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Biophysics

DeMYSTiFieD®

Daniel Goldfarb

Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher.

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THE WORK IS PROVIDED AS IS. McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise.

For Sora Rivka, and for our children, Levi Yitzhok, Shaindel, and Menachem Mendel.

About the Author

Daniel Goldfarb has a Ph.D. in biophysics from the University of Virginia. He has done post-doctoral biophysics research, taught chemistry at Rutgers University, and written for the Biophysical Journal. Daniel is a Chartered Financial Analyst charterholder and currently applies his background in physics and math to designing and developing trading and risk analysis software for the financial industry.

Contents

Preface

Acknowledgments

CHAPTER 1 Introduction

What Is Biophysics?

Prerequisites for Biophysics

A Brief History of Biophysics

The Scope and Topics of Biophysics

Quiz

CHAPTER 2 Biophysical Topics

Molecular and Subcellular Biophysics

Physiological and Anatomical Biophysics

Environmental Biophysics

Putting It All Together

Quiz

CHAPTER 3 Biophysical Techniques and Applications

Ultracentrifugation

Electrophoresis

Size Exclusion Chromatography

Spectroscopy

Absorption Spectroscopy

Fluorescence Spectroscopy

Mass Spectrometry

X-Ray Crystallography

Nuclear Magnetic Resonance Spectroscopy

Electron Microscopy

Atomic Force Microscopy

Optical Tweezers

Voltage Clamp

Current Clamp

Patch Clamp

Calorimetry

Quiz

CHAPTER 4 Energy and Life

The First Law of Thermodynamics

Simplifying Assumptions

Enthalpy

Entropy

Gibbs Energy

The Second Law of Thermodynamics

The Gibbs Function as the Driver of Biophysical Processes

Quiz

CHAPTER 5 Statistical Mechanics

What Is Statistical Mechanics?

Statistical Mechanics: A Simple Example

Permutations

Boltzmann Distribution

Gibbs Energy and the Biophysical Partition Function

Quiz

CHAPTER 6 Forces Affecting Conformation in Biological Molecules

Chemical Bonds

Forces That Affect Conformation in Biomolecules

Charge-Charge Forces

Dipole Forces

Hydrogen Bonds and Water

Aromatic Ring Structures: Cation-Pi Interactions and Stacking

Dispersion Forces

Steric Interactions

Hydrophobic Interactions

Hydrophilic Interactions

Quiz

CHAPTER 7 Biomolecules 101

Classes of Biomolecules

Functional Groups

Carbohydrates

Lipids

Proteins

Nucleic Acids

Quiz

CHAPTER 8 The Cell

What Is a Cell?

Cell Structure

The Cell Membrane

Cell Organelles

Cell Life Cycle

Quiz

CHAPTER 9 Protein Biophysics

Protein Folding

Factors Influencing Protein Structure

Membrane Proteins

Analysis of Polypeptide Backbone Bond Angles

Common Protein Secondary Structures

Quiz

CHAPTER 10 Nucleic Acid Biophysics

Introduction

DNA Secondary Structure

DNA Melting

DNA Tertiary Structure

Quiz

CHAPTER 11 Membrane Biophysics

Membrane Functions

Phospholipid Behavior and Self-Assembly

Lipid Bilayer Energetics and Permeability

Fluid Mosaic Model

Phase Transitions in Phospholipid Bilayers

Membrane Growth

Membrane Permeability and Transport

Quiz

CHAPTER 12 Physiological and Anatomical Biophysics

The Scope of Physiological and Anatomical Biophysics

Jumping in the Air

Pumping Blood

Hummingbird Hovering

Quiz

Final Exam

Answers to Quizzes and Final Exam

Appendix: Units, Conversions, and Constants

Glossary

Index

Preface

Biophysics is a fascinating and relatively new science. After centuries of studying the physical properties and behavior of inanimate objects, we finally got the idea to use physics to study living things. The hope is to reveal the most basic principles of life, in much the same way that physics has illuminated fundamental principles of matter and energy.

