Analytical study on the generalized Davydov model in the alpha helical proteins

In this paper, we investigate the dynamics of a generalized Davydov model derived from an infinite chain of alpha helical protein molecules which contain three hydrogen bonding spines running almost parallel to the helical axis. Through the introduction of the auxiliary function, the bilinear form, one-, two- and three-soliton solutions for the generalized Davydov model are obtained firstly. Propagation and interactions of solitons have been investigated analytically and graphically. The amplitude of the soliton is only related to the complex parameter [Formula: see text] and real parameter [Formula: see text] with a range of [Formula: see text]. The velocity of the soliton is only related to the complex parameter [Formula: see text], real parameter [Formula: see text], lattice parameter [Formula: see text], and physical parameters [Formula: see text], [Formula: see text] and [Formula: see text]. Overtaking and head-on interactions of two and three solitons are presented. The common in the interactions of three solitons is the directions of the solitons change after the interactions. The soliton derived in this paper is expected to have potential applications in the alpha helical proteins.

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Integrability and soliton solutions for an inhomogeneous generalized fourth-order nonlinear Schrödinger equation describing the inhomogeneous alpha helical proteins and Heisenberg ferromagnetic spin chains

Physica B Condensed Matter ◽

10.1016/j.physb.2012.11.038 ◽

2013 ◽

Vol 411 ◽

pp. 166-172 ◽

Cited By ~ 10

Author(s):

Pan Wang ◽

Bo Tian ◽

Yan Jiang ◽

Yu-Feng Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Spin Chains ◽

Nonlinear Schrödinger ◽

Alpha Helical Proteins ◽

Helical Proteins

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First-Principles Calculations of High-Pressure Physical Properties of Ti0.5Ta0.5 Alloy

Symmetry ◽

10.3390/sym12050796 ◽

2020 ◽

Vol 12 (5) ◽

pp. 796

Author(s):

Fang Yu ◽

Yu Liu

Keyword(s):

High Pressure ◽

Physical Properties ◽

First Principles ◽

Theoretical Study ◽

Applied Pressure ◽

Lattice Parameter ◽

Physical Parameters ◽

First Principles Calculations ◽

Analysis Method ◽

Metallic Bond

In this paper, an in-depth theoretical study on some physical properties of Ti0.5Ta0.5 alloy with systematic symmetry under high pressure is conducted via first-principles calculations, and relevant physical parameters are calculated. The results demonstrate that the calculated parameters, including lattice parameter, elastic constants, and elastic moduli, fit well with available theoretical and experimental data when the Ti0.5Ta0.5 alloy is under T = 0 and P = 0 , indicating that the theoretical analysis method can effectively predict the physical properties of the Ti0.5Ta0.5 alloy. The microstructure and macroscopic physical properties of the alloy cannot be destroyed as the applied pressure ranges from 0 to 50GPa, but the phase transition of crystal structure may occur in the Ti0.5Ta0.5 alloy if the applied pressure continues to increase according to the TDOS curves and charge density diagram. The value of Young’s and shear modulus is maximized at P = 25 GPa . The anisotropy factors A ( 100 ) [ 001 ] and A ( 110 ) [ 001 ] are equal to 1, suggesting the Ti0.5Ta0.5 alloy is an isotropic material at 28 GPa, and the metallic bond is strengthened under high pressure. The present results provide helpful insights into the physical properties of Ti0.5Ta0.5 alloy.

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Intermediate Filaments and other Alpha-Helical Proteins

Molecules of the Cytoskeleton ◽

10.1007/978-1-349-21739-7_2 ◽

1991 ◽

pp. 23-41 ◽

Cited By ~ 1

Author(s):

Linda A. Amos ◽

W. Bradshaw Amos

Keyword(s):

Intermediate Filaments ◽

Alpha Helical Proteins ◽

Helical Proteins

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Real Perturbation of Complex Analytic Families: Points to Regions

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127498000061 ◽

1998 ◽

Vol 08 (01) ◽

pp. 73-93 ◽

Cited By ~ 12

Author(s):

Bruce B. Peckham

Keyword(s):

Numerical Study ◽

Sufficient Conditions ◽

Real Parameter ◽

Complex Parameter ◽

Mandelbrot Set ◽

Complex Conjugate ◽

Real Plane ◽

Phase Variable ◽

Bifurcation Points ◽

Quadratic Family

This study provides some connections between bifurcations of one-complex-parameter complex analytic families of maps of the complex plane C and bifurcations of more general two-real-parameter families of real analytic (or Ck or C∞) maps of the real plane ℛ2. We perform a numerical study of local bifurcations in the families of maps of the plane given by [Formula: see text] where z is a complex dynamic (phase) variable, [Formula: see text] its complex conjugate, C is a complex parameter, and α is a real parameter. For α=0, the resulting family is the familiar complex quadratic family. For α≠ 0, the map fails to be complex analytic, but is still analytic (quadratic) when viewed as a map of ℛ2. We treat α in this family as a perturbing parameter and ask how the two-parameter bifurcation diagrams in the C parameter plane change as the perturbing parameter α is varied. The most striking phenomenon that appears as α is varied is that bifurcation points in the C plane for the quadratic family (α=0) evolve into fascinating bifurcation regions in the C plane for nonzero α. Such points are the cusp of the main cardioid of the Mandelbrot set and contact points between "bulbs" of the Mandelbrot set. Arnold resonance tongues are part of the evolved scenario. We also provide sufficient conditions for more general perturbations of complex analytic maps of the plane of the form: [Formula: see text] to have bifurcation points for α=0 which evolve into nontrivial bifurcation regions as α grows from zero.

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