arXiv subjects

V. L. Lorman

Publications and source records attributed to V. L. Lorman.

9 recordsLinked to original sources

arXiv2015

Theory of morphological transformation of viral capsid shells during maturation process

In the frame of the Landau-Ginzburg formalism we propose a minimal phenomenological model for a morphological transformation in viral capsid shells. The transformation takes place during virus maturation process which renders virus infectious. The theory is illustrated on the example of the HK97 bacteriophage and viruses with similar morphological changes in the protective protein shell. The transformation is shown to be a structural phase transition driven by two order parameters. The first order parameter describes the isotropic expansion of the protein shell while the second one is responsible for the shape symmetry breaking and the resulting shell faceting. The group theory analysis and the resulting thermodynamic model make it possible to choose the parameter which discriminates between the icosahedral shell faceting often observed in viral capsids and the dodecahedral one observed in viruses of the Parvovirus family. Calculated phase diagram illustrates the discontinuous character of the virus morphological transformation and shows two qualitatively different paths of the transformation in a function of two main external thermodynamic parameters of the in vitro and in vivo experiments.

physics.bio-ph↗

arXiv2015

Structures of Spherical Viral Capsids as Quasicrystalline Tilings

Spherical viral shells with icosahedral symmetry have been considered as quasicrystalline tilings. Similarly to known Caspar-Klug quasi-equivalence theory, the presented approach also minimizes the number of conformations necessary for the protein molecule bonding with its neighbors in the shell, but is based on different geometrical principles. It is assumed that protein molecule centers are located at vertices of tiles with identical edges, and the number of different tile types is minimal. Idealized coordinates of nonequivalent by symmetry protein positions in six various capsid types are obtained. The approach describes in a uniform way both the structures satisfying the well-known Caspar-Klug geometrical model and the structures contradicting this model.

cond-mat.soft↗

arXiv2015

Instabilities and shape variation phase transitions in tubular lipid membranes

Changes of external parameters in proximity of critical point can increase thermal fluctuations of tubular lipid membrane (TLM) and result in variation of the membrane shape. The phase transitions in the system are shown to be controlled by a single effective parameter, which depends on the pressure difference between inner and outer regions of membrane and the applied stretching force. We determine an interval of the parameter values corresponding to the stability region of the cylindrical shape of TLM and investigate the behavior of the system in the vicinity of critical instabilities, where the cylindrical shape of membrane becomes unstable with respect to thermal fluctuations. The applied boundary conditions strongly influence the behavior of TLM. For example, small negative effective parameter corresponds to chiral shape of TLM only in the case of periodic boundary conditions. We also discuss other three types of phase transitions emerging in the system.

cond-mat.soft↗

arXiv2014

Density waves, dodecahedral geometry and structures of some spherical viral capsids

A pentagonal order formed by 360 proteins in the bovine papilloma viral capsid and structures of some smaller viral capsids are considered from a unified point of view based on the Landau crystallization theory. To simulate the capsid structures we map the planar pentagonal Penrose quasilattice (PPQ) constructed in the frames of the Landau theory onto a sphere through the dodecahedron nets of different sizes. Six different simplest nets containing from 60 to 360 positions occupied by proteins are proposed. Buckling of the initially planar capsid faces and a smooth conjugation of the protein orders at the adjacent faces are taken into account by means of two conditions imposed on the minimization of the capsid free energy. This conditional minimization results in two-component phason strain field, which describes the self-consistent reconstruction of quasicrystalline orders located at twelve faces of spherical dodecahedron. All six chiral structures obtained in this way are very similar to those of well-known spherical viral capsids. The theory proposed explains some general peculiarities of protein organization in capsids of small and medium-sized viruses.

cond-mat.soft↗

arXiv2013

Two-dimensional elasticity determines the low-frequency dynamics of single- and double-walled carbon nanotubes

