Biomolecular Thermodynamics: From Theory to Application

553 Pages·2017·100.277 MB·English

by  Douglas Barrick

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BIOCHEMISTRY AND BIOPHYSICS
A FOUNDATIONS OF BIOCHEMISTRY AND BIOPHYSICS
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DOUGLAS E. BARRICK
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BIOMOLECULAR
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THERMODYNAMICS
From Theory to Application
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“an impressive text that addresses a glaring gap in the teaching of physical chemistry, O
being specifically focused on biologically-relevant systems along with a practical focus….
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the ample problems and tutorials throughout are much appreciated.”
–Tobin R. Sosnick, Professor and Chair of Biochemistry and Molecular Biology,
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University of Chicago
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DOUGLAS E. BARRICK
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“Presents both the concepts and equations associated with statistical thermodynamics in
a unique way that is at once visual, intuitive, and rigorous. This approach will greatly C
benefit students at all levels.” U
–Vijay S. Pande, Henry Dreyfus Professor of Chemistry, Stanford University BIOMOLECULAR
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“a masterful tour de force…. Barrick’s rigor and scholarship come through in
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every chapter.”
–Rohit V. Pappu, Edwin H. Murty Professor of Engineering, Washington University THERMODYNAMICS
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in St. Louis
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This book provides a comprehensive, contemporary introduction to developing a
From Theory to Application
quantitative understanding of how biological macromolecules behave using classical and R
statistical thermodynamics. The author focuses on the practical skills needed to apply M
the underlying equations in real-life examples. The text develops mechanistic models,
showing how they connect to thermodynamic observables, presenting simulations of O
thermodynamic behavior, and analyzing experimental data. The reader is presented with
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plenty of exercises and problems to facilitate hands-on learning through mathematical
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simulation.
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Douglas E. Barrick is a a professor in the Department of Biophysics at Johns Hopkins
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University. He earned a PhD in biochemistry at Stanford University and a PhD in
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biophysics and structural biology at the University of Oregon.
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K10030
ISBN: 978-1-4398-0019-5
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Biomolecular
Thermodynamics
From Theory to Application
Foundations of Biochemistry and Biophysics
Founding Series Editor: John J. (Jack) Correia
Currently available
Quantitative Understanding of Biosystems: An Introduction to Biophysics
Thomas M. Nordlund
Biomolecular Thermodynamics: From Theory to Application
Douglas E. Barrick
Biomolecular Kinetics: A Step-by-Step Guide
Clive R. Bagshaw
Forthcoming
Physical Principles in Nucleic Acid Chemistry
David E. Draper
RNA Biophysics
Kathleen B. Hall
Biomolecular
Thermodynamics
From Theory to Application
Douglas E. Barrick
MATLAB® is trademarks of the Math Works, Inc. and are used with permission. The Mathworks does not warrant the accuracy of the text or exercises in
this book. This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by the Math Works
of a particular pedagogical approach or particular use of the MATLAB® software.
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Library of Congress Cataloging-in-Publication Data
Names: Barrick, Douglas, author.
Title: Biomolecular thermodynamics : from theory to application / Douglas Barrick.
Other titles: Foundations of biochemistry and biophysics.
Description: Boca Raton : Taylor & Francis, 2017. | Series: Foundations of
biochemistry and biophysics
Identifiers: LCCN 2017005294| ISBN 9781439800195 (pbk. : alk. paper) | ISBN
9781138068841 (hardback)
Subjects: | MESH: Thermodynamics | Biochemical Phenomena | Models, Theoretical
Classification: LCC QP517.T48 | NLM QU 34 | DDC 572/.436--dc23
LC record available at https://lccn.loc.gov/2017005294
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To Debbie and Timmy, who together are my role models for science,
love, and life.

Contents
Series Preface xv
Preface xvii
Acknowledgments xxiii
Note to Instructors xxv
Author xxvii
Chapter 1 Probabilities and Statistics in Chemical
and Biothermodynamics 1
Chapter 2 Mathematical Tools in Thermodynamics 29
Chapter 3 The Framework of Thermodynamics
and the First Law 87
Chapter 4 The Second Law and Entropy 131
Chapter 5 Free Energy as a Potential for the
Laboratory and for Biology 173
Chapter 6 Using Chemical Potentials to Describe
Phase Transitions 209
Chapter 7 The Concentration Dependence of Chemical
Potential, Mixing, and Reactions 233
Chapter 8 Conformational Equilibrium 273
Chapter 9 Statistical Thermodynamics and the
Ensemble Method 303
Chapter 10 Ensembles That Interact with Their
Surroundings 327
Chapter 11 Partition Functions for Single Molecules and
Chemical Reactions 359
Chapter 12 The Helix–Coil Transition 373
Chapter 13 Ligand Binding Equilibria from a Macroscopic
Perspective 403
Chapter 14 Ligand Binding Equilibria from a Microscopic
Perspective 441
Appendix: How to Use Mathematica 485
Bibliography 507
Index 511

Detailed Contents
Series Preface xv Chapter 2
Preface xvii Mathematical Tools in Thermodynamics 29
Acknowledgments xxiii
Note to Instructors xxv CALCULUS IN THERMODYNAMICS 29
Author xxvii Derivatives of single-variable functions 29
Differentials involving single-variable
Chapter 1 functions 31
Integrals of single-variable functions 32
Probabilities and Statistics in
Derivatives of multivariable functions 34
Chemical and Biothermodynamics 1 Maximizing (and minimizing) multivariable
functions 36
ELEMENTARY EVENTS 2
The gradient of multivariable functions 46
Relationship between probabilities, random
FITTING CONTINUOUS CURVES TO DISCRETE DATA 47
samples, and populations 2
Set theory diagrams depict elementary and The least-squares approach to compare discrete
composite outcomes 4 data and with a continuous curve 48
Solving the least-squares optimization problem 50
HOW PROBABILITIES COMBINE 5
A visual picture of least-squares 50
Combining probabilities for mutually exclusive An analytical approach: Linear least squares 50
outcomes within a single events 6 A search approximation: Nonlinear least squares 54
Combining probabilities for outcomes from Pitfalls in NLLS 56
multiple independent events 8 Putting quantitative error bars on fitted
“And” combinations of independent outcomes parameters 60
of separate events involve multiplication 8 Analysis of parameter distributions using the
“Or” combinations of independent outcomes “bootstrap” method 62
for separate events involve addition and Analysis of parameter uncertainties and
multiplication 9 comparing models using the f test 65
PERMUTATION VERSUS COMPOSITION 11 PROBLEMS 69
Calculating the number of permutations 12
APPENDIX 2.1: DETERMINING THE COVARIANCE
Discrete probability distributions 14
MATRIX IN LEAST-SQUARES FITTING 78
The binomial distribution 15
The Poisson distribution 16
APPENDIX 2.2: TESTING PARAMETERS AND
The FFT (“for the first time”) and geometric
MODELS WITH THE χ2 AND f-RATIO PROBABILITY
distributions 17
DISTRIBUTIONS 81
The multinomial distribution 17
Average values for discrete outcomes 19
Chapter 3
CONTINUOUS DISTRIBUTIONS 20
The Framework of Thermodynamics
The exponential decay distribution 23
and the First Law 87
The Gaussian distribution 24
Average values for continuous distributions 25
WHAT IS THERMODYNAMICS AND WHAT
PROBLEMS 25 DOES IT TREAT? 87