دانلود کتاب Biomolecular Thermodynamics: From Theory to Application

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Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Detailed Contents
Series Preface
Preface
Acknowledgments
Note to Instructors
Author
Chapter 1: Probabilities and Statistics in Chemical and Biothermodynamics
Elementary Events
Relationship between probabilities, random samples, and populations
Set theory diagrams depict elementary and composite outcomes
How Probabilities Combine
Combining probabilities for mutually exclusive outcomes within a single events
Combining probabilities for outcomes from multiple independent events
“And” combinations of independent outcomes of separate events involve multiplication
“Or” combinations of independent outcomes for separate events involve addition and multiplication
Permutation Versus Composition
Calculating the number of permutations
Discrete probability distributions
The binomial distribution
The Poisson distribution
The FFT (“for the first time”) and geometric distributions
The multinomial distribution
Average values for discrete outcomes
Continuous Distributions
The exponential decay distribution
The Gaussian distribution
Average values for continuous distributions
Problems
Chapter 2: Mathematical Tools in Thermodynamics
Calculus in Thermodynamics
Derivatives of single-variable functions
Differentials involving single-variable functions
Integrals of single-variable functions
Derivatives of multivariable functions
Maximizing (and minimizing) multivariable functions
The gradient of multivariable functions
Fitting Continuous Curves to Discrete Data
The least-squares approach to compare discrete data and with a continuous curve
Solving the least-squares optimization problem
A visual picture of least-squares
An analytical approach: Linear least squares
A search approximation: Nonlinear least squares
Pitfalls in NLLS
Putting quantitative error bars on fitted parameters
Analysis of parameter distributions using the “bootstrap” method
Analysis of parameter uncertainties and comparing models using the f test
Problems
Appendix 2.1: Determining the Covariance Matrix in Least-Squares Fitting
Appendix 2.2: Testing parameters and models with the .~2 and f-ratio probability distributions
Chapter 3: The Framework of Thermodynamics and the First Law
What Is Thermodynamics and What Does It Treat?
Classical and statistical thermodynamics
Dividing up the Universe: System and Surroundings
Equilibrium, Changes of State, and Reversibility
The meaning of equilibrium in classical thermodynamics
Irreversible and reversible changes of state
The surroundings as a “reservoir”
Thermodynamic Variables and Equations of State
Variables in thermodynamics
Ways to derive the ideal gas equation of state
A graphical representation of the ideal gas law
The First law of Thermodynamics
The first law in words
The first law in equation form
The importance of pathways in first law calculations
Work
The work associated with expansion of a gas
The Reversible Work Associated with Four Fundamental Changes of State
Work done in reversible constant-pressure (isobaric) expansion
Work done in constant volume pressure change
Work done in reversible isothermal expansion of an ideal gas
Work done in reversible adiabatic expansion of an ideal gas
Heat
Types of heat capacities
The Heat Flow Associated with the Four Fundamental Changes in an Ideal Gas
Heat flow for reversible constant-pressure (isobaric) expansion of an ideal gas
Heat flow for reversible constant-volume (isochoric) heating of an ideal gas
Heat flow for reversible isothermal expansion of an ideal gas
Heat flow for reversible adiabatic expansion of an ideal gas
The Work Associated with the Irreversible Expansion of an Ideal Gas
Adiabatic irreversible expansion of a small system against a mechanical reservoir
Expansion to mechanical equilibrium with the surroundings
Expansion to a stopping volume where psys > psurr
Expansion against vacuum
The Connection between Heat Capacities and State Functions
The relationship between CV and Cp
A Nonideal Model: The Van der Walls Equation of State
Problems
Chapter 4: The Second Law and Entropy
Some Familiar Examples of Spontaneous Change
Spontaneous Change and Statistics
Spontaneous change and the mixing of simple fluids
Spontaneous change and the dissipation of temperature differences
The Directionality of Heat Flow at the Macroscopic (Classical) Level
The Clausius and Kelvin statements of the second law
Heat engines
Carnot heat engines and efficiencies
From the Carnot Cycle to More General Reversible Processes
Entropy Calculations for Some Simple Reversible Processes
Comparison of Reversible and Irreversible Cycles
A General form for Irreversible Entropy Changes
Entropy As a Thermodynamic Potential
Entropy Calculations for Some Irreversible Processes
Heat flow between two identical bodies at different temperatures
Heat flow between a small body and a thermal reservoir
Entropy Changes for Irreversible Expansions
Entropy change for irreversible expansion to mechanical equilibrium with a constant pressure surroundings
