Fundamental Concepts in Biophysics: Volume 1

262 Pages·2009·8.054 MB·English

by  Rajiv R.P. Singh (auth.), Thomas Jue (eds.)

H M B
ANDBOOK OF ODERN IOPHYSICS
Series Editor
Thomas Jue
University of California Davis
Davis, California
For other titles published in this series, go to
www.springer.com/series/7845
Thomas Jue
Editor
Fundamental Concepts
in Biophysics
Volume 1
Editor
Thomas Jue, Ph.D.
Department of Biochemistry and Molecular Medicine
University of California Davis
One Shields Avenue
Davis, CA 95616, USA
[email protected]
ISBN: 978-1-58829-973-4 e-ISBN: 978-1-59745-397-4
DOI: 10.1007/978-1-59745-397-4
Library of Congress Control Number: 2009921740
© Humana Press, a part of Springer Science+Business Media, LLC 2009
All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher
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Cover Illustration: Patch-Clamp fluorometry of an excised inside-out membrane patch.
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P
REFACE
Over the past several years, I have organized and taught a core course in Modern Biophysics
Techniques at the University of California Davis. Graduate students in biophysics, chemistry,
physics, and engineering enroll in the class to survey the physical techniques that scientists use
to study biology.
Introducing the diverse and complex field of biophysics in an academically rigorous but in-
teresting way poses daunting challenges. Indeed, the course has undergone many transforma-
tions and has tried on many styles: seminar/journal club, lecture/lab, and just plain didactic lec-
ture formats. These, however, have achieved limited success, because they either assume a
strong mathematics/physical-science background or reduce the physical science to a pedestrian
level of knowledge, or demand that students trudge along with the expert researchers. None
have attracted the interest of biology, physiology, or medical students, who must search for the
biological meaning within biophysics.
One major obstacle to developing an attractive but scholarly course centers on the balance
between formalism and perspective. Each biophysics technique requires a mastery of a chal-
lenging set of physical-science/mathematics formalism. Yet even with mastery the reader may
still not gain a biomedical perspective. How will these biophysical techniques help clarify the
complex issues in biology? Moreover, how will the course deal with biomedical students’ reluc-
tance to overcome the imposing physical-science/mathematical formalism in order to gain new
perspectives on biology?
These considerations have given rise to the series Handbook of Modern Biophysics. The
books in this series will bring current biophysics topics into focus and expand as the field of
biophysics expands, so that biology and physical-science students or researchers can learn fun-
damental concepts and apply new biophysics techniques to address biomedical questions. How-
ever, the chapter structure will recognize the demand for explicating the conceptual framework
of the underlying physics formalism and for casting perspectives on the biomedical applica-
tions. Each chapter will have a bipartite structure: the first part establishes the fundamental
physics concepts and describes the instrumentation or technique, while the second illustrates
current applications in addressing complex questions in biology. With the addition of problem
sets, further study, and references, the interested reader will be able to further explore the ideas
presented.
In the first volume, Fundamental Concepts in Biophysics, the authors lay down a foundation
for biophysics study. Rajiv Singh opens the book by pointing to the central importance of
“Mathematical Methods in Biophysics.” William Fink follows with a discussion on “Quantum
Mechanics Basic to Biophysical Methods.” Together, these two chapters establish some of the
principles of mathematical physics underlying many biophysics techniques. Because computer
modeling forms an intricate part of biophysics research, Subhadip Raychaudhuri and colleagues
introduce the use of computer modeling in “Computational Modeling of Receptor–Ligand Bind-
ing and Cellular Signaling Processes.” Yin Yeh and coworkers bring to the reader’s attention
the physical basis underlying the common use of fluorescence spectroscopy in biomedical re-
search in their chapter “Fluorescence Spectroscopy.” Electrophysiologists have also applied
biophysics techniques in the study of membrane proteins, and Tsung-Yu Chen et al. explore
v
vi PREFACE
stochastic processes of ion transport in their “Electrophysiological Measurements of Membrane
Proteins.” Michael Saxton takes up a key biophysics question about particle distribution and
behavior in systems with spatial or temporal inhomogeneity in his chapter “Single-Particle
Tracking.” Finally, in “NMR Measurement of Biomolecule Diffusion,” Thomas Jue explains
how magnetic resonance techniques can map biomolecule diffusion in the cell to a theory of
respiratory control .
This book thus launches the Handbook of Modern Biophysics series and sets up for the
reader some of the fundamental concepts underpinning the biophysics issues to be presented in
future volumes.
Thomas Jue
Biochemistry & Molecular Medicine
University of California Davis
C
ONTENTS
1 Mathematical Methods in Biophysics
Rajiv R.P. Singh
1.1. Functions of One Variable and Ordinary Differential Equations........................................ 1
1.2. Functions of Several Variables: Diffusion Equation in One Dimension............................. 2
1.3. Random Walks and Diffusion............................................................................................. 4
1.4. Random Variables, Probability Distribution, Mean, and Variance..................................... 7
1.5. Diffusion Equation in Three Dimensions............................................................................ 8
1.6. Complex Numbers, Complex Variables, and Schrödinger's Equation................................ 9
1.7. Solving Linear Homogeneous Differential Equations......................................................... 10
1.8. Fourier Transforms.............................................................................................................. 13
1.9. Nonlinear Equations: Patterns, Switches and Oscillators.................................................... 14
2 Quantum Mechanics Basic to Biophysical Methods
William Fink
2.1. Quantum Mechanics Postulates........................................................................................... 17
2.2. One-Dimensional Problems................................................................................................. 23
2.3. The Harmonic Oscillator..................................................................................................... 27