This is an introductory textbook. Ideally we would cover the entire field of biophysics. You will certainly agree, as you read this book, that a thorough coverage of the entire field of biophysics is just not possible in a single volume. However, what you can gain from this book is a solid foundation, and a knowledge of biophysical principles and how they are applied. Once gained, that foundation will be easy to build on.

The book is organized as follows. The first three chapters give a broad overview of and introduction to the science of biophysics. In Chap. 1 you will learn to define biophysics, understand the prerequisites needed to study Biophysics Demystified®, and learn about the brief history of biophysics. You will also get to know the major divisions of biophysics and how the various topics in biophysics are categorized into these major divisions.

Chapters 2 and 3 then provide a broad overview of the science of biophysics. There are several reasons to gain a broad understanding of the field before getting into the details. First, you will need to build up some vocabulary, that is, the language of biophysics. Understanding the most commonly used terms from the outset will be a help later on. Second, the various topics of biophysics are interconnected. Although each can be studied independently, a broad overview will give you the ability to understand the context of each topic as you learn its details. Similarly, knowing the interconnections will underscore the importance and usefulness of each branch of biophysics to the others. Finally, the broad overview of Chaps. 2 and 3 will enable us to cover a lot of topics that may not be covered in great detail later in the text, so at least you will understand how they fit into the whole. This will be part of your foundation for later learning.

Chapters 4 through 8 teach the principles of physics, biology, and chemistry that are necessary for a journey into biophysics. The focus is on aspects of these sciences that apply most directly to biophysics. This includes, in Chaps. 4 and 5, an understanding of free energy, the laws of thermodynamics, entropy, and statistical mechanics. Next, Chaps. 6 and 7 delve into the physical forces that come into play at the molecular level, again paying special attention to those that are most relevant to living things. We then review the major categories of biomolecules—what they are made of and aspects of their structure and function—sort of a quick overview of biochemistry from a biophysical point of view. Chapter 8 provides an overview of the living cell, its structures, and what these structures do.

In Chaps. 9 through 11 the focus is on subcellular biophysics. This is the most common and largest branch of biophysics, and so we go into it in more detail. This branch includes protein biophysics, DNA biophysics, and membrane biophysics. Finally, Chap. 12 explores some aspects of anatomical biophysics, including blood flow and winged flight in animals.

You can use this book as a self-teaching guide, to lay the foundation for further study or just to satisfy your immediate curiosity. It can also be used as a classroom supplement, explaining and clarifying topics that are not as simple in other texts. My hope is that in reading this book you will truly find hard stuff made easy.

Daniel Goldfarb

Acknowledgments

Thanks to Judy Bass, my editor at McGraw-Hill, for the opportunity to write this book, and for her advice and guidance throughout; to Dr. Kenneth Breslauer, a role-model biophysicist, for coming to my aid on short notice and helping me find a good technical reviewer; and to Pragati Sharma, for her great job in finding errors, and for her valuable suggestions for clarity in many places. I especially thank my wife, Sora Rivka, for her sound advice, her encouragement, helping schedule time for me to write, and everything else she did to help make this project possible. Finally, I thank my children for their exceptional curiosity, and for always being there (when I was trying to write).

Biophysics

DeMYSTiFieD®

chapter 1

Introduction

What Is Biophysics?

Plain and simple, biophysics is the physics of biology, just as astrophysics is the physics of astronomy and nuclear physics is the physics of atomic nuclei.

What does this mean? What is the physics of biology? Physics is the study of matter and energy. Biophysics tries to understand how the laws of matter and energy are at work in living systems. Another way to say this is that biophysics uses of the principles, theories, and methods of physics to understand biology.

Biophysics is an interdisciplinary science. One could say it is the place where physics, chemistry, biology, and mathematics all meet. In practice, most biophysicists study things at the molecular level, but biophysics also includes physiological, anatomical, and even environmental approaches to the physics of living things.

