Session L34: Focus Session: Virus-Inspired Supramolecular Structures

Size regulation of ss RNA viruses

Under the right circumstances, single-stranded RNA viruses self assemble spontaneously from aqueous solutions containing the subunit proteins and genome molecules. While a monodisperse size distribution is common for most icosasedral viruses, the size of the spherical viral shells can vary from one type of virus to another. We study the effect of genome length, genome concentration and protein concentration on the size of spherical viral capsids in the absence of spontaneous curvature and bending energy. We find that based on the size of genome, it could be advantageous to have relatively small spherical shells with higher curvature rather than bigger and thus flatter shells. Furthermore, we find that the small ratio of genome to protein concentration could, quite interestingly, result in larger spherical shells. Experimental data on the encapsidation of model genome supports these findings.   

Synthesis and properties of virus-like particles

The principles underlying self-assembly of virus-like particles (VLP), which are composed of an icosahedral virus protein coat encapsulating a nanoparticle core are discussed. Such VLPs have potential practical utility as biomedical imaging and sensing tools, as novel functional materials, and as experimental models for molecular self-assembly of quasi-spherical molecular cages. Moreover, we show that, as a consequence of their regular protein surface, VLPs readily form three-dimensional crystals having optical properties influenced by multipolar plasmonic coupling.   

Soft modes near the buckling transition of icosahedral shells

Closed shells comprised of pentamers and hexamers may be smooth and nearly spherical, or sharply faceted and icosahedral, depending on the elastic constants of the shell. We interpret the transition from smooth to faceted as a soft-mode transition. Our analysis is based on the phonon spectrum of a simplified mass-and-spring model of the shell. In contrast to the case of a disclinated planar network, where the transition is sharply defined, the mean curvature of the sphere smooths the transition rather like a magnetic field smears out a ferromagnetic phase transition. We define susceptibilities of the transition as the response to forces applied at vertices, edges and faces of an icosahedron. At the soft-mode transition the vertex susceptibility is largest, but as the shell becomes faceted the edge and face susceptibilities greatly exceed the vertex susceptibility.   

A Precise Packing Sequence for Self-Assembled Convex Structures

We present molecular simulations of the self-assembly of cone-shaped particles with patchy, attractive interactions[1,2]. Upon cooling from random initial conditions, we find that the cones self assemble into clusters and that clusters comprised of particular numbers of cones have a unique and precisely packed structure that is robust over a range of cone angles. These precise clusters form precise packing sequence that for small sizes is identical to that observed in evaporation-driven assembly of colloidal spheres. This sequence is reproduced and extended in simulations of two simple models of spheres self-assembling from random initial conditions subject to convexity constraints, and contains six of the most common virus capsid structures obtained in vivo including large chiral clusters, and a cluster that may correspond to several non- icosahedral, spherical virus capsid structures obtained in vivo. For prolate spheroidal convexity conditions, we demonstrate the formation of several prolate virus structures from self-assembling hard spheres[3]. \newline [1] Chen T, Zhang ZL, Glotzer SC, PNAS, in press (http://xxx.lanl.gov/pdf/cond-mat/ 0608592) [2] Chen T, Zhang ZL, Glotzer SC, http://xxx.lanl.gov/pdf/cond-mat/0608613 [3] Chen T, Glotzer SC http://xxx.lanl.gov/pdf/q-bio.BM/0608040   

Charge profiles inside sigle-stranded viruses

Many single stranded viruses pack their genome using flexible peptide arms of capsid proteins. Genome binding may then be mapped onto interaction between polyelectrolyte and charged brush. In this talk we pursue an electrostatic model of genome binding and address several questions on charge profiles inside capsids.   

Buckling and Mechanical Failure of Viral Shells

We present a combined theoretical and experimental study of the structural failure of viral shells under mechanical stress due to indentation by atomic force microscopy. Modeling the indentation of icosahedral viruses with two-dimensional continuum shell elasticity theory, we find that the fivefold-symmetric disclinations precipitate geometric ``buckling'' instabilities, leading to structural collapse at indentation loads that are significantly lower than those which buckle perfectly spherical shells. Coincident with these instabilities, discontinuities in the force-indentation curve appear when the so-called F\"oppl-von K\'arm\'an (FvK) number exceeds a critical value. A nano-indentation study of a viral shell subject to a soft-mode instability, where the stiffness of the shell decreases with increasing pH, confirms the predicted onset of failure as a function of the FvK number.   

