Vibron Self--trapped States in Biological Macromolecules: Comparison of Different Theoretical Approaches

A study of the applicability of the variational treatments based on using of the modified Lang-Firsov unitary transformation (MLF method) in the investigation of the vibron self-trapped states in biological macromolecular chains are presented. We compare the values of the ground state energy predicted by MLF methods with the values of the ground state energy predicted by the standard small-polaron theory, for various values of the basic energy parameters of the system. We obtain regions in system parameter space where MLF approach gives better description of the vibron states.Comment: 8 pages, 4 figures, To appear in the Proceedings of Conference Dubna-Nano2012 (July 9 - 14, 2012

Vibron transport in macromolecular chains

We study the hopping mechanism of the vibron excitation transport in the simple 1D model of biological macromolecular chains. We supposed that the vibron interaction with thermal oscillations of the macromolecular structural elements will result in vibron self -trapping, and the formation of the partial dressed vibron state. With use of the modified Holstein polaron model, we calculate vibron diffusivity in dependence of the basic system parameters and temperature. We obtain that the vibron diffusivity smoothly decreases in non adiabatic limit when the strength of the vibron-phonon coupling grows. However this dependence becomes by discontinuous one in case of growth of the adiabaticity of the system. The value of the critical point depends of the system temperature, and at room temperatures it belongs to the low or intermediate coupling regime. We discuss an application of these results to study of vibron transport to 3D bundles of such macromolecules chains considering it as polymer nanorods and to 2D polymer films organized from such macromolecules.Comment: 4 pages, 6 figures, contribution to the Proceedings of the Conference "Physical mesomechanics of multi-level systems`2014", September 3-5 2014, Tomsk, Russi

From Davydov solitons to decoherence-free subspaces: self-consistent propagation of coherent-product states

The self-consistent propagation of generalized $D_{1}$ [coherent-product] states and of a class of gaussian density matrix generalizations is examined, at both zero and finite-temperature, for arbitrary interactions between the localized lattice (electronic or vibronic) excitations and the phonon modes. It is shown that in all legitimate cases, the evolution of $D_{1}$ states reduces to the disentangled evolution of the component $D_{2}$ states. The self-consistency conditions for the latter amount to conditions for decoherence-free propagation, which complement the $D_{2}$ Davydov soliton equations in such a way as to lift the nonlinearity of the evolution for the on-site degrees of freedom. Although it cannot support Davydov solitons, the coherent-product ansatz does provide a wide class of exact density-matrix solutions for the joint evolution of the lattice and phonon bath in compatible systems. Included are solutions for initial states given as a product of a [largely arbitrary] lattice state and a thermal equilibrium state of the phonons. It is also shown that external pumping can produce self-consistent Frohlich-like effects. A few sample cases of coherent, albeit not solitonic, propagation are briefly discussed.Comment: revtex3, latex2e; 22 pages, no figs.; to appear in Phys.Rev.E (Nov.2001

Continuum Surface Energy from a Lattice Model

We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with general binary interactions in two dimensions. A new bond counting approach is used, which reduces the problem to the lattice point problem of number theory. The main contribution is an explicit formula for the surface energy density as a function of the deformation gradient and boundary normal. The result is valid for a large class of domains, including faceted (polygonal) shapes and regions with piecewise smooth boundaries.Comment: V. 1: 10 pages, no fig's. V 2: 23 pages, no figures. Misprints corrected. Section 3 added, (new results). Intro expanded, refs added.V 3: 26 pages. Abstract changed. Section 2 split into 2. Section (4) added material. V 4, 28 pages, Intro rewritten. Changes in Sec.5 (presentation only). Refs added.V 5,intro changed V.6 address reviewer's comment

Two-vibron bound states in alpha-helix proteins : the interplay between the intramolecular anharmonicity and the strong vibron-phonon coupling

The influence of the intramolecular anharmonicity and the strong vibron-phonon coupling on the two-vibron dynamics in an $\alpha$-helix protein is studied within a modified Davydov model. The intramolecular anharmonicity of each amide-I vibration is considered and the vibron dynamics is described according to the small polaron approach. A unitary transformation is performed to remove the intramolecular anharmonicity and a modified Lang-Firsov transformation is applied to renormalize the vibron-phonon interaction. Then, a mean field procedure is realized to obtain the dressed anharmonic vibron Hamiltonian. It is shown that the anharmonicity modifies the vibron-phonon interaction which results in an enhancement of the dressing effect. In addition, both the anharmonicity and the dressing favor the occurrence of two different bound states which the properties strongly depend on the interplay between the anharmonicity and the dressing. Such a dependence was summarized in a phase diagram which characterizes the number and the nature of the bound states as a function of the relevant parameters of the problem. For a significant anharmonicity, the low frequency bound states describe two vibrons trapped onto the same amide-I vibration whereas the high frequency bound states refer to the trapping of the two vibrons onto nearest neighbor amide-I vibrations.Comment: may 2003 submitted to Phys. Rev.

Nodal domains of Maass forms I

This paper deals with some questions that have received a lot of attention since they were raised by Hejhal and Rackner in their 1992 numerical computations of Maass forms. We establish sharp upper and lower bounds for the $L^2$-restrictions of these forms to certain curves on the modular surface. These results, together with the Lindelof Hypothesis and known subconvex $L^\infty$-bounds are applied to prove that locally the number of nodal domains of such a form goes to infinity with its eigenvalue.Comment: To appear in GAF

Backup Mechanisms Maintain PACAP/VIP-Induced Arterial Relaxations in Pituitary Adenylate Cyclase-Activating Polypeptide-Deficient Mice

BACKGROUND: Pituitary adenylate cyclase-activating polypeptide (PACAP) is a multifunctional neuropeptide in the VIP/secretin/glucagon peptide superfamily. Two active forms, PACAP1-38 and PACAP1-27, act through G protein-coupled receptors, the PAC1 and VPAC1/2 receptors. Effects of PACAP include potent vasomotor activity. Vasomotor activity and organ-specific vasomotor effects of PACAP-deficient mice have not yet been investigated; thus, the assessment of its physiological importance in vasomotor functions is still missing. We hypothesized that backup mechanisms exist to maintain PACAP pathway activity in PACAP knockout (KO) mice. Thus, we investigated the vasomotor effects of exogenous vasoactive intestinal peptide (VIP) and PACAP polypeptides in PACAP wild-type (WT) and PACAP-deficient (KO) male mice. METHODS: Carotid and femoral arteries were isolated from 8- to 12-week-old male WT and PACAP-KO mice. Vasomotor responses were measured with isometric myography. RESULTS: In the arteries of WT mice the peptides induced relaxations, which were significantly greater to PACAP1-38 than to PACAP1-27 and VIP. In KO mice, PACAP1-38 did not elicit relaxation, whereas PACAP1-27 and VIP elicited significantly greater relaxation in KO mice than in WT mice. The specific PAC1R and VPAC1R antagonist completely blocked the PACAP-induced relaxations. CONCLUSION: Our data suggest that in PACAP deficiency, backup mechanisms maintain arterial relaxations to polypeptides, indicating an important physiological role for the PACAP pathway in the regulation of vascular tone