Multiple Unfolding Intermediates Obtained by Molecular Dynamic Simulations under Stretching for Immunoglobulin-Binding Domain of Protein G

We have studied the mechanical properties of the immunoglobulin-binding domain of protein G at the atomic level under stretching at constant velocity using molecular dynamics simulations. We have found that the unfolding process can occur either in a single step or through intermediate states. Analysis of the trajectories from the molecular dynamic simulations showed that the mechanical unfolding of the immunoglobulin-binding domain of protein G is triggered by the separation of the terminal β-strands and the order in which the secondary-structure elements break is practically the same in two- and multi-state events and at the different extension velocities studied. It is seen from our analysis of 24 trajectories that the theoretical pathway of mechanical unfolding for the immunoglobulin-binding domain of protein G does not coincide with that proposed in denaturant studies in the absence of force

Конструктивное решение проблемы эллиптичности системы дифференциальных уравнений первого порядка

We built first order elliptic systems with any possible number of unknown functions and the maximum possible number of unknowns, i.e, in general. These systems provide the basis for studying the properties of any first order elliptic systems. The study of the Cauchy-Riemann system and its generalizations led to the identification of a class of elliptic systems of first-order of a special structure. An integral representation of solutions is of great importance in the study of these systems. Only by means of a constructive method of integral representations we can solve a number of problems in the theory of elliptic systems related mainly to the boundary properties of solutions. The obtained integral representation could be applied to solve a number of problems that are hard to solve, if you rely only on the non-constructive methods. Some analogues of the theorems of Liouville, Weierstrass, Cauchy, Gauss, Morera, an analogue of Green’s formula are established, as well as an analogue of the maximum principle. The used matrix operators allow the new structural arrangement of the maximum number of linearly independent vector fields on spheres of any possible dimension. Also the built operators allow to obtain a constructive solution of the extended problem ”of the sum of squares” known in algebra. Построены эллиптические системы первого порядка с любым возможным числом неизвестных функций и максимально возможным числом неизвестных, т.е. в общем случае. Эти системы служат основой для изучения свойств любых эллиптических систем первого порядка. Проведенное изучение системы Коши–Римана и ее обобщений привело к выделению целого класса эллиптических систем первого порядка специальной структуры. Важное значение в исследовании этих систем играет интегральное представление их решений. Лишь при помощи конструктивного метода интегральных представлений можно решить ряд проблем в теории эллиптических систем, связанных, в основном, с граничными свойствами решений. Найденное интегральное представление удалось применить также для решения ряда задач, которые трудно решить, если опираться только на неконструктивные методы. Установлены, в частности, аналоги теорем Лиувилля, Вейерштрасса, Коши, Гаусса, Морера, аналог формулы Грина, а также аналог принципа максимума модуля. Используемые матричные операторы позволяют осуществить новое конструктивное построение максимально возможного числа линейно независимых векторных полей на сферах в общем случае любой возможной размерности. Кроме того, построенные операторы позволяют получить конструктивное решение расширенной задачи «о сумме квадратов», известной в алгебре.

The potency of monoethanolamine in biogas purification and upgrading

Abstract: Please refer to full text to view abstrac

Development and testing of new force fields for molecular dynamics simulations

Recent progress in modeling of protein folding in Dr. Shaw laboratory has been achieved only after some improvements of potentials of covalent forces, taken from the standard AMBER force field; and still, the force field used is not quite satisfactory to reproduce folded structures of some larger proteins, having significant, about 5A, RMS deviation between the computed and experimentally determined 3D structures. The objective of this research is to develop and test new polarizable atomic force fields (FFs) for "in-vacuum" and "in-water" non-bonded interactions based on AMBER ff99SBILDN force fields, improved by inclusion of new terms. FFs parameter optimization will be done using our set of molecular crystals with crystallographic data from the Cambridge Structural Database and sublimation/solvation thermodynamics characteristics from various sources

Properties of unsaturated phospholipid bilayers: Effect of cholesterol

Theoretical and experimental study of the liquid crystalline phase of five different hydrated unsaturated phosphatidylcholine (PC) lipid bilayers built up by 18:0/18: 1(n-9)cis PC, 18:0/18:2(n-6)cis PC, 18:0/18:3(n-3)cis PC, 18:0/20:4(n-6)cis PC, and 18:0/22:6(n-3)cis PC molecules with 40 mol% cholesterol, and the same five pure PC bilayers have been performed at 303 K. Molecular dynamics (MD) computer simulations and self-consistent field (SCF) calculations for the study of model pure unsaturated PC and PC/cholesterol membrane systems, and the pulsed field gradient nuclear magnetic resonance (pfg NMR) technique for the study of corresponding real pure PC and PC/cholesterol membranes have been used. The lateral diffusion coefficients of the lipids in these systems, atom mass density distributions with respect to the bilayer normal, the C-H and C-C bond order parameter profiles of the lipid hydrocarbon chains have been analyzed. It has been found that mobility of PC molecules increases as the degree of their unsaturation increases (i.e., the lateral diffusion coefficients of PC molecules increase with increasing a number of double bonds in one of the lipid chains), both in pure bilayers and in bilayers with cholesterol. It has been found as well that the lateral diffusion coefficient of PC molecules of a lipid bilayer with 40 mol% cholesterol is smaller than that for the corresponding pure PC bilayer. The presence of cholesterol in a bilayer is found to promote extending of both saturated and polyunsaturated lipid chains. The effect of cholesterol on the order parameters of the double C=C bonds of polyunsaturated chains is found to be more appreciable than that for single C-C bonds of saturated chains. The theoretical (MD and SCF) results are in agreement with the results of the pfg NMR experimental study

Operator method in solving non-linear equations of the Hartree-Fock type

The operator method is used to construct the solutions of the problem of the polaron in the strong coupling limit and of the helium atom on the basis of the Hartree-Fock equation. $E_0=-0.1085128052\alpha^2$ is obtained for the polaron ground-state energy. Energies for 2s- and 3s-states are also calculated. The other excited states are briefly discussed.Comment: 7 page

Curvature in the construction of smooth invariant manifolds of dynamic models

В рамках данной статьи рассматривается метод кривизны потока применительно к построению инвариантных многообразий автономных динамических систем. В работе рассмотрены модели трехмерного автокаталатора и самосопряженная модель ФитцХью-Нагумо. Показано существование для них достаточно гладких инвариантных многообразий с переменной устойчивостью. In the framework of this paper we regard a flow curvature method applied to constructing of invariant manifolds of dynamical models. We show that a self-coupled FitzHugh-Nagumo model and 3d-autocatalator model have sufficiently smooth invariant surfaces