Buckling transition in icosahedral shells subjected to volume conservation constraint and pressure: relations to virus maturation

Minimal energy shapes of closed, elastic shells with twelve pentagonal disclinations introduced in otherwise hexagonally coordinated crystalline lattice are studied. The geometry and the total energy of shells are studied as a function of the elastic properties of the material they are made of. Particular emphasis is put on the buckling transition of the shells, that is a strong preference of the shell shapes to 'buckle out' in spatial regions close to the pentagonal disclinations for certain range of the elastic parameters of the problem. The transition effectively increases the mean square aspherity of shapes, making them look more like an icosahedron, rather than a sphere which is a preferred shape prior to the onset of the transition. The properties of the buckling transition are studied in cases when (i) the total volume enclosed by the elastic shell has to be fixed and when (ii) there is an internal pressure acting on the shell. This may be related to maturation process in non-enveloped dsDNA viruses, where the insertion of the genetic material in a pre-formed protein shell (viral coating) may effectively impose the fixed volume and/or pressure constraint. Several scenarios that may explain the experimentally observed feature of mature viruses being more aspherical (facetted) from their immature precursors are discussed and new predictions for the elastic properties of viral coatings are obtained on the basis of the presented studies.Comment: Version that is published in Phys. Rev. E 73, 061915 (2006). Elastic parameters of viral coatings (HK97) reestimated (Y_3D=1.1 GPa

Energies of sp2 carbon shapes with pentagonal disclinations and elasticity theory

Energies of a certain class of fullerene molecules (elongated, contracted, and regular icosahedral fullerenes) are numerically calculated using a microscopic description of carbon-carbon bonding. It is shown how these results can be interpreted and comprehended using the theory of elasticity that describes bending of a graphene plane. Detailed studies of a wide variety of structures constructed by application of the same general principle are performed, and analytical expressions for energies of such structures are derived. Comparison of numerical results with the predictions of a simple implementation of elasticity theory confirms the usefulness of the latter approach.Comment: A version published in Nanotechnolog

Coating the carbon nanotubes: Geometry of incommensurate long-range ordered physisorbed monolayers

The structures of long-range ordered physisorbed monolayer on a carbon nanotube are examined. Geometrical and energetical constraints determining the order of such monolayers are discussed. A number of symmetrically different, strongly bound adsorbate structures is found for Xe adsorbates, some of which differ very little in energy. The presented results suggest that the atomically uniform coating of carbon nanotubes is possible and offer a clear visualization of such coatings

Icosadeltahedral geometry of fullerenes, viruses and geodesic domes

I discuss the symmetry of fullerenes, viruses and geodesic domes within a unified framework of icosadeltahedral representation of these objects. The icosadeltahedral symmetry is explained in details by examination of all of these structures. Using Euler's theorem on polyhedra, it is shown how to calculate the number of vertices, edges, and faces in domes, and number of atoms, bonds and pentagonal and hexagonal rings in fullerenes. Caspar-Klug classification of viruses is elaborated as a specific case of icosadeltahedral geometry

Influence of salt and viral protein charge distribution on encapsidation of single-stranded viral RNA molecules

We examine the limits on viral composition that are set by the electrostatic interactions effected by the charge on the viral proteins, the single-stranded viral RNA molecule and monovalent salt ions in the solution. Within the mean-field model of viral energetics we demonstrate the prime importance of the salt concentration for the assembly of a virus. We find that the encapsidation of the viral RNA molecule is thermodynamically suppressed in solutions with high concentrations of monovalent salt. This effect is significantly less important in viruses with proteins whose charge distribution protrudes into the interior of the capsid, leading to an increase in the stability of such viruses in solutions with high salt concentrations. The delocalization of positive charge on the capsid protein arms thus profoundly increases reliability of viral assembly in high-salt solutions

Linear vs. nonlinear coupling effects in single- and multi-phonon atom-surface scattering

