Statistical Physics of Biomolecules : An Introduction book cover
1st Edition

Statistical Physics of Biomolecules
An Introduction

ISBN 9781420073782
Published June 2, 2010 by CRC Press
356 Pages 98 B/W Illustrations

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Book Description

From the hydrophobic effect to protein-ligand binding, statistical physics is relevant in almost all areas of molecular biophysics and biochemistry, making it essential for modern students of molecular behavior. But traditional presentations of this material are often difficult to penetrate. Statistical Physics of Biomolecules: An Introduction brings "down to earth" some of the most intimidating but important theories of molecular biophysics.

With an accessible writing style, the book unifies statistical, dynamic, and thermodynamic descriptions of molecular behavior using probability ideas as a common basis. Numerous examples illustrate how the twin perspectives of dynamics and equilibrium deepen our understanding of essential ideas such as entropy, free energy, and the meaning of rate constants. The author builds on the general principles with specific discussions of water, binding phenomena, and protein conformational changes/folding. The same probabilistic framework used in the introductory chapters is also applied to non-equilibrium phenomena and to computations in later chapters. The book emphasizes basic concepts rather than cataloguing a broad range of phenomena.

Focuses on what students need to know now

Students build a foundational understanding by initially focusing on probability theory, low-dimensional models, and the simplest molecular systems. The basics are then directly developed for biophysical phenomena, such as water behavior, protein binding, and conformational changes. The book’s accessible development of equilibrium and dynamical statistical physics makes this a valuable text for students with limited physics and chemistry backgrounds.

Table of Contents

Proteins Don’t Know Biology
Prologue: Statistical Physics of Candy, Dirt, and Biology
Guiding Principles
About This Book
Molecular Prologue: A Day in the Life of Butane
What Does Equilibrium Mean to a Protein?
A Word on Experiments
Making Movies: Basic Molecular Dynamics Simulation
Basic Protein Geometry
A Note on the Chapters

The Heart of It All: Probability Theory
Basics of One-Dimensional Distributions
Fluctuations and Error
Two+ Dimensions: Projection and Correlation
Simple Statistics Help Reveal a Motor Protein’s Mechanism
Additional Problems: Trajectory Analysis

Big Lessons from Simple Systems: Equilibrium Statistical Mechanics in One Dimension
Energy Landscapes Are Probability Distributions
States, Not Configurations
Free Energy: It’s Just Common Sense If You Believe in Probability
Entropy: It’s Just a Name
Summing Up
Molecular Intuition from Simple Systems
Loose Ends: Proper Dimensions, Kinetic Energy

Nature Doesn’t Calculate Partition Functions: Elementary Dynamics and Equilibrium
Newtonian Dynamics: Deterministic but Not Predictable
Barrier Crossing—Activated Processes
Flux Balance: The Definition of Equilibrium
Simple Diffusion, Again
More on Stochastic Dynamics: The Langevin Equation
Key Tools: The Correlation Time and Function
Tying It All Together
So Many Ways to ERR: Dynamics in Molecular Simulation
Mini-Project: Double-Well Dynamics

Molecules Are Correlated! Multidimensional Statistical Mechanics
A More-Than-Two-Dimensional Prelude
Coordinates and Force Fields
The Single-Molecule Partition Function
Multimolecular Systems
The Free Energy Still Gives the Probability

From Complexity to Simplicity: The Potential of Mean Force
Introduction: PMFs Are Everywhere
The Potential of Mean Force Is Like a Free Energy
The PMF May Not Yield the Reaction Rate or Transition State
The Radial Distribution Function
PMFs Are the Typical Basis for "Knowledge-Based" ("Statistical") Potentials
Summary: The Meaning, Uses, and Limitations of the PMF

What’s Free about "Free" Energy? Essential Thermodynamics
Statistical Thermodynamics: Can You Take a Derivative?
You Love the Ideal Gas
Boring but True: The First Law Describes Energy Conservation
G vs. F: Other Free Energies and Why They (Sort of ) Matter
Overview of Free Energies and Derivatives
The Second Law and (Sometimes) Free Energy Minimization
Calorimetry: A Key Thermodynamic Technique
The Bare-Bones Essentials of Thermodynamics
Key Topics Omitted from This Chapter

The Most Important Molecule: Electro-Statistics of Water
Basics of Water Structure
Water Molecules Are Structural Elements in Many Crystal Structures
The pH of Water and Acid–Base Ideas
Hydrophobic Effect
Water Is a Strong Dielectric
Charges in Water + Salt = Screening
A Brief Word on Solubility
Additional Problem: Understanding Differential Electrostatics

Basics of Binding and Allostery
A Dynamical View of Binding: On- and Off-Rates
Macroscopic Equilibrium and the Binding Constant
A Structural-Thermodynamic View of Binding
Understanding Relative Affinities: ∆∆G and Thermodynamic Cycles
Energy Storage in "Fuels" Like ATP
Direct Statistical Mechanics Description of Binding
Allostery and Cooperativity
Elementary Enzymatic Catalysis
pH AND pKa

Kinetics of Conformational Change and Protein Folding
Introduction: Basins, Substates, and States
Kinetic Analysis of Multistate Systems
Conformational and Allosteric Changes in Proteins
Protein Folding

Ensemble Dynamics: From Trajectories to Diffusion and Kinetics
Introduction: Back to Trajectories and Ensembles
One-Dimensional Ensemble Dynamics
Four Key Trajectory Ensembles
From Trajectory Ensembles to Observables
Diffusion and Beyond: Evolving Probability Distributions
The Jarzynski Relation and Single-Molecule Phenomena

A Statistical Perspective on Biomolecular Simulation
Introduction: Ideas, Not Recipes
First, Choose Your Model: Detailed or Simplified
"Basic" Simulations Emulate Dynamics
Metropolis Monte Carlo: A Basic Method and Variations
Another Basic Method: Reweighting and Its Variations
Discrete-State Simulations
How to Judge Equilibrium Simulation Quality
Free Energy and PMF Calculations
Path Ensembles: Sampling Trajectories
Protein Folding: Dynamics and Structure Prediction


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