Entropy change for an irreversible expansion against vacuum
Entropy and Molecular Statistics
Statistical entropy and multiplicity
Counting the microstates
The statistical entropy of a simple chemical reaction
The statistical entropy of an expanding two-dimensional lattice gas
The statistical entropy of heat flow
Entropy and Fractional Populations
Problems
Further Reading
Chapter 5: Free Energy as a Potential for the Laboratory and for Biology
Internal Energy As a Potential: Combining the First and Second Laws
An example of the internal energy potential U = U(S,V) for an ideal gas
Other Energy Potentials for Different Types of Systems
A more formal approach to generate H, A, and G: The Legendre transforms
Legendre transforms of multivariable functions
Relationships among Derivatives from the Differential Forms of U, H, G, and A
Derivatives of the energy potentials
Maxwell relations
Manipulation of thermodynamic derivative relations
The behavior of energy derivatives in changes of state
Contributions of Different Chemical Species to Thermodynamic State Functions—Molar Quantities
Molar quantities
Molar volumes for systems made of only one species
Molar volumes in mixtures
Mixing volume ideality
Mixing volume nonideality
Molar free energies: The chemical potential
A Constraint on the Chemical Potentials: the Gibbs–Duhem Relationship
The relationship between the chemical potential and other thermodynamic potential functions
Maxwell relations involving variations in composition
Partial Pressures of Mixtures of Gases
Problems
Appendix 5.1: Legendre Transforms of a Single Variable
Chapter 6: Using Chemical Potentials to Describe Phase Transitions
Phases and Their Transformations
The Condition for Equilibrium Between two Phases
How Chemical Potentials of Different Phases Depend on Temperature and Pressure: Deriving a T–p Phase Diagram for Water
Temperature dependence of heat capacities for ice, water, and steam
Temperature dependence of enthalpies and entropies of ice, liquid water, and steam
Temperature dependences of chemical potentials for ice, water, and steam
Temperature-driven phase transitions
Adding the effects of pressure to chemical potential relationships
Combining pressure and temperature into a single phase diagram
Additional Restrictions from the Phase Diagram: The Clausius–Clapeyron Equation and Gibbs’ Phase Rule
A three-dimensional representation of the Gibbs–Duhem equation
Intersection of Gibbs–Duhem planes and the Clausius–Clapeyron equation
The number of coexisting phases and the phase rule
Problems
Further Reading
Chapter 7: The Concentration Dependence of Chemical Potential, Mixing, and Reactions
The Dependence of Chemical Potential on Concentration
Concentration scales
The difference between concentrations and mole amounts
Concentration dependence of chemical potential for an ideal gas
Choosing standard states
Standard states are like reference points on maps
The concentration dependence of chemical potential for “ideal” liquid mixtures
The Gibbs free energy of mixing of ideal solutions
Concentration dependence of chemical potentials for nonideal solutions
A Simple Lattice Model for Nonideal Solution Behavior
Chemical potential on the molar scale
Chemical Reactions
A formalism for chemical reactions
Reaction free energy from a finite difference approach
Reaction free energy from differentials
Similarities (and Differences) between Free Energies of Reaction and Mixing
How Chemical Equilibrium Depends on Temperature
How Chemical Equilibrium Depends on Pressure
Problems
Further Reading
Historical Development
Curvature, Convexity, and Phase Stability
Reaction Thermodynamics
Chapter 8: Conformational Equilibrium
Macromolecular Structure
A simple Two-State model for conformational transitions
Simultaneous visualization of N and D
The Thermal Unfolding Transition As a Way to Determine Kfold and .G°
A simple geometric way to connect Yobs to Kfold
An equation to fit unfolding transitions
A Simple Model for Thermal Transitions: Constant .H° AND .S°
Fitting Conformational Transitions to Analyze the Thermodynamics of Unfolding
Extrapolation of conformational transitions
A More Realistic Model FOR Thermal Unfolding of Proteins: The Constant Heat Capacity Model
A form of the constant heat capacity model that is good for fitting data
A form of the constant heat capacity model that is suited for entropy and enthalpy analysis
Cold denaturation of proteins
Measurement of Thermal Denaturation by Differential Scanning Calorimetry
Chemical Denaturation of Proteins
Problems
Appendix 8.1: Differential Scanning Calorimetry
References
Chapter 9: Statistical Thermodynamics and the Ensemble Method
The Relationship between the Microstates of Molecular Models and Bulk Thermodynamic Properties
The Ensemble Method and the Ergodic Hypothesis
The Ensemble Method of Building Partition Functions
Isolated thermodynamic systems and the microcanonical ensemble
The Microcanonical partition function and entropy
A Microcanonical Ensemble from the Heat Exchange Model
A four-particle isolated system
