Advancing Theory for Kinetics and Dynamics of Complex, Many-Dimensional Systems E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Advances in Chemical Physics
• Sprache: Englisch

Seitenzahl: 458

Veröffentlichungsjahr: 2011

Beschreibung

This series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. Volume 145 in the series continues to report recent advances with significant, up-to-date chapters by internationally recognized researchers.

Leseprobe

Contents

Cover

Editorial Board

Title Page

Copyright

Contributors to Volume 145

Introduction

Preface

Chapter 1: Non-Markovian Theory of Vibrational Energy Relaxation and its Applications to Biomolecular Systems

I. Introduction

II. Normal Mode Concepts Applied to Protein Dynamics

III. Derivation of non-Markovian VER formulas

IV. Applications of the VER Formulas to Vibrational Modes in Biomolecules

V. Summary and Discussion

Acknowledgments

Chapter 2: Protein Functional Motions: Basic Concepts and Computational Methodologies

I. Introduction

II. Experiments on Protein Dynamics

III. Equilibrium Dynamics of Proteins

IV. Nonequilibrium Dynamics of Proteins

V. Concluding Remarks

Note added in proof

Acknowledgments

Chapter 3: Non-Brownian Phase Space Dynamics of Molecules, the Nature of Their Vibrational States, and Non-RRKM Kinetics

I. Introduction

II. Fractional Behavior in Classical Systems with Mixed Phase Space

III. Anomaly in Diffusion in Spatiotemporal Multiscale Classical Systems

IV. Energy Flow and Localization in Quantum Systems with Mixed State Space and Reaction Kinetics

V. Conclusions

Acknowledgments

Chapter 4: Dynamical Reaction Theory Based on Geometric Structures in Phase Space

I. Introduction

II. Dynamical Reaction Theory

III. Remnants of Invariants Buried in Phase Space of Many-Degrees-of-Freedom Systems

IV. Dimension Reduction by Normal Form Theory

V. Bifurcation and Breakdown of NHIM: The Origin of Stochasticity of Passage Through Rank-One Saddle

VI. Conclusions

Chapter 5: Ergodic Problems for Real Complex Systems in Chemical Physics

I. Introduction

II. Origin of Statistical Reaction Theory Revisited

III. Ergodicity in Isomerization of Small Clusters

IV. Exploring how proteins wander in state space using the ergodic measure and its application

V. Extracting the Local Equilibrium State (LES) and Free Energy Landscape from Single-Molecule Time Series

VI. Future Perspectives

Acknowledgments

Subject Index

Author Index

Editorial Board

Moungi G. Bawendi, Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

Kurt Binder, Condensed Matter Theory Group, Institut für Physik, Johannes Gutenberg-Universität Mainz, Mainz, Germany

William T. Coffey, Department of Electronics and Electrical Engineering, Trinity College, University of Dublin, Dublin, Ireland

Karl F. Freed, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois, USA

Daan Frenkel, Department of Chemistry, Trinity College, University of Cambridge, Cambridge, United Kingdom

Pierre Gaspard, Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Brussels, Belgium

Martin Gruebele, School of Chemical Sciences and Beckman Institute, Director of Center for Biophysics and Computational Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA

Jean-Pierre Hansen, Department of Chemistry, University of Cambridge, Cambridge, United Kingdom

Gerhard Hummer, Chief, Theoretical Biophysics Section, NIDDK-National Institutes of Health, Bethesda, Maryland, USA

Ronnie Kosloff, Department of Physical Chemistry, Institute of Chemistry and Fritz Haber Center for Molecular Dynamics, The Hebrew University of Jerusalem, Israel

Ka Yee Lee, Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois, USA

Todd J. Martinez, Department of Chemistry, Stanford University, Stanford, California, USA

Shaul Mukamel, Department of Chemistry, University of California at Irvine, Irvine, California, USA

Jose Onuchic, Department of Physics, Co-Director Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, California, USA

Steven Quake, Department of Physics, Stanford University, Stanford, California, USA

Mark Ratner, Department of Chemistry, Northwestern University, Evanston, Illinois, USA

David Reichmann, Department of Chemistry, Columbia University, New York, New York, USA

George Schatz, Department of Chemistry, Northwestern University, Evanston, Illinois, USA

Norbert Scherer, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois, USA

Steven J. Sibener, Department of Chemistry, James Franck Institute, University of Chicago, Chicago, Illinois, USA

Andrei Tokmakoff, Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

Donald G. Truhlar, Department of Chemistry, University of Minnesota, Minneapolis, Minnesota, USA

John C. Tully, Department of Chemistry, Yale University, New Haven, Connecticut, USA

