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Single Molecule Science
Physical Principles and Models




ISBN 9781466559516
Published June 9, 2015 by CRC Press
214 Pages - 53 B/W Illustrations

 
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Book Description

The observation and manipulation of individual molecules is one of the most exciting developments in modern molecular science. Single Molecule Science: Physical Principles and Models provides an introduction to the mathematical tools and physical theories needed to understand, explain, and model single-molecule observations.

This book explains the physical principles underlying the major classes of single-molecule experiments such as fluorescence measurements, force-probe spectroscopy, and nanopore experiments. It provides the framework needed to understand single-molecule phenomena by introducing all the relevant mathematical and physical concepts, and then discussing various approaches to the problem of interpreting single-molecule data.

The essential concepts used throughout this book are explained in the appendices and the text does not assume any background beyond undergraduate chemistry, physics, and calculus. Every effort has been made to keep the presentation self-contained and derive results starting from a limited set of fundamentals, such as several simple models of molecular dynamics and the laws of probability. The result is a book that develops essential concepts in a simple yet rigorous way and in a manner that is accessible to a broad audience.

Table of Contents

A Brief History of Thought and Real Single-Molecule Experiments

How the Properties of Individual Molecules Are Measured
Typical Size of a Molecule
Optical Detection of an Individual Molecule
Scanning Probe Microscopies
Optical Tweezers
Nanopore Experiments

The Kinetics of Chemical Reactions: Single-Molecule Versus "Bulk" View

How Molecules Explore their Energy Landscapes
The Potential Energy Surface
What Are the Equations of Motion Obeyed by a Molecule?
Stochasticity in the Dynamics of Individual Molecules
Properties of Stochastic Trajectories
Further Discussion: Some Mathematical Properties of the Master Equation
Further Discussion: How Does a Molecule "Know" Its Own Entropy?

Microscopic View of the Rate of a Chemical Reaction: A Single-Molecule Perspective
From Microscopic Dynamics to Rate Coefficients
Overcoming the Rare Event Problem: Transition State Theory
Why Transition State Theory Is Not Exact
The Transmission Factor
Relationship Between the Transmission Factor and the Number of Crossings
The Transmission Factor for Langevin Dynamics
Extension to Many Degrees of Freedom
Reaction Kinetics in Complex Systems: Floppy Chain Molecules, Random Walks and Diffusion Controlled Processes
Further Discussion: Derivation of Eq.5.35

Molecular Transition Paths: Why Going Uphill May Be Faster
Transit Times vs. First Passage Times
Time Reversal Symmetry and its Consequences for Transit Times
Transit Time Through a Parabolic Barrier
Further Discussion: How to Follow a Langevin Trajectory Backward in Time

Properties of Light Emitted by a Single Molecule and What It Can Tell Us About Molecular Motion
Poisson Process and Non-Single-Molecule Light Sources
Single-Molecule Emitters: Photon Antibunching
Monitoring Conformational Changes with Fluorescence Resonance Energy Transfer (FRET)
Random Thoughts on Computer-Aided Approaches to Discovering Single-Molecule Dynamics

Single-Molecule Mechanics
Single-Molecule Springs: Origins of Molecular Elasticity
Thermodynamics and Kinetics of Mechanically Ruptured Bonds
Slip vs. Catch Bonds
Force-Induced Unfolding and Other Conformational Transitions Influenced by Forces
Further Discussion: Elastic Response of a Freely Jointed Chain Beyond Hook’s Law

Nonequilibrium Thermodynamics of Single Molecules: The Jarzynski and Crooks Identities
Stretching and Contraction of Molecular Springs: Energy Dissipation and the Second Law of thermodynamics
Exact Relationships Between Free Energy and Nonequilibrium Work
Energy Dissipation in Biological Molecules: Sacrificial Bonds and Molecular Shock Absorbers
Further Discussion: Proof of the Crooks Identity

Single-Molecule Phenomena in Living Systems
Single-Molecule View of Enzyme Catalysis
Enzymes as Molecular Motors

Appendix A Probability Theory, Random Numbers and Random Walks
Rules for Calculating Probabilities
Random Numbers and Their Distributions
Random Walks

Appendix B Appendix B: Elements of Statistical Mechanics
Canonical (Gibbs) Distribution
The Partition Function and the Free Energy
Maxwell-Boltzmann Distribution and the Equipartition Theorem

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Author(s)

Biography

Dmitrii E. Makarov is a professor of chemistry at the University of Texas at Austin. He earned a PhD in theoretical physics from the Institute of Chemical Physics in Moscow. His expertise is in theoretical and computational chemical physics and in biophysics.

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Author - Dmitrii E Makarov
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Dmitrii E Makarov

Professor, University of Texas
Austin, Texas, United States

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