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Unlike double-stranded DNA, single-stranded RNA can be spontaneously packaged into spherical capsids by viral capsid protein (CP) because it is a more compact and flexible polymer. Many systematic investigations of this self-assembly process have been carried out using CP from cowpea chlorotic mottle virus, with a wide range of sequences and lengths of single-stranded RNA. Among these studies are measurements of the relative packaging efficiencies of these RNAs into spherical capsids. In this work, we address a fundamental issue that has received very little attention, namely the question of the preferred curvature of the capsid formed around different RNA molecules. We show in particular that homopolymers of RNA—polyribouridylic acid and polyriboadenylic acid—form exclusively T = 2-sized (∼22-nm diameter) virus-like particles (VLPs) when mixed with cowpea chlorotic mottle virus CP, independent of their length, ranging from 500 to more than 4000 nucleotides. This is in contrast to “normal-composition” RNAs (i.e., molecules with comparable numbers of each of the four nucleotides and hence capable of developing a large amount of secondary structure because of intramolecular complementarity/basepairing); a curvature corresponding to T = 3-size (∼28 nm in diameter) is preferred for the VLPs formed with such RNAs. Our work is consistent with the preferred curvature of VLPs being a consequence of interaction of CP with RNA—in particular, the presence or absence of short RNA duplexes—and suggests that the equilibrium size of the capsid results from a trade-off between this optimum size and the cost of confinement.

Metabolite-dependent conformational switching in RNA riboswitches is now widely accepted as a critical regulatory mechanism for gene expression in bacterial systems. More recently, similar gene regulation mechanisms have been found to be important for viral systems as well. One of the most abundant and best-studied systems is the tRNA-like structure (TLS) domain, which has been found to occur in many plant viruses spread across numerous genera. In this work, folding dynamics for the TLS domain of Brome Mosaic Virus have been investigated using single-molecule fluorescence resonance energy transfer techniques. In particular, burst fluorescence methods are exploited to observe metal-ion ([Mn+])-induced folding in freely diffusing RNA constructs resembling the minimal TLS element of brome mosaic virus RNA3. The results of these experiments reveal a complex equilibrium of at least three distinct populations. A stepwise, or consecutive, thermodynamic model for TLS folding is developed, which is in good agreement with the [Mn+]-dependent evolution of conformational populations and existing structural information in the literature. Specifically, this folding pathway explains the metal-ion dependent formation of a functional TLS domain from unfolded RNAs via two consecutive steps: 1) hybridization of a long-range stem interaction, followed by 2) formation of a 3′-terminal pseudoknot. These two conformational transitions are well described by stepwise dissociation constants for [Mg2+] (K1 = 328 ± 30 μM and K2 = 1092 ± 183 μM) and [Na+] (K1 = 74 ± 6 mM and K2 = 243 ± 52 mM)-induced folding. The proposed thermodynamic model is further supported by inhibition studies of the long-range stem interaction using a complementary DNA oligomer, which effectively shifts the dynamic equilibrium toward the unfolded conformation. Implications of this multistep conformational folding mechanism are discussed with regard to regulation of virus replication.

Coarse-grained elastic network models elucidate the fluctuation dynamics of proteins around their native conformations. Low-frequency collective motions derived by simplified normal mode analysis are usually involved in biological function, and these motions often possess noteworthy symmetries related to the overall shape of the molecule. Here, insights into these motions and their frequencies are sought by considering continuum models with appropriate symmetry and boundary conditions to approximately represent the true atomistic molecular structure. We solve the elastic wave equations analytically for the case of spherical symmetry, yielding a symmetry-based classification of molecular motions together with explicit predictions for their vibrational frequencies. We address the case of icosahedral symmetry as a perturbation to the spherical case. Applications to lumazine synthase, satellite tobacco mosaic virus, and brome mosaic virus show that the spherical elastic model efficiently provides insights on collective motions that are otherwise obtained by detailed elastic network models. A major utility of the continuum models is the possibility of estimating macroscopic material properties such as the Young's modulus or Poisson's ratio for different types of viruses.

Cowpea chlorotic mottle virus (CCMV) forms highly elastic icosahedral protein capsids that undergo a characteristic swelling transition when the pH is raised from 5 to 7. Here, we performed nano-indentation experiments using an atomic force microscope to track capsid swelling and measure the shells’ Young’s modulus at the same time. When we chelated Ca2+ ions and raised the pH, we observed a gradual swelling of the RNA-filled capsids accompanied by a softening of the shell. Control experiments with empty wild-type virus and a salt-stable mutant revealed that the softening was not strictly coupled to the swelling of the protein shells. Our data suggest that a pH increase and Ca2+ chelation lead primarily to a loosening of contacts within the protein shell, resulting in a softening of the capsid. This appears to render the shell metastable and make swelling possible when repulsive forces among the capsid proteins become large enough, which is known to be followed by capsid disassembly at even higher pH. Thus, softening and swelling are likely to play a role during inoculation.

The capsid is modeled as a region of constant electron density located between inner and outer envelopes that exhibit icosahedral symmetry. For computational purposes the envelopes are represented as truncated sums of weighted icosahedral harmonics. Methods are described for estimating the weights from x-ray solution scattering patterns based on nonlinear least squares, and two examples of the procedure, for viruses with known atomic-resolution structures, are given.