Prerequisites for Biophysics

Biophysics is an advanced science. It requires some basic knowledge of biology, physics, chemistry, and mathematics. However, since this book is meant as an introduction to biophysics, to demystify biophysics, then as much as possible along the way, I will introduce or review the necessary background information.

Still, I do need to make some assumption as to your level of understanding in the physical sciences. For this purpose I will assume that you have had at least an introductory college-level (or advanced high school–level) course in physics or chemistry. This may be self-taught. Notice the or in physics or chemistry. If you have one or the other, it should be enough to get you through this book.

Let’s see two examples. For our first example, take the equation

This should look somewhat familiar to you. It means that if you apply a force F to an object of mass m, you will cause that object to accelerate with a rate of acceleration a.

The equation also says that for any given force F on an object of mass m, the acceleration rate will be exactly the rate that causes the product (mass × acceleration) to be equal to the force. This means, if we replace the object with a more massive object so that m is larger and we apply the same force, then the acceleration must be smaller (so that the mass times the acceleration will still be equal to the force). Similarly, applying the same force to a less massive object will cause the object to accelerate faster.

Let’s put this in concrete terms. Say we apply a force of 12 newtons (N) to an object with a mass of 2 kilograms (kg). The object will accelerate at a rate of 6 meters per second per second (or 6 m/s²). That is, every second, the object will be going 6 meters per second (or 6 m/s) faster than it was the previous second, for as long as we continue to apply that force. If the object is standing still when we first apply the force, then after 1 s, it will be moving at 6 m/s, after 2 s, it will be moving 12 m/s, and after 3 s, 18 m/s [about 40 miles/hour (mi/h)].

But, if we now apply that same force, 12 N, to a more massive object, say 24 kg, that object will accelerate much more slowly, only ¹/2 m/s² (see Fig. 1-1).

To take this example a step further, we write Eq. (1-1) as

Notice that the F and a are now bold. This means that they are vectors. A vector is a quantity that has not only a size but a direction as well. A force is always applied in a specific direction. Acceleration also occurs in a specific direction, and the acceleration will occur in the same direction as the force. The mass of the object, however, is not a vector quantity, but is called a scalar: a quantity that has only size.

FIGURE 1-1 • If we apply the same force to two objects of different mass, the more massive object accelerates slower. The product, force = mass × acceleration.

All of this should sound familiar to you. By now you should at least be thinking, Yes, I remember that. It’s all coming back to me. (Unless you’re already thinking, I know this. When’s he going to get to the biophysics? I knew I should have skipped this section.)

Let’s take one more example. Consider the chemical reaction

The concept of a chemical reaction and this way of representing it needs to be, if not familiar, at least something you can grasp quickly and become comfortable with. Equation (1-3) means that carbon dioxide and water can react together to form sugar and oxygen. This is one of the most basic biological reactions. It is how plants capture carbon and energy from the environment and store that energy in a form (sugar) that we (and other animals) can later consume and use to stay alive and to go about our daily business.

Strictly speaking, this reaction should have been written with a double arrow, like this:

The double arrow means that the reaction can occur in both directions. Going from left to right, carbon dioxide and water combine to create sugar and oxygen. This direction requires the input of energy. Plants get that energy from sunlight and, through the process of photosynthesis, store some of that solar energy in the chemical bonds of the sugar.

The reverse direction, from right to left, releases energy through the oxidation or combustion of sugar. In living things this process is also known as respiration. It is the way living things release stored energy that can be used for moving around, growing, and so on.

To emphasize the fact that energy is required to combine the carbon dioxide and water and that energy is released when the sugar is oxidized, we can also show energy as part of the chemical reaction.

The preceding discussions of forces and chemical reactions should be something that you can feel comfortable with.

Still Struggling

If you lack the necessary prerequisites to be familiar with or to feel comfortable with the preceding discussion, then I highly recommend you begin with Physics Demystified by Stan Gibilisco. Alternatively (or additionally) you may prefer Chemistry Demystified by Linda Williams. If you have a strong preference to start with physics or chemistry, then by all means go with your natural inclination.

