Single Molecule Science: Physical Principles and Models, 1st Edition (Hardback) book cover

Single Molecule Science

Physical Principles and Models, 1st Edition

By Dmitrii E. Makarov

CRC Press

214 pages | 53 B/W Illus.

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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

About the Author

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.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Chemistry / General
SCIENCE / Chemistry / Physical & Theoretical
SCIENCE / Nuclear Physics