Biomolecular Thermodynamics

From Theory to Application

Douglas Barrick

• Publisher: CRC Press
• Year: 2017
• ISBN:
  9781439800201
• Edition: 1
• Topic: Medicine
• Subtopic: Biochemistry in Medicine

" an impressive text that addresses a glaring gap in the teaching of physical chemistry, being specifically focused on biologically-relevant systems along with a practical focus…. the ample problems and tutorials throughout are much appreciated."
–Tobin R. Sosnick, Professor and Chair of Biochemistry and Molecular Biology, University of Chicago

"Presents both the concepts and equations associated with statistical thermodynamics in a unique way that is at visual, intuitive, and rigorous. This approach will greatly benefit students at all levels."
–Vijay S. Pande, Henry Dreyfus Professor of Chemistry, Stanford University

" a masterful tour de force …. Barrick's rigor and scholarship come through in every chapter."
–Rohit V. Pappu, Edwin H. Murty Professor of Engineering, Washington University in St. Louis

This book provides a comprehensive, contemporary introduction to developing a quantitative understanding of how biological macromolecules behave using classical and statistical thermodynamics. The author focuses on practical skills needed to apply the underlying equations in real life examples. The text develops mechanistic models, showing how they connect to thermodynamic observables, presenting simulations of thermodynamic behavior, and analyzing experimental data. The reader is presented with plenty of exercises and problems to facilitate hands-on learning through mathematical simulation.

Douglas E. Barrick is a professor in the Department of Biophysics at Johns Hopkins University. He earned his Ph.D. in biochemistry from Stanford University, and a Ph.D. in biophysics and structural biology from the University of Oregon.

chapter 1 Probabilities and Statistics in Chemical and Biothermodynamics

Goals and Summary

The goals of this chapter are to familiarize students with the concepts of probabilities and statistics to understand physical chemical principles and to analyze complex problems in chemical and biothermodynamics. The first part of the chapter will focus on events, outcomes, and their combinations. We will develop the concept of the probability distribution as a collection of probabilities for all possible outcomes. We will emphasize the differences between specific sequences of elementary events, and collections composed of specific sequences that share some overall property. This distinction is essential to statistical thermodynamics, where we are often limited to measurements of overall composition, where each composition is consistent with many different arrangements of molecules. The “indistinguishability” of these different arrangements is directly related to important thermodynamic concepts such as entropy.

In the process we will introduce a number of key probability distributions, including both discrete distributions (most importantly the binomial and multinomial distributions) and continuous distributions (emphasizing Gaussian and decaying exponential distributions). We will describe how to derive various average quantities from probability distributions; in subsequent chapters, such derivations provide a means to directly test and refine statistical thermodynamic models and learn about molecular systems.

One of the most important subjects in chemistry and biology is the reaction of molecules to form new molecules of different sizes, shapes, and types. New covalent bonds are formed, new configurations can be adopted, new complexes and assemblies are built, and old ones are taken apart and rearranged. The application of physical chemistry allows these kinds of transformations to be described quantitatively, providing access to underlying forces and mechanisms, and providing predictive power to describe how complex systems of molecules will react as conditions change.

Biochemical systems almost always involve very large numbers of molecules. Rather than describing the behavior of each individual molecule, which is difficult even for small systems (and yields much more information than is of practical value for large systems), we will seek to understand reactions and material transformations in terms of “distribut...