Contributors to Volume 145

Akinori Baba, Molecule & Life Nonlinear Sciences Laboratory, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan; Core Research for Evolutional Science and Technology (CREST), Japan Science and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan

R. Stephen Berry, Department of Chemistry, The University of Chicago, 929 East 57th Street, Chicago, IL 60637, USA

Sotaro Fuchigami, Department of Supramolecular Biology, Graduate School of Nanobioscience, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan

Hiroshi Fujisaki, Molecular Scale Team, Integrated Simulation of Living Matter Group, Computational Science Research Program, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan, and Department of Physics, Nippon Medical School, 2-297-2 Kosugi-cho, Nakahara, Kawasaki, Kanagawa 211-0063, Japan

Shinnosuke Kawai, Molecule & Life Nonlinear Sciences Laboratory, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan

Akinori Kidera, Department of Supramolecular Biology, Graduate School of Nanobioscience, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan; Molecular Scale Team, Integrated Simulation of Living Matter Group, Computational Science Research Program, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan

Tamiki Komatsuzaki, Molecule & Life Nonlinear Sciences Laboratory, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan; Core Research for Evolutional Science and Technology (CREST), Japan Science and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan

David M. Leitner, Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, NV 89557-0216, USA

Chun-Biu Li, Molecule & Life Nonlinear Sciences Laboratory, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan

Yasuhiro Matsunaga, Molecular Scale Team, Integrated Simulation of Living Matter Group, Computational Science Research Program, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan

Akira Shojiguchi, Department of Physics, Faculty of Science, Nara Women's University, Kitauoyahigashimachi, Nara 630-8506, Japan

John E. Straub, Department of Chemistry, Boston University, 590 Commonwealth Avenue, SCI 503, Boston, MA 02215, USA

Hiroshi Teramoto, Molecule & Life Nonlinear Sciences Laboratory, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kitaku, Sapporo 001-0020, Japan

Mikito Toda, Department of Physics, Faculty of Science, NaraWomen's University, Kitauoyahigashimachi, Nara 630-8506, Japan

Yong Zhang, Department of Chemical and Biomolecular Engineering, University of Notre Dame, 182 Fitzpatrick Hall, Notre Dame, IN 46556-5637, USA

Introduction

Few of us can any longer keep up with the flood of scientific literature, even in specialized subfields. Any attempt to do more and be broadly educated with respect to a large domain of science has the appearance of tilting at windmills. Yet the synthesis of ideas drawn from different subjects into new, powerful, general concepts is as valuable as ever, and the desire to remain educated persists in all scientists. This series, Advances in Chemical Physics, is devoted to helping the reader obtain general information about a wide variety of topics in chemical physics, a field that we interpret very broadly. Our intent is to have experts present comprehensive analyses of subjects of interest and to encourage the expression of individual points of view. We hope that this approach to the presentation of an overview of a subject will both stimulate new research and serve as a personalized learning text for beginners in a field.

Stuart A. Rice

Preface

The simple descriptions of molecular dynamics that we envision for small molecules, and apply to other areas of chemical physics, such as chemical kinetics, are often incomplete or even inappropriate when carried over to large, complex molecules, such as those encountered in biology or nanoscale materials. New tools are needed to sort through the dynamics on the energy landscape that underlie the functional motion of biological molecules and energy transport within them. The aim of this volume is to present some of the theoretical and computational methods that have been developed recently to address this challenge. The following chapters provide a summary of topics presented by the authors at several recent workshops in Japan and the United States.

The first two chapters address dynamics and energy flow in biological molecules. Chapter 1 focuses on fast motions and energy transfer in biomolecules, mainly proteins, on the pico- to nanosecond timescale. Besides providing a general introduction to the field, this chapter presents a review of a non-Markovian theory for calculating vibrational energy transfer rates and provides a number of examples. Chapter 2 addresses functional motions of proteins, which can span a wide range of timescales, from nanoseconds to seconds. This chapter provides a review of general concepts and recent computational tools that have been put forth to elucidate functional motions.

Chapter 3 addresses dynamics and energy flow within basins on the energy landscape. While developing kinetic models for transitions between such basins is relatively simple if the dynamics within a basin is ergodic, the situation is much more complex when the assumptions of ergodicity break down. This chapter summarizes our understanding of the nature of nonergodic dynamics and the corresponding mixed phase space from a classical perspective, and reviews a quantum mechanical theory for corresponding systems with a mixed vibrational state space. The latter is also used to correct Rice–Ramsperger–Kassel–Marcus (RRKM) theory predictions of the unimolecular reaction rate when dynamics of the reactant is nonergodic. Continuing along these lines, Chapter 4 presents a review of recent work on non-RRKM kinetics from a classical phase space geometrical perspective. Finally, ergodicity in biological systems is further explored in Chapter 5, where local measures of ergodic and chaotic behavior are related to the topography of the energy landscape.

