1st Edition

Statistical Physics of Biomolecules An Introduction

By Daniel M. Zuckerman Copyright 2010
    356 Pages 98 B/W Illustrations
    by CRC Press

    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.

    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



    Daniel M. Zuckerman