A Brief History of Biophysics

How old is biophysics? As a separate discipline, biophysics is a relatively new science. In the big scheme of things, it is far, far younger than physics, mathematics, chemistry, or biology, but somewhat older than genetic engineering or computer science.

Although we find some physical studies of living things scattered throughout history, biophysics as a discipline is only about 60 to 100 years old. The first published use of the word biophysics was in 1892, in The Grammar of Science by Karl Pearson. In the book, Pearson tells us that there is a need for a new scientific discipline. In Pearson’s words, The reader might conceive that our classification [of the sciences] is now completed, but there still remains a branch of science to which it is necessary to refer. He explains that there appears to be no link between the physical and biological sciences and points out that a branch of science is therefore needed dealing with the application of the laws of inorganic phenomena, or Physics, to the development of organic forms. He proposes that the new branch of science be called bio-physics.

Although Pearson coined the term, I like to mark the birth of biophysics with the series of lectures given by Erwin Schrödinger in 1943. Schrödinger won the 1933 Nobel Prize in Physics for his work on quantum mechanics. In the 1930s a small handful of physicists began turning their attention to the questions of biology and biochemistry. Then in February 1943, Schrödinger gave his now famous lecture series titled What Is Life? The Friday afternoon lectures were so popular they had to be repeated on Monday for those unable to fit into the lecture hall. A year later the lecture series was published as the book, What Is Life? The Physical Aspects of the Living Cell.

The lecture series and book had a major impact on several notable scientists of the time. Only a few years later, in 1946, the Medical Research Council of King’s College in London established the Biophysics Research Unit of King’s College. Their goal was to hire physicists and put them to work on questions of biological significance. The physicist Maurice Wilkins and the physical chemist Rosalind Franklin were among those who joined the unit to become biophysicists. There at King’s College they used X-ray diffraction to investigate the structure of DNA.

The particle physicist Francis Crick at Cambridge University was also inspired to turn his attention to biophysics. He was soon joined by the biologist James Watson. In 1953 Watson and Crick made one of the most far-reaching discoveries of our time when they used Rosalind Franklin’s X-ray diffraction data to discover the double helix structure of DNA.

In 1957 the Biophysical Society was founded, to encourage growth and dissemination of knowledge in biophysics. Since then, interest in biophysics has only increased. By the early 1980s numerous universities offered graduate degrees in biophysics, but only a few, if any, colleges offered undergraduate degrees. Today over 60 colleges and universities offer undergraduate degrees in biophysics, and the Biophysical Society has over 9000 members. Figure 1-2 shows a time line of science and biophysics to put the age of biophysics in perspective.

The Scope and Topics of Biophysics

Biophysics is a very broad science, including a wide range of activities such as

• Studying the forces between atoms that determine the shape of a protein or DNA molecule

• Developing algorithms for a computer to analyze and display a three-dimensional image of the brain in real time during brain surgery

• Investigating and comparing the mechanics of limb movements or blood flow in various organisms

• Researching the effects of radioactivity on the environment

There are many ways we can classify the long list of topics that make up the field of biophysics. One very convenient and typical way to organize the broad scope of biophysics is according to the relative size of what we’re studying. For example, are we studying molecules, cells, or whole organisms? Another common and useful way is according to technique employed and application. With this in mind, and with some overlap, we will classify the many topics of biophysics into two broad classifications subdivided up into six categories.

FIGURE 1-2 • How old is biophysics?

• Biophysical topics based on relative size of subject

1. Molecular and subcellular biophysics

2. Physiological and anatomical biophysics

3. Environmental biophysics

• Biophysical techniques and applications

4. General biophysical techniques

5. Imaging biophysics

6. Medical biophysics

The next two chapters briefly describe many of the topics found in biophysics, organized according to the two major classifications just given. The purpose is to give you a broad overview of the scope of biophysics and to introduce vocabulary specific to biophysics. This will aid in understanding the detailed chapters that follow.

