2,572 research outputs found

    Local stress and elastic properties of lipid membranes obtained from elastic energy variation

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    A theory and computational method are provided for the calculation of lipid membranes elastic parameters, which overcomes the difficulties of the existing approaches and can be applied not only to single-component but also to multi-component membranes. It is shown that the major elastic parameters can be determined as the derivatives of the stress-profile moments with respect to stretching. The more general assumption of the global incompressibility, instead of the local one, is employed, which allows the measurement of the local Poisson's ratio from the response of the stress profile to the isotropic ambient pressure. In the case of the local incompressibility and quadratic energy law, a direct relation between the bending modulus and Gaussian curvature modulus is established

    Connection formulae for the radial Toda equations I

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    This paper is the first in a forthcoming series of works where the authors study the global asymptotic behavior of the radial solutions of the 2D periodic Toda equation of type AnA_n. The principal issue is the connection formulae between the asymptotic parameters describing the behavior of the general solution at zero and infinity. To reach this goal we are using a fusion of the PDE analysis and the Riemann-Hilbert nonlinear steepest descent method of Deift and Zhou which is applicable to 2D Toda in view of its Lax integrability. A principal technical challenge is the extension of the nonlinear steepest descent analysis to Riemann-Hilbert problems of matrix rank greater than 22. In this paper, we meet this challenge for the case n=2n=2 (the rank 33 case) and it already captures the principal features of the general nn case.Comment: 68 pages, 16 figure

    Universal geometrical factor of protein conformations as a consequence of energy minimization

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    The biological activity and functional specificity of proteins depend on their native three-dimensional structures determined by inter- and intra-molecular interactions. In this paper, we investigate the geometrical factor of protein conformation as a consequence of energy minimization in protein folding. Folding simulations of 10 polypeptides with chain length ranging from 183 to 548 residues manifest that the dimensionless ratio (V/(A)) of the van der Waals volume V to the surface area A and average atomic radius of the folded structures, calculated with atomic radii setting used in SMMP [Eisenmenger F., et. al., Comput. Phys. Commun., 138 (2001) 192], approach 0.49 quickly during the course of energy minimization. A large scale analysis of protein structures show that the ratio for real and well-designed proteins is universal and equal to 0.491\pm0.005. The fractional composition of hydrophobic and hydrophilic residues does not affect the ratio substantially. The ratio also holds for intrinsically disordered proteins, while it ceases to be universal for polypeptides with bad folding properties.Comment: 6 pages, 1 table, 4 figure
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