We present a comparative assessment of the features of inelastic atom-surface scattering spectra that are produced by several different forms of linear and nonlinear phonon coupling to the projectile atom. Starting from a simple theoretical model of atom-surface scattering and employing several recently developed exact numerical and approximate analytical methods we calculate and compare the scattering probabilities ensuing from each form of interaction and from each calculational scheme. This enables us to demonstrate that in the regime of thermal energy atom scattering from surfaces the dominant contributions to the zero-, one- and multi-phonon excitation probabilities obeying unitarity arise from linear coupling treated to all orders in the interaction.Comment: 3 figure

Debye-Waller factor in He => Cu(001) collisions revisited: the role of the interaction potentials

Following the recently accumulated information on the vibrational properties of the Cu(001) surface acquired through single- and multiphonon He atom scattering experiments and the concomitant theoretical investigations, we have reexamined the properties of the Debye-Waller factor (DWF) characteristic of the He \to Cu(001) collisions using the recently developed fully quantal and three-dimensional model of inelastic He atom scattering from surfaces. We have focused our attention on the role which the various He-surface model potentials with their characteristic interaction parameters (range of the interaction, momentum and energy transfer cut-offs etc.) employed in the interpretation of the scattering data may play in determining the magnitude of the DWF. By combining the He-Cu(001) potential whose repulsive and attractive components are both allowed to vibrate with the substrate phonon density of states encompassing anharmonic effects, we obtain the values of the DWF which agree nicely with the experimental data without invoking additional fitting parameters. On the other hand, by taking the phonon momentum transfer cut-off Q_c as an adjustable parameter, as has been frequently exploited in the literature, all the considered potentials can produce agreement with experiments by varying Q_c. The magnitudes of such best fit Q_c values are compared with those available in the literature and their physical significance is discussed

Role of electrostatic interactions in the assembly of empty spherical viral capsids

We examine the role of electrostatic interactions in the assembly of empty spherical viral capsids. The charges on the protein subunits that make the viral capsid mutually interact and are expected to yield electrostatic repulsion acting against the assembly of capsids. Thus, attractive protein-protein interactions of non-electrostatic origin must act to enable the capsid formation. We investigate whether the interplay of repulsive electrostatic and attractive interactions between the protein subunits can result in the formation of spherical viral capsids of a preferred radius. For this to be the case, we find that the attractive interactions must depend on the angle between the neighboring protein subunits (i.e. on the mean curvature of the viral capsid) so that a particular angle(s) is (are) preferred energywise. Our results for the electrostatic contributions to energetics of viral capsids nicely correlate with recent experimental determinations of the energetics of protein-protein contacts in Hepatitis B virus [P. Ceres and A. Zlotnick, Biochemistry {\bf 41}, 11525 (2002).Comment: Sent to publicatio

Electrostatic self-energy of a partially formed spherical shell in salt solution: application to stability of tethered and fluid shells -- viruses and vesicles

We investigate the electrostatics of a partially formed, charged spherical shell in a salt solution. We solve the problem numerically at the Poisson-Boltzmann level and analytically in the Debye-Huckel regime. From the results on energetics of partially formed shells we examine the stability of tethered (crystalline) and fluid shells towards rupture. We clearly delineate different regimes of stability towards rupture, where, for fluid shells, we also include the effects of bending elasticity of the shells. Our analysis shows how charging of the shell induces its instability towards rupture but also provides insight regarding growth of charged shells.Comment: 15 pages, 8 figures; submitte

Recovery temperature for nonclassical energy transfer in atom-surface scattering

Nonperturbative expressions are derived for the angular resolved energy transfer spectra in the quantum regime of multiphonon scattering of inert gas atoms from surfaces. Application to He atom scattering from a prototype heatbath Xe/Cu(111) shows good agreement with experiments. This enables a full quantum calculation of the total energy transfer $\mu$ and therefrom the much debated recovery or equilibrium temperature $T_{r}$ characteristic of zero energy transfer in gas-surface collisions in the free molecular flow regime. Classical universal character of $\mu$ and $T_{r}$ is refuted.Comment: 3 figure