The long wavelength, low-frequency modes of motion are the relevant motions for understanding the continuum mechanical properties of biomolecules. By examining these low-frequency modes, in the context of a spherical harmonic basis set, we identify four elastic moduli that are required to describe the two-dimensional elastic behavior of capsids. This is in contrast to previous modeling and theoretical studies on elastic shells, which use only the two-dimensional Young's modulus (Y) and the bending modulus (κ) to describe the system. Presumably, the heterogeneity of the structure and the anisotropy of the biomolecular interactions lead to a deviation from the homogeneous, isotropic, linear elastic shell theory. We assign functional relevance of the various moduli governing different deformation modes, including a mode primarily sensed in atomic force microscopy nanoindentation experiments. We have performed our analysis on the T = 3 cowpea chlorotic mottle virus and our estimate for the nanoindentation modulus is in accord with experimental measurements.

The major protective coat of most viruses is a highly symmetric protein capsid that forms spontaneously from many copies of identical proteins. Structural and mechanical properties of such capsids, as well as their self-assembly process, have been studied experimentally and theoretically, including modeling efforts by computer simulations on various scales. Atomistic models include specific details of local protein binding but are limited in system size and accessible time, while coarse grained (CG) models do get access to longer time and length scales but often lack the specific local interactions. Multi-scale models aim at bridging this gap by systematically connecting different levels of resolution. A CG model for CCMV (Cowpea Chlorotic Mottle Virus), a virus with an icosahedral shell of 180 identical proteins, is developed, where parameters are derived from atomistic simulations of capsid protein dimers in aqueous solution. In particular, a new method is introduced to combine the MARTINI CG model with a supportive elastic network based on structural fluctuations of individual proteins. In the parametrization process, both network connectivity and strength are optimized. This elastic-network optimized CG model, which solely relies on atomistic data of small units (dimers), is able to correctly predict inter- protein conformational flexibility and properties of larger aggregates. Here, aggregates of 20 and more capsid proteins are chosen that are possible intermediates in the assembly process or otherwise relevant for the mechanical stability of the CCMV virus shell. Furthermore, it is shown that this CG model reproduces experimental (Atomic Force Microscopy) indentation measurements of the entire viral capsid. Thus it is shown that one obvious goal for hierarchical modeling, namely predicting elastic aspects of larger protein complexes from models that are carefully parametrized on smaller units, is achievable.

X-ray scattering data and electron microscope observations are presented for bromegrass mosaic virus. Its radial density distribution is obtained from the Fourier transform of the amplitudes of the scattered x-rays. The results indicate that the virus is 260 A in diameter, it has an almost empty central cavity which is about 80 A in diameter, and the regions occupied by RNA and protein are approximately equal in average density. Electron micrographs of negatively stained preparations also give an outside diameter of 260 A and indicate that there is a central region about 90 A in diameter into which uranyl acetate can penetrate. Positively stained preparations indicate that the nucleic acid is concentrated in a shell-shaped region which is in turn surrounded by a shell of protein. In order for the RNA and protein regions to have the same average electron density the RNA must have a hydration of 1.29 gm of water per gm of RNA and the protein must have a hydration of 0.24 gm of water per gm of protein.

A series of recent nanoindentation experiments on the protein shells (capsids) of viruses has established atomic force microscopy (AFM) as a useful framework for probing the mechanics of large protein assemblies. Specifically these experiments provide an opportunity to study the coupling of the global assembly response to local conformational changes. AFM experiments on cowpea chlorotic mottle virus, known to undergo a pH-controlled swelling conformational change, have revealed a pH-dependent mechanical response. Previous theoretical studies have shown that homogeneous changes in shell geometry can play a significant role in the mechanical response. This article develops a method for accurately capturing the heterogeneous geometry of a viral capsid and explores its effect on mechanical response with a nonlinear continuum elasticity model. Models of both native and swollen cowpea chlorotic mottle virus capsids are generated from x-ray crystal structures, and are used in finite element simulations of AFM indentation along two-, three-, and fivefold icosahedral symmetry orientations. The force response of the swollen capsid model is observed to be softer by roughly a factor of two, significantly more nonlinear, and more orientation-dependent than that of a native capsid with equivalent elastic moduli, demonstrating that capsid geometric heterogeneity can have significant effects on the global structural response.

Bromegrass mosaic virus undergoes a reversible decrease in its sedimentation coefficient when the pH is raised above pH 6.7. At pH 6 the sedimentation coefficient is 87 S, at pH 7 it is 79 S. Intrinsic viscosities determined at pH 6 and 7 are 3.64 and 5.5 x 10(-2) dl/gm. Diffusion coefficients are 1.56 x 10(-7) cm(2)/sec. and 1.44 x 10(-7) cm(2)/sec., respectively. Radii of gyration, measured by x-ray scattering, are 106 and 128 A. However, appropriate combination of sedimentation, diffusion, and viscosity coefficients at pH 6 and 7 yield the same molecular weight. Also, the zero-angle value of x-ray-scattered intensity, which is a function of molecular weight, is the same at the two pH's. These results suggest that bromegrass mosaic virus particles undergo a pH-induced change in structure. This change causes, among other things, an increase in the susceptibility of the particles to degradation by pancreatic ribonuclease. The shape of the titration curve between pH 6.3 and 6.9 is anomalous.