Throughout the book, vocabulary words that are important for you to learn will be in italics when first defined and will appear in the glossary in the back of the book.

QUIZ

Refer to the text in this chapter if necessary. Answers are in the back of the book.

1. An object of mass 3 kg is not moving. It is then pushed with a constant force of 12 N, causing it to accelerate at a rate of 4 m/s². After 5 s how fast will the object be going?

A. 12 m/s

B. 15 m/s

C. 20 m/s

D. 60 m/s

2. An average-size adult cheetah (50 kg) can accelerate from a standstill to 30 m/s in just 3 s. If we approximate the forward thrust provided by the cheetah’s leg muscles as a constant force, what force is necessary to cause this acceleration (10 m/s²)?

A. 50 N

B. 150 N

C. 300 N

D. 500 N

3. If a cheetah accelerates from a standstill at a rate of 10 m/s² and reaches its top speed in just 3 s, how far will the cheetah have traveled in that time?

A. 45 m

B. 30 m

C. 15 m

D. 10 m

FIGURE 1-3 • The cheetah is the fastest land animal. An average adult cheetah weighs about 110 pounds (lb). Its powerful leg muscles generate enough forward thrust to accelerate the cheetah from standing still to a top speed of about 70 mi/h in just 3 s.

4. A major source of energy for animals is carbohydrates (sugars) from plants (grains, fruits, vegetables, etc.). Where does this energy primarily come from?

A. Plants use their roots to draw energy from the ground.

B. Potential energy was stored in the seed before the plant grew.

C. Plants breathe oxygen at night and carbon dioxide during the day.

D. Photosynthesis extracts energy from sunlight and stores it in chemical bonds.

5. A chemical equation is a symbolic representation of a chemical reaction. A double arrow in a chemical equation indicates

A. we are not certain about the chemical reaction.

B. the chemical equation is balanced.

C. the reaction involves both physics and chemistry.

D. the reaction can occur in either direction.

6. Although Watson and Crick are credited with the 1953 discovery of the double-helical structure of DNA, they were only able to do this with data obtained by Rosalind Franklin at the Biophysical Research Unit of King’s College in London. What kind of data did she obtain?

A. Temperature measurements of DNA crystals

B. Electron microscopic images

C. X-ray diffraction

D. Magnetic resonance

7. Biophysics is an interdisciplinary science; this means that

A. the internal aspects of living things are studied.

B. it takes a lot of discipline to be a biophysicist.

C. biophysics is less rigorous than other sciences such as physics and biology.

D. biophysics combines physics, chemistry, and biology into a single science.

8. Two common and convenient ways to classify the various branches of biophysics are by

A. size of what is studied and by technique utilized.

B. size of what is studied and by whether mathematics is used.

C. technique used and by application.

D. technique used and by percentage of physics, chemistry, biology, and mathematics used.

chapter 2

Biophysical Topics

In this chapter, we present an overview of the various topics of biophysics according to the following three major divisions: molecular and subcellular biophysics, physiological and anatomical biophysics, and environmental biophysics.

CHAPTER OBJECTIVES

In this chapter, you will

• Gain an understanding of the broad scope of biophysics.

• Acquire some vocabulary of biophysics, learning the most commonly used terms and how they apply to the branches of biophysics.

• Learn to classify the topics of biophysics into the three major divisions of

• Molecular and subcellular biophysics.

• Physiological and anatomical biophysics.

• Environmental biophysics.

• Learn how the topic areas of biophysics are interrelated.

Just a reminder: Throughout the book, vocabulary words that are important for you to learn will be in italics when first defined and can also be found in the glossary in the back of the book.

