Stochastic Dynamics of Reacting Biomolecules.
Title:
Stochastic Dynamics of Reacting Biomolecules.
Author:
Ebeling, Werner.
ISBN:
9789812795434
Personal Author:
Physical Description:
1 online resource (343 pages)
Contents:
Contents -- Preface -- Chapter 1 Introduction to the reaction theory and cluster dynamics of enzymes -- 1.1 Arrhenius law and basic ideas of reaction theory -- 1.2 Breaking of the peptide and ester bonds -- 1.3 Basic principles and methods of protein dynamics -- 1.4 Effects of coupling and resonances on transition rates -- 1.5 Basic variables. Block and cluster models -- 1.6 The problems under consideration -- Chapter 2 Tools of Stochastic Dynamics -- 2.1 Introduction -- 2.2 Fluctuations in statistical physics -- 2.2.1 The canonical distribution -- 2.2.2 Einstein's formula -- 2.2.3 Fluctuations around equilibrium -- 2.2.4 Perrin's pendulum -- 2.2.5 General approach -- 2.3 Linear relaxation processes -- 2.4 Correlations and spectra -- 2.5 Linear response -- 2.5.1 Colored noise -- 2.5.2 Harmonic noise -- 2.5.3 Fluctuation dissipation theorem -- 2.5.4 Nyquist theorem. White noise -- 2.5.5 White noise and the Wiener process -- 2.6 Brownian Motion -- 2.6.1 Einstein's relation -- 2.6.2 Brownian motion as Markovian dynamics -- 2.6.3 Langevin's approach -- 2.6.4 The overdamped limit -- 2.6.5 Generalized Langevin equations -- 2.7 The Fokker-Planck equation -- 2.7.1 Kolmogorov's forward and backward equations -- 2.7.2 Moments of the transition probabilities -- 2.8 The bistable oscillator -- 2.9 The escape problem -- 2.9.1 Transition state theory -- 2.9.2 Kramers' rate formulae -- 2.9.3 Transition rates in multidimensional landscapes -- 2.10 Pontryagin's equation -- 2.10.1 Boundary conditions for the forward and the backward equation -- 2.10.2 The first passage time distribution -- 2.10.3 Splitting probability -- 2.10.4 Examples -- Chapter 3 Motion of test particles in a 2-d potential landscape -- 3.1 Formulation of the mathematical model.
3.2 Lyapunov spectra for the conservative system. Toda area for the landscape with two minima -- 3.3 Stratonovich method of calculating escape times in the chaotic regime and some applications. Dynamic model of the cluster dissociation -- 3.3.1 The role of a dynamic theory of cluster dissociation -- 3.3.2 The simplest dissociation model -- 3.3.3 The calculation of the rate of cluster dissociation using dynamic theory -- 3.3.4 Mean time of escape from a potential well under the action of noise. Metastable approximation -- 3.4 Test particle motion in a three-minima potential landscape -- 3.5 The problem of a test particle transition in the potential field with periodically changing parameters -- Chapter 4 Microscopic simulations of activation and dissociation -- 4.1 Discussion of the Heat Bath Model -- 4.2 Molecular dynamics of transitions between potential wells -- 4.3 Dissociation of Morse Molecules -- 4.4 Dynamics of Recombination Reactions -- 4.5 Spectrum of atomistic collisional forces -- 4.6 Discussion of activation processes in an atomistic heat bath -- Chapter 5 Excitations on rings of molecules -- 5.1 Solitary excitations in Toda systems -- 5.2 Statistical and stochastic theory of Toda rings -- 5.3 Energy accumulation at nonuniformities -- 5.4 Fluctuations in Toda rings and time correlations -- 5.5 Spatio-temporal excitations on rings -- 5.6 A ring model of enzymes -- 5.7 A polymer reaction model including entropy effects -- Chapter 6 Fermi resonance and Kramers problem in 2-d force field -- 6.1 2-d potential landscape and Fermi resonance -- 6.2 Basic 2-d cluster model -- 6.3 Analytical study -- 6.4 Numerical study -- 6.5 Stochastization of the vibrations -- 6.6 Basic model including damping and external harmonic action.
