Influence of boundary conditions on instabilities and shape phase transitions in tubular lipid membranes

Physical models of unconventional capsid structures and assembly thermodynamics

Contrary to the usual “rigid supermolecular assembly” paradigm of chromatin structure, we propose to analyze its eventual ordered state in terms of symmetry properties of individual nucleosomes that give rise to mesophase order parameters, like in many other soft-matter systems. Basing our approach on the Landau–de Gennes phenomenology, we describe the mesoscale order in chromatin by antipolar and anticlinic correlations of chiral individual nucleosomes. This approach leads to a unifying physical picture of a whole series of soft locally ordered states with different apparent structures, including the recently observed heteromorphic chromatin, stemming from the antipolar arrangement of nucleosomes complemented by their chiral twisting. Properties of these states under an external force field can reconcile apparently contradictory results of single-molecule experiments.

Spherical viral shells with icosahedral symmetry are 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 and Klug geometrical model and the structures contradicting this model.

We model the ParABS system, which is a bacterial DNA Segregation Apparatus.

We develop methods based on theory of representations of continuous and discrete groups; theory of invariants for the groups not-generated by reflections; and theory of bifurcations of invariants functionals. It is applied to the protein arrangement in Satellite Tobacco Mosaic virus, Cowpea Chlorotic Mottle virus and Sindbis virus (which verify Caspar and Klug selection rules) and in L-A virus, Dengue virus and Murine Polyoma virus (which violate Caspar and Klug rules).

In the present work we develop an approach which associates viral capsid formation with the unconventional crystallization process and propose to describe the capsid self-assembly using a generalization of the Landau theory of crystallization. It is based on the successive application of methods of a) theory of representations of continuous and discrete groups; b) theory of invariants for the groups not-generated by reflections; c) theory of bifurcations of invariant functionals. To compare the predictions of the theory with the available cryoelectronic microscopy and AFM data we use irreducible density distribution functions which generate the protein positions on a spherical capsid.