arXiv subjects

A. L. Talis

Publications and source records attributed to A. L. Talis.

4 recordsLinked to original sources

arXiv2013

Symmetrical laws of structure of helicoidally-like biopolymers in the framework of algebraic topology. IV. Topological stability of alpha helix and DNA structures

The structural parameters of alpha helix and some forms of DNA-structures are determined by methods of algebraic topology. These structures are locally periodic and correspond to the bifurcation point for minimal surfaces given by Weierstrass representation. The index of an unstable surface equals zero for them. As predicted by a theory of catastrophes, formation of such structures corresponds to lifting of configurational degeneration. Formation turns by half- turns from different helices in the implementation of double-structure as a single system, may indicate a kind of local crossing-over between motherboard and paternal helices (at least for some part of the helix). The role of the exchange have yet to understand given the impossibility of exchange between different turns spirals going counter rotating and shifted axis.

cond-mat.mtrl-sci↗

arXiv2013

Symmetrical laws of structure of helicoidally-like biopolymers in the framework of algebraic topology. III. Nature of the double and relations between the alpha helix and the various forms of DNA structures

In the frameworks of algebraic topology α-helix and different DNA-conformations are determined as the local latticed packing, confined by peculiar minimal surfaces which are similar to helicoids. These structures are defined by Weierstrass representation and satisfy to a zero condition for the instability index of the surface and availability of bifurcation points for these surfaces. The topological stability of such structures corresponds to removing of the configuration degeneracy and to existence of bifurcation points for these surfaces. The considered ordered non-crystalline structures are determined by homogeneous manifolds - algebraic polytopes, corresponding to the definite substructures the 8-dimensional lattice E8.The joining of two semi-turns of two spirals into the turn of a single two-spiral (helical) system is effected by the topological operation of a connected sum. The applied apparatus permits to determine a priori the symmetry parameters of the double spirals in A, B and Z forms DNA structures.

cond-mat.mtrl-sci↗

arXiv2012

Symmetrical laws of structure of helicoidally-like biopolymers in the framework of algebraic topology. II. α-helix and DNA structures

In the framework of algebraic topology the closed sequence of 4-dimensional polyhedra (algebraic polytopes) was defined. This sequence is started by the polytope {240}, discovered by Coxeter, and is determined by the second coordination sphere of 8-dimensional lattice E8. The second polytope of sequence allows to determine a topologically stable rod substructure that appears during multiplication by a non-crystallographic axis 40/11 of the starting union of 4 tetrahedra with common vertex. When positioning the appropriate atoms tin positions of special symmetry of the staring 4 tetrahedra, such helicoid determines an α-helix. The third polytope of sequence allows to determine the helicoidally-like union of rods with 12-fold axis, which can be compare with Z-DNA structures. This model is defined as a local lattice rod packing, contained within a surface of helicoidally similar type, which ensures its topological stability, as well as possibility for it to be transformed into other forms of DNA structures. Formation of such structures corresponds to lifting a configuration degeneracy, and the stability of a state - to existence of a point of bifurcation. Furthermore, in the case of DNA structures, a second "security check" possibly takes place in the form of local lattice (periodic) property using the lattices other than the main ones.

cond-mat.mtrl-sci↗

arXiv2012

Symmetrical laws of structure of helicoidally-like biopolymers in the framework of algebraic topology. I. Root lattice E8 and the closed sequence of algebraic polytopes

In the framework of algebraic topology the closed sequence of 4-dimensional polyhedra(algebraic polytopes) was defined. These polytopes were determined by the second coordination sphere of 8-dimensional lattice E8. The ordered non-crystalline structure is determined by a chain of constructions of algebraic topology: an algebraic polytope, a homogeneous manifold in a 3-dimensional Euclidean space E3, locally-homogeneous manifold, locally minimal surface, one-parameter family of helicoids, bundle (cover) with a base of cell complexes, local-lattice packing of cell complexes into a substructure of E3, determined by helicoids. The formalism being developed allows one to surmount restrictions of classical crystallography and to single out a class of ordered non-crystalline structures, invariant with respect to structures determined by the lattice E8. The topological stability of such substructures is determined by their relatedness to Weierstrass' representation, as well as the condition that the instability index of the surface equals zero. Formation of such structures corresponds to lifting a configuration degeneracy, and the stability of a state - to existence of a point of bifurcation.

math-ph↗