6.7 Computer simulation of the nonautonomous system with damping -- 6.8 Kramers problem for 2-d potential landscape -- Chapter 7 Molecular scissors. Cluster model of acetylcholinesterase -- 7.1 The role of acetylcholinesterase in the synaptic transfer -- 7.2 ACE computer model based on X-ray data -- 7.3 Electrostatic field of ACE molecule -- 7.3.1 Charge distribution inside the molecule -- 7.3.2 Calculation of the potential -- 7.3.3 Determination of the dipole moment -- 7.4 Substrate enters the pocket: 2-d "toy" model -- 7.4.1 AC molecules enter ACE AS -- 7.4.2 The problem of the reaction products escape from ACE AS -- 7.5 Kinetics of the enzymatic reaction of ester bond breaking -- 7.5.1 Michaelis-Menten equation -- 7.5.2 Mathematical model -- 7.5.3 Determination of the rate constant k1 -- 7.5.4 Determination of constants k-1 and k2 -- 7.5.5 Determination of the constant k5 -- 7.5.6 Substrate inhibition -- Chapter 8 Dynamics of proton transfer in the active site of chymotrypsin -- 8.1 The basic model -- 8.2 Determination of the wave function by symmetrization of the evolution operator -- 8.3 Checking the results -- 8.4 Mathematical model of the active site of a-chymotrypsin and acetylcholinesterase -- 8.5 Proton transfer in the H-bond of the active site -- 8.6 Discussion -- Chapter 9 On the damping of cluster oscillations in protein molecules -- 9.1 The estimate of damping of an oscillating ball by Stokes - Lamb - Landau theory -- 9.2 Estimating of Q-factor by the methods of statistical physics -- 9.3 Simulation by molecular dynamics -- 9.4 General discussion. Development of the model -- Chapter 10 Protein dynamics and new approaches to the molecular mechanisms of protein functioning -- 10.1 Topology of hypersurfaces of conformational energy levels.
10.2 Dynamic correlation functions and free energy maps -- 10.3 Restricted diffusion along a given pathway -- 10.4 The mechanism of non-Kramers kinetic effects in proteins and glass forming liquids under diffusion limited conditions -- 10.5 Mass transfer energy transformation and control in structured media -- 10.6 Conclusions -- Chapter 11 Conclusions -- List of authors -- Index.
Abstract:
This is a book about the physical processes in reacting complex molecules, particularly biomolecules. In the past decade scientists from different fields such as medicine, biology, chemistry and physics have collected a huge amount of data about the structure, dynamics and functioning of biomolecules. Great progress has been achieved in exploring the structure of complex molecules. However, there is still a lack of understanding of the dynamics and functioning of biological macromolecules. In particular this refers to enzymes, which are the basic molecular machines working in living systems. This book contributes to the exploration of the physical mechanisms of these processes, focusing on critical aspects such as the role of nonlinear excitations and of stochastic effects. An extensive range of original results has been obtained in the last few years by the authors, and these results are presented together with a comprehensive survey of the state of the art in the field. Contents: Introduction to the Reaction Theory and Cluster Dynamics of Enzymes (W Ebeling, A Netrebko & Yu Romanovsky); Tools of Stochastic Dynamics (L Schimansky-Geier & P Talkner); Motion of Test Particles in a 2-D Potential Landscape (O A Chichigina, A V Netrebko & N V Netrebko); Microscopic Simulations of Activation and Dissociation (W Ebeling, V Yu Podlipchuk, M G Sapeshinsky & A A Valuev); Excitations on Rings of Molecules (A Chetverikov, W Ebeling, M Jenssen & Yu Romanovsky); Fermi Resonance and Kramers Problem in 2-D Force Field (S V Kroo, A V Netrebko, Yu M Romanovsky & L Schimansky-Geier); Molecular Scissors. Cluster Model of Acetylcholinesterase (A Yu Chikishev, S V Kroo, A V Netrebko, N V Netrebko & Yu Romanovsky); Dynamics of Proton Transfer in the Active Site of Chymotrypsin (A Yu Chikishev, B A Grishanin & E V Shuvalova); On the Damping of Cluster Oscillations in
Protein Molecules (A Yu Chikishev, A V Netrebko & Yu M Romanovsky); Protein Dynamics and New Approaches to the Molecular Mechanisms of Protein Functioning (K V Shaitan). Readership: Researchers and graduate students in physics, biophysics, molecular biology and the life sciences; experts on nonlinear dynamics and the stochastic process in molecular systems and biomolecules.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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