An isolated system with the two subsystems combined
Another way to look at the energy distribution
Problems
Chapter 10: Ensembles That Interact with Their Surroundings
Heat Exchange and the Canonical Ensemble
The Canonical Partition Function
A canonical ensemble with just two microstates
A canonical ensemble with three microstates, and Lagrange maximization
A canonical ensemble with an arbitrary number m of microstates
Thermodynamic variables and the canonical partition function
The internal energy
The entropy
The thermodynamic value of ß
Thermodynamic relations from the canonical partition function
A Canonical Ensemble Representing a Three Particle Isothermal System
Population distributions as a function of temperature
Bulk thermodynamic properties for the three-particle ladder
The Isothermal–Isobaric Ensemble and Gibbs Free Energy
The isothermal–isobaric partition function
The Lagrange multipliers of the isothermal–isobaric partition function, and relationship to thermodynamic quantities
Problems
Chapter 11: Partition Functions for Single Molecules and Chemical Reactions
A Canonical Partition Function for a System with One Molecule
Temperature dependence of the molecular partition function
Thermodynamic quantities from q
The Relationship between the Molecular and Canonical Partition Functions
Indistinguishable particles
An Isothermal–Isobaric Molecular Partition Function
A Statistical Thermodynamic Approach to Chemical Reaction
Single Molecule Ensembles for Chemical Reactions
Building a Single Molecule Reaction Partition Function
Building a Multimolecular Reaction Partition Function
Using reaction partition functions
Problems
Chapter 12: The Helix–Coil Transition
General reaction partition functions for the helix–coil transition
The Noncooperative Homopolymer Model
The Noncooperative Heteropolymer Model
Coupling between the Sites and the Basis for Cooperativity
Coupling between Residues through “Nearest-Neighbor” Models
The zipper model—a “one-helix” approximation for cooperative homopolymers
An exact nearest-neighbor description using matrices
Fraction helix from the matrix partition function
Extending the matrix approach to accommodate sequence variation
Problems
Appendix 12.1: Other Representations of the Helix–Coil Transition
Chapter 13: Ligand Binding Equilibria from a Macroscopic Perspective
Ligand Binding to a Single Site
Fractional saturation and average ligation number for the single-site model
Graphical representation of the fractional saturation
The binding capacity
Practical Issues in Measuring and Analyzing Binding Curves
Discrete data and data selection
Indirect measurement of
Total (rather than free) ligand as an independent variable
Measurements of binding are subject to experimental error
Binding of Multiple Ligands
A Macroscopic Representation of Multiple Ligand Binding
Average ligation number and fractional saturation
The Binding Polynomial P: A Partition Function for Ligand Binding
A concise relationship between the fractional saturation and P
Populations from the binding polynomial
The binding capacity from the binding polynomial
An Example—The Macroscopic Binding of Two Ligands
K2>>K1: Positive cooperativity
K1>>K2: Negative cooperativity (or heterogeneous sites)
Binding capacity representation of two-step binding
Hill plots as a graphical representation of cooperativity
An analytical formula for the Hill coefficient
A simple limiting model for the Hill coefficient
Strengths and limitations of the macroscopic approach
Binding to Multiple Different Ligands: “Heterotropic” Binding
Effects of thermodynamic cycles on the stepwise constants
A General Framework to Represent Thermodynamic Linkage between Multiple Independent Ligands
Linkage coefficients for the simple two-site heterotropic model
Problems
Chapter 14: Ligand Binding Equilibria from a Microscopic Perspective
An Example of General Microscopic Binding: Three Ligand Binding Sites
A stepwise microscopic description
An overall microscopic description
A geometric picture of the relationship between stepwise and overall microscopic constants
Binding polynomials in terms of microscopic constants
Generating P using stepwise microscopic stepwise constants
Generating P using overall microscopic constants
Simplifications to Microscopic Binding Models
Binding to three identical, independent sites
Saturation curves for three independent identical sites
Binding to s Identical, Independent Sites
Binding to Two Classes of Independent Sites
Binding to Identical Coupled Sites
A simple model for identical coupling: One interaction per ligand
A more involved model for identical coupling: Interactions among all sites
Explicit Structural Models for Coupling Among Binding Sites
An example of rotational symmetry: Binding to a hexagon
Allostery in Ligand Binding
A general (macrostate) allosteric model
A two-conformation, two-site general allosteric model
Microscopic allosteric models and approximations
Allosteric models involving subunits
The KNF model
Problems
References
Symmetry in Macromolecular Structure
Allosteric Models
Appendix: How to Use Mathematica
Bibliography
Index