theoretical techniques that have been used to characterize capsid assembly, and we highlight aspects of virus assembly which are likely to receive significant attention in the near future.Comment: Submitted to Annual Review of Physical Chemistr

Dynamics of Self-Propelled Particles Under Strong Confinement

We develop a statistical theory for the dynamics of non-aligning, non-interacting self-propelled particles confined in a convex box in two dimensions. We find that when the size of the box is small compared to the persistence length of a particle's trajectory (strong confinement), the steady-state density is zero in the bulk and proportional to the local curvature on the boundary. Conversely, the theory may be used to construct the box shape that yields any desired density distribution on the boundary. When the curvature variations are small, we also predict the distribution of orientations at the boundary and the exponential decay of pressure as a function of box size recently observed in 3D simulations in a spherical box.Comment: 6 pages, 5 figure

Faceted particles formed by the frustrated packing of anisotropic colloids on curved surfaces

We use computer simulations and simple theoretical models to analyze the morphologies that result when rod-like particles end-attach onto a curved surface, creating a finite-thickness monolayer aligned with the surface normal. This geometry leads to two forms of frustration, one associated with the incompatibility of hexagonal order on surfaces with Gaussian curvature, and the second reflecting the deformation of a layer with finite thickness on a surface with non-zero mean curvature. We show that the latter effect leads to a faceting mechanism. Above threshold values of the inter-particle attraction strength and surface mean curvature, the adsorbed layer undergoes a transition from orientational disorder to an ordered state that is demarcated by reproducible patterns of line defects. The number of facets is controlled by the competition between line defect energy and intra-facet strain. Tuning control parameters thus leads to a rich variety of morphologies, including icosahedral particles and irregular polyhedra. In addition to suggesting a new strategy for the synthesis of aspherical particles with tunable symmetries, our results may shed light on recent experiments in which rod-like HIV GAG proteins assemble around nanoscale particles.Comment: 9 pages, 8 figure

Active Particles on Curved Surfaces

Recent studies have highlighted the sensitivity of active matter to boundaries and their geometries. Here we develop a general theory for the dynamics and statistics of active particles on curved surfaces and illustrate it on two examples. We first show that active particles moving on a surface with no ability to probe its curvature only exhibit steady-state inhomogeneities in the presence of orientational order. We then consider a strongly confined 3D ideal active gas and compute its steady-state density distribution in a box of arbitrary convex shape.Comment: 9 pages, 1 figur