The chapters of this volume summarize important areas in our current understanding of dynamics and configurational changes of biological molecules and other many-dimensional systems. We hope that the material presented here will contribute further to the rapid development in the theory of these complex processes.

Tamiki KomatsuzakiR. Stephen BerryDavid M. Leitner

Guest Editors

Chapter 1

Non-Markovian Theory of Vibrational Energy Relaxation and its Applications to Biomolecular Systems

Hiroshi Fujisaki,1,2 Yong Zhang,3 and John E. Straub4

1Molecular Scale Team, Integrated Simulation of Living Matter Group, Computational Science Research Program, RIKEN, 2-1 Hirosawa, Wako-shiSaitama 351-0198, Japan

2Department of Physics, Nippon Medical School 2-297-2 Kosugi-cho, Nakahara, Kawasaki, Kanagawa 211-0063, Japan

3Department of Chemical and Biomolecular Engineering, University of Notre Dame, 182 Fitzpatrick Hall, Notre Dame, IN 46556-5637, USA

4Department of Chemistry, oston University, 590 Commonwealth Avenue, SCI 503, Boston, MA 02215, USA

I. Introduction

Energy transfer (relaxation) phenomena are ubiquitous in nature. At a macroscopic level, the phenomenological theory of heat (Fourier law) successfully describes heat transfer and energy flow. However, its microscopic origin is still under debate. This is because the phenomena can contain many-body, multiscale, nonequilibrium, and even quantum mechanical aspects, which present significant challenges to theories addressing energy transfer phenomena in physics, chemistry, and biology [1]. For example, heat generation and transfer in nanodevices is a critical problem in the design of nanotechnology. In molecular physics, it is well known that vibrational energy relaxation (VER) is an essential aspect of any quantitative description of chemical reactions [2]. In the celebrated RRKM theory of an absolute reaction rate for isolated molecules, it is assumed that the intramolecular vibrational energy relaxation (IVR) is much faster than the reaction itself. Under certain statistical assumptions, the reaction rate can be derived [3]. For chemical reactions in solutions, the transition state theory and its extension such as Kramer's theory and the Grote–Hynes theory have been developed [4, 5] and applied to a variety of chemical systems including biomolecular systems [6]. However, one cannot always assume separation of timescales. It has been shown that a conformational transition (or reaction) rate can be modulated by the IVR rate [7]. As this brief survey demonstrates, a detailed understanding of IVR or VER is essential to study the chemical reaction and conformation change of molecules.

A relatively well-understood class of VER is a single vibrational mode embedded in (vibrational) bath modes. If the coupling between the system and the bath modes is weak (or assumed to be weak), a Fermi's-golden-rule style formula derived using second-order perturbation theory [8–10] may be used to estimate the VER rate. However, the application of such theories to real molecular systems poses several (technical) challenges, including how to choose force fields, how to separate quantum and classical degrees of freedom, or how to treat the separation of timescales between system and bath modes. Multiple solutions have been proposed to meet those challenges leading to a variety of theoretical approaches to the treatment of VER [11–16]. These works using Fermi's golden rule are based on quantum mechanics and are suitable for the description of high-frequency modes (more than thermal energy 200 cm−1), on which nonlinear spectroscopy has recently focused [17–20].

In this chapter, we summarize our recent work on VER of high-frequency modes in biomolecular systems. In our previous work, we have concentrated on the VER rate and mechanisms for proteins [21]. Here we shall focus on the time course of the VER dynamics. We extend our previous Markovian theory of VER to a non-Markovian theory applicable to a broader range of chemical systems [22, 23]. Recent time-resolved spectroscopy can detect the time course of VER dynamics (with femtosecond resolution), which may not be accurately described by a single timescale. We derive new formulas for VER dynamics and apply them to several interesting cases, where comparison to experimental data is available.

This chapter is organized as follows: In Section II, we briefly summarize the normal mode concepts in protein dynamics simulations, on which we build our non-Markovian VER theory. In Section III, we derive VER formulas under several assumptions and discuss the limitations of our formulas. In Section IV, we apply the VER formulas to several situations: the amide I modes in isolated and solvated -methylacetamide and cytochrome , and two in-plane modes (ν and ν modes) in a porphyrin ligated to imidazole. We employ a number of approximations in describing the potential energy surface (PES) on which the dynamics takes place, including the empirical CHARMM [24] force-field and density functional calculations [25] for the small parts of the system (-methylacetamide and porphyrin). We compare our theoretical results with experiment when available, and find good agreement. We can deduce the VER mechanism based on our theory for each case. In Section V, we summarize and discuss the further aspects of VER in biomolecules and in nanotechnology (molecular devices).