We develop a continuous theory of low-frequency dynamics for nanotubes with truly two-dimensional (2D) walls constituted by single-atom monolayer. In this frame topological bending elasticity of the monolayer is not related to its vanishing macroscopic thickness. The proposed approach predicts completely new sound dispersions and radius dependences of non-resonant Raman-active modes frequencies in single-walled carbon nanotubes (SWCNT). Resulting relations are suitable for nanotubes identification and more complete or alternative characterization. The theory is also applied to describe the low-frequency dynamics of double-walled carbon nanotubes (DWCNT). It establishes a clear-cut relation between the radial breathing mode in SWCNT and breathing-like modes in DWCNT and fits the existing Raman data better than previously developed 3D continuous or discrete models. The results obtained constitute the basis for new quantitative studies of the low-frequency vibrational spectrum, heat capacity and heat transfer properties of carbon nanotubes.

cond-mat.mtrl-sci↗

arXiv2012

Bridging the Landau theory of crystallization and the cluster approach to quasicrystals

We propose the theory which unifies the description of quasicrystal assembly thermodynamics and quasicrystal structure formation by combining the Landau theory of crystallization and the cluster approach to quasicrystals. The theory is illustrated on the example of pentagonal Penrose quasilattice. The coordinates of the quasilattice nodes are calculated by minimizing the Landau free energy with the constraint imposed by internal organization of atomic clusters, without explicit use of high-dimensional crystallography. The procedure proposed establishes direct relations between the cluster organization, quasicrystalline structure and thermodynamic properties of the quasicrystalline state. The correspondence is shown between the basic features of the proposed algorithm for quasilattice construction, on the one hand, and the conventional projection method, on the other hand. It provides a new physical justification for high-dimensional crystallography methods application.

cond-mat.stat-mech↗

arXiv2012

Chiral Quasicrystalline Order and Dodecahedral Geometry in Exceptional Families of Viruses

On the example of exceptional families of viruses we i) show the existence of a completely new type of matter organization in nanoparticles, in which the regions with a chiral pentagonal quasicrystalline order of protein positions are arranged in a structure commensurate with the spherical topology and dodecahedral geometry, ii) generalize the classical theory of quasicrystals (QCs) to explain this organization, and iii) establish the relation between local chiral QC order and nonzero curvature of the dodecahedral capsid faces.

physics.bio-ph↗

arXiv2006

Density waves theory of the capsid structure of small icosahedral viruses

We apply Landau theory of crystallization to explain and to classify the capsid structures of small viruses with spherical topology and icosahedral symmetry. We develop an explicit method which predicts the positions of centers of mass for the proteins constituting viral capsid shell. Corresponding density distribution function which generates the positions has universal form without any fitting parameter. The theory describes in a uniform way both the structures satisfying the well-known Caspar and Klug geometrical model for capsid construction and those violating it. The quasiequivalence of protein environments in viral capsid and peculiarities of the assembly thermodynamics are also discussed.

cond-mat.soft↗

arXiv2006

Cytoskeleton influence on normal and tangent fluctuation modes in the red blood cells

We argue that the paradoxal softness of the red blood cells (RBC) in fluctuation spectra experiments is apparent. We show that the effective surface shear modulus $μ_s$ of the RBC obtained from fluctuation data and that measured in static deformation experiments have the same order of magnitude. A simple micromechanical model of the RBC developped for this purpose accounts for the influence of a finite-thickness cytoskeleton on the fluctuations of the composite membrane-cytoskeleton system. The spectrin network cytoskeleton with the bulk shear modulus estimated as $μ\approx105÷165$ Pa contributes to both normal and tangent fluctuations of the system and confines the fluctuations of the lipid membrane. The ratio of mean square amplitudes of the RBC normal and tangent fluctuations $ /< X_t^2>$ calculated in the frame of the model is 2-3 orders of magnitude smaller that it is in the free membrane with the same bending and shear moduli

physics.bio-ph↗