Molecular and Subcellular Biophysics

By far the most common branches of biophysics are those dealing with molecules and subcellular function. This division of biophysics is sometimes also called biochemical physics, physical biochemistry, or biophysical chemistry. All three terms mean the same thing—what we will call molecular and subcellular biophysics. It is the place where biology, chemistry, and physics all meet. Within this division of biophysics we find the following topics.

The Structure and Conformation of Biological Molecules

This branch of biophysics deals with determining the structure, size, and shape of biological molecules.

Many biological molecules are polymers. A polymer is a large molecule made by connecting together many smaller molecules. Each of the smaller molecules is called a residue (because that’s what’s left over when you break a polymer into pieces). The residues making up a polymer may be identical, like links in a typical chain where the links are all ovals. The residues may also be a set of related but not identical molecules—imagine a chain where the links are various shapes: circles, triangles, squares, and rectangles.

Biopolymers (biological polymers) often fall into the latter case, where the residues have something in common but are not identical. For example, proteins are made by linking together smaller molecules called amino acids. The details of what an amino acid is are not important right now. For now, all you need to know is that each of the residues making up a protein is an amino acid and there are about 20 or so different amino acids found in proteins. Various amounts of these 20 or so amino acids can be linked together in various sequences to make different proteins, just as the 26 letters of the alphabet can be put together in various amounts and various sequences to form different words and sentences.

There are four levels of structure in biological molecules: primary, secondary, tertiary, and quaternary.

Primary structure specifies the atoms or groups of atoms making up a molecule and the order in which they are connected to one another. In polymers, rather than describe the primary structure in terms of specific atoms, we typically indicate only which residues we find and in what order we find them.

Secondary structure refers to the initial, simple, three-dimensional structure of a molecule. For example, a molecule, or part of a molecule, may take the shape of a helix or a shape similar to a pleated sheet.

Tertiary structure refers to the fact that a secondary structure, such as a helix or pleated sheet, can fold back on itself (sometimes over and over) and form a globular shape. As an analogy, if we consider an inflated balloon to be the three-dimensional secondary structure, then tertiary structure is folding and twisting that balloon into a balloon animal or some other creative shape.

FIGURE 2-1 • The four levels of structure in biological molecules are illustrated here using the example of a protein, but apply as well to other molecules and sub-cellular complexes. (Courtesy of National Institutes of Health: National Human Genome Research Institute.)

Quaternary structure refers to the case where two or more tertiary shapes attach to one another to form an even larger molecule or complex. Extenting our balloon analogy, quaternary structure refers to using more than one balloon to make our balloon animal.

Not all biomolecules exhibit all four levels of structure. Small molecules (for example, simple sugars or amino acids) typically exhibit only primary and secondary structures. Biopolymers most commonly exhibit all levels up to tertiary structure, and sometimes exhibit quaternary structure.

The structure and conformation of biological molecules, as a branch of biophysics, also includes analyzing the forces and energy required for a molecule to maintain a particular shape. With this information, biophysicists develop geometric and mathematical models to predict the secondary and tertiary structure of a molecule, given its primary structure.

Structure Function Relationships

Closely related to determining the structure and shape of biomolecules is determining which parts of a molecule are involved in its biological function, and determining how changes to its structure or shape affect its biological function. When a one particular part of a molecule or complex is involved in carrying out its function, that part is referred to as the active site of the molecule. It is also possible for a molecule or complex to have more than one active site.

Conformational Transitions

Conformational transition is just a fancy term for a change in shape. Although the word conformation can mean structure or shape, in the context of biophysics it almost always means shape, specifically the three-dimensional arrangement of atoms in a molecule (that is, the secondary, tertiary, and quaternary structures).

Biomolecules often change their shape as part of their function. For example, the DNA double helix must temporarily unwind in order for the genetic instructions to be read or in order for the DNA to replicate itself for the next generation. Biophysicists use a variety of techniques to measure conformational changes in biomolecules, to measure the energy associated with them and to determine the relationship between the various conformations and their biological function. It is also possible to induce conformational changes in the laboratory. These induced changes may or may not happen in nature. In either