Search results for: G. V. Novikov

Authors: Anupma Bansal, R. K. Gupta

Abstract:

In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.

Keywords: New Modified Novikov Equation, Lie Classical Method, Nonclassical Method, Modified (G'/G)-Expansion Method, Traveling Wave Solutions.

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Authors: Fadi Awawdeh, O. Alsayyed

Abstract:

New exact three-wave solutions including periodic two-solitary solutions and doubly periodic solitary solutions for the (2+1)-dimensional asymmetric Nizhnik-Novikov- Veselov (ANNV) system are obtained using Hirota's bilinear form and generalized three-wave type of ansatz approach. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an e¤ective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.

Keywords: Soliton Solution, Hirota Bilinear Method, ANNV System.

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Authors: G. V. Novikov, V. S. Sivozhelezov, S. S. Kolesnikov, K. V. Shaitan

Abstract:

The study reports about the influence of binding of orthosteric ligands as well as point mutations on the conformational dynamics of β-2-adrenoreceptor. Using molecular dynamics simulation we found that there was a little fraction of active states of the receptor in its apo (ligand free) ensemble corresponded to its constitutive activity. Analysis of MD trajectories indicated that such spontaneous activation of the receptor is accompanied by the motion in intracellular part of its alpha-helices. Thus receptor’s constitutive activity directly results from its conformational dynamics. On the other hand the binding of a full agonist resulted in a significant shift of the initial equilibrium towards its active state. Finally, the binding of the inverse agonist stabilized the receptor in its inactive state. It is likely that the binding of inverse agonists might be a universal way of constitutive activity inhibition in vivo. Our results indicate that ligand binding redistribute pre-existing conformational degrees of freedom (in accordance to the Monod-Wyman-Changeux-Model) of the receptor rather than cause induced fit in it. Therefore, the ensemble of biologically relevant receptor conformations is encoded in its spatial structure, and individual conformations from that ensemble might be used by the cell in conformity with the physiological behavior.

Keywords: Seven-transmembrane receptors, constitutive activity, activation, x-ray crystallography, principal component analysis, molecular dynamics simulation.

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