Preface ........................................................ ix
Chapter 1 A Brief History of Thought and Real Single-
Molecule Experiments ............................................ 1
Chapter 2 How the Properties of Individual Molecules Are
Measured ........................................................ 9
2.1 Typical size of a molecule ................................. 9
2.2 Optical detection of an individual molecule ............... 10
2.3 Scanning probe microscopies ............................... 12
2.4 Optical tweezers .......................................... 15
2.5 Nanopore experiments ...................................... 15
Chapter 3 The Kinetics of Chemical Reactions: Single-
Molecule Versus "Bulk" View .................................... 19
Chapter 4 How Molecules Explore Their Energy Landscapes ....... 29
4.1 The potential energy surface .............................. 29
4.2 What are the equations of motion obeyed by a molecule? .... 30
4.3 Stochasticity in the dynamics of individual molecules ..... 33
4.4 Properties of stochastic trajectories ..................... 38
4.4.1 Free diffusion ..................................... 38
4.4.2 Motion in a single potential well .................. 41
4.4.3 Multiple potential wells ........................... 43
4.5 Further discussion: Some mathematical properties of the
master equation ........................................... 47
4.6 Further discussion: How does a molecule "know" its own
entropy? .................................................. 50
Chapter 5 Microscopic View of the Rate of a Chemical
Reaction: A Single-Molecule Perspective ........................ 59
5.1 From microscopic dynamics to rate coefficients ............ 59
5.2 Overcoming the rare event problem: Transition state
theory .................................................... 62
5.3 Why transition state theory is not exact .................. 66
5.4 The transmission factor ................................... 68
5.5 Relationship between the transmission factor and the
number of crossings ....................................... 70
5.6 The transmission factor for Langevin dynamics ............. 71
5.7 Extension to many degrees of freedom ...................... 74
5.8 Reaction kinetics in complex systems: Floppy chain
molecules, random walks, and diffusion controlled
processes ................................................. 78
5.9 Further discussion: Derivation of Eq. 5.35 ................ 85
Chapter 6 Molecular Transition Paths: Why Going Uphill May
Be Faster ...................................................... 87
6.1 Transit times vs. first passage times ..................... 88
6.2 Time reversal symmetry and its consequences for transit
times ..................................................... 90
6.3 Transit time through a parabolic barrier .................. 91
6.4 Further discussion: How to follow a Langevin trajectory
backward in time .......................................... 94
Chapter 7 Properties of Light Emitted by a Single Molecule
and What It Can Tell Us about Molecular Motion ................. 97
7.1 Poisson process and nonsingle-molecule light sources ...... 97
7.2 Single-molecule emitters: Photon antibunching ............ 102
7.3 Monitoring conformational changes with Fluorescence
Resonance Energy Transfer (FRET) ......................... 105
7.3.1 The basics of FRET ................................ 105
7.3.2 Binning ........................................... 109
7.3.3 Interphoton lag times and intensity
autocorrelation functions ......................... 112
7.3.4 The maximum likelihood approach ................... 115
7.4 Random thoughts on computer-aided approaches
to discovering single-molecule dynamics .................. 120
Chapter 8 Single-Molecule Mechanics .......................... 125
8.1 Single-molecule springs: Origins of molecular
elasticity ............................................... 125
8.2 Thermodynamics and kinetics of mechanically ruptured
bonds .................................................... 132
8.3 Slip vs. catch bonds ..................................... 138
8.4 Force-induced unfolding and other conformational
transitions influenced by forces ......................... 140
8.5 Further discussion: Elastic response of a freely
jointed chain beyond Hooke's law ......................... 142
Chapter 9 Nonequilibrium Thermodynamics of Single
Molecules: The Jarzynski and Crooks Identities ................ 147
9.1 Extension and contraction of molecular springs: Energy
dissipation and the second law of thermodynamics ......... 147
9.2 Exact relationships between free energy and
nonequilibrium work ...................................... 152
9.3 Energy dissipation in biological molecules:
Sacrificial bonds and molecular shock absorbers .......... 159
9.4 Further discussion: Proof of the Crooks identity ......... 164
Chapter 10 Single-Molecule Phenomena in Living Systems ........ 167
10.1 Single-molecule view of enzyme catalysis ................. 169
10.2 Enzymes as molecular motors .............................. 179
Appendix A Probability Theory, Random Numbers, and Random
Walks ......................................................... 189
A.1 Rules for calculating probabilities ...................... 189
A.2 Random numbers and their distributions ................... 191
A.3 Random walks ............................................. 192
Appendix В Elements of Statistical Mechanics ................ 195
B.l Canonical (Gibbs) distribution ........................... 195
B.2 The partition function and the free energy ............... 196
B.3 Maxwell-Boltzmann distribution and the equipartition
theorem .................................................. 200
Index ......................................................... 201
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