Using The Interfaces In Self-Assembled Protein Cage Architectures For Materials Synthesis

The self-assembled architectures of viral capsids have been used as models for understanding processes of encapsulation of both hard and soft materials. We have explored modifications to the exterior and interior interfaces of viral (and other protein cage architectures) while maintaining the assembly of stable icosahedral capsid particles. This has allowed us to utilize the high symmetry of the viral capsid to engineer unique functionality for highly ordered multivalent presentation for controlled nucleation of hard inorganic materials and packaging of soft organic materials. Of particular interest is the nature of the hard-soft interface in these systems. Through the incorporation of peptides derived from phage display we can direct the nucleation and growth of specific inorganic phases, constrained within the protein cage architecture. The coupled synthesis of cage-constrained ferrimagnetic and antiferromagnetic nanoparticles results in formation of stable composites that exhibit unique exchange bias magnetic coupling. To understand the role of the protein in directing inorganic materials synthesis, we have probed the protein-mineral interface using genetic and chemical modifications, spatially controlled inorganic synthesis, high-resolution transmission electron microscopy, and cryo-electron microscopy and image reconstruction. The role of protein interfaces in these assembled protein cage architectures has been explored to understand and exploit packaging of a wide range of materials as diverse as nucleic acids, drugs, and inorganic nano-materials.   

Direct measurement of the elastic properties of the Wiseana Iridovirus (WIV) capsid using Brillioun Spectroscopy

Viral capsids are of great interest for their potential as templates or scaffolds to direct the growth of secondary structures for various sensing, energy harvesting, and photonic devices. However, due to their size (10's-100's nms) and complex structure (symmetrically repeating protein subunits); the mechanical properties of viruses and viral films has yet to be directly measured. We measured the phononic spectra of virus capsids assembled on silicon substrates using Brillioun Light Scattering at different scattering wave vectors. The phononic spectrum provides a direct measurement of the mechanical properties of individual viruses as well as that of the collective assemblage. The spectra are analyzed to understand the origins of both the propagating phonons as well as those that remain localized within individual viruses. Understanding the mechanical properties of the viruses is critical for the reliable utilization of viral technologies, as well as contributing to the understanding of the impact of capsid flexibility and rigidity on cellular infection by viruses.   

Viral Capsid Assembly in a crowded environment

While many experimental and all theoretical studies of viral capsid assembly dynamics focus on assembly in dilute solution, viruses replicate in the cell, which presents a crowded environment composed of numerous confining sub-volumes. We examine the effects of crowding and confinement on the formation of T1 capsidlike objects by using Newtonian dynamics simulations[1]. Subunits have excluded volume and asymmetric pairwise bonding interactions between complementary sides [1] and are confined to a three-dimensional box. We address the effects of finite system size on assembly dynamics by varying the system size with a fixed volume fraction of capsid subunits, and by varying the system size with a fixed number of subunits. In both cases, we find a non-monotonic variation in capsid formation times as the system dimensions become comparable with the size of a capsid. By analyzing assembly mechanisms, we probe the nature of assembly in crowded and confined environments. This work is supported by NSF DMR-0403997. \newline [1] M. Hagan and D. Chandler, Biophys. J. v 91, 2006   

Microrheology of Viscoelastic Shells: Applications to Viral Capsids

We study the microrheology of nanoparticles shells [cite: Dinsmore et al. Science 298, 1006 (2002)] and viral capsids by computing the fluctuation spectrum of a viscoelastic spherical shell that is permeable to the surrounding solvent. We determine analytically the overdamped dynamics of the shear, bend, and compression modes of the shell coupled to the solvent both inside and outside the sphere in the zero Reynolds number limit. In this talk we identify fundamental length and time scales in the system, and compute the thermal correlation function of displacements of antipodal points on the sphere. We describe how such an antipodal correlation function, which should be measurable in new AFM-based microrheology experiments, can probe the viscoelasticity of these synthetic and biological shells constructed of nanoparticles. We then discuss some of the remaining challenges in interpreting these measurements.