2.4. The Hydrogen Atom............................................................................................................ 30
2.5. Approximate Methods......................................................................................................... 33
2.6. Many Electron Atoms and Molecules................................................................................. 36
2.7. The Interaction of Matter and Light.................................................................................... 38
3 Computational Modeling of Receptor–Ligand Binding and
Cellular Signaling Processes
Subhadip Raychaudhuri, Philippos Tsourkas, and Eric Willgohs
3.1. Introduction......................................................................................................................... 41
3.2. Differential Equation-Based Mean-Field Modeling............................................................ 42
3.3. Application: Clustering of Receptor–Ligand Complexes.................................................... 45
3.4. Modeling Membrane Deformation as a Result of
Receptor–Ligand Binding................................................................................................... 46
3.5. Limitations of Mean-Field Differential Equation-Based Modeling.................................... 47
3.6. Master Equation: Calculating the Time Evolution of a Chemically
Reacting System.................................................................................................................. 47
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3.7. Stochastic Simulation Algorithm (SSA) of Gillespie.......................................................... 48
3.8. Application of the Stochastic Simulation Algorithm (SSA)................................................ 49
3.9. Free Energy-Based Metropolis Monte Carlo Simulation.................................................... 49
3.10. Application of Metropolis Monte Carlo Algorithm............................................................. 50
3.11. Stochastic Simulation Algorithm with Reaction and Diffusion:
Probabilistic Rate Constant–Based Method........................................................................ 51
3.12. Mapping Probabilistic and Physical Parameters.................................................................. 51
3.13. Modeling Binding between Multivalent Receptors and Ligands......................................... 53
3.14. Multivalent Receptor–Ligand Binding and Multimolecule Signaling
Complex Formation............................................................................................................. 54
3.15. Application of Stochastic Simulation Algorithm with
Reaction and Diffusion........................................................................................................ 55
3.16. Choosing the Most Efficient Simulation Method................................................................ 55
3.17. Summary............................................................................................................................. 56
4 Fluorescence Spectroscopy
Yin Yeh, Samantha Fore, and Huawen Wu
4.1. Introduction......................................................................................................................... 63
4.2. Fundamental Process of Fluorescence................................................................................. 64
4.3. Fluorescence Microscopy.................................................................................................... 71
4.4. Types of Biological Fluorophores....................................................................................... 76
4.5. Application of Fluorescence in Biophysical Research........................................................ 86
4.6. Dynamic Processes Probed by Fluorescence....................................................................... 96
5 Electrophysiological Measurements of Membrane Proteins
Tsung-Yu Chen, Yu-Fung Lin, and Jie Zheng
5.1. Membrane Bioelectricity..................................................................................................... 111
5.2. Electrochemical Driving Force............................................................................................ 112
5.3. Voltage Clamp versus Current Clamp................................................................................. 114
5.4. Principles of Silver Chloride Electrodes.............................................................................. 115
5.5. Capacitive Current and Ionic Current.................................................................................. 115
5.6. Gating and Permeation Functions of Ion Channels............................................................. 116
5.7. Two-Electrode Voltage Clamp for Xenopus Oocyte Recordings........................................ 118
5.8. Patch-Clamp Recordings..................................................................................................... 122
5.9. Patch-Clamp Fluorometry................................................................................................... 137
HANDBOOKOFMODERNBIOPHYSICS, VOLUME 1 ix
6 Single-Particle Tracking
Michael J. Saxton
6.1. Introduction......................................................................................................................... 147
6.2. The Broader Field................................................................................................................ 148
6.3. Labeling the Dots................................................................................................................ 150
6.4. Locating the Dots................................................................................................................ 153
6.5. Connecting the Dots............................................................................................................ 158
6.6. Interpreting the Dots: Types of Motion............................................................................... 158
6.7. Is It Really a Single Particle?.............................................................................................. 163
6.8. Enhancing z-Resolution....................................................................................................... 164
6.9. Can a Single Fluorophore Be Seen in a Cell?...................................................................... 165
6.10. Colocalization...................................................................................................................... 165
6.11. Example: Motion in the Plasma Membrane Is More
Complicated than is Often Assumed................................................................................... 167
6.12. Example: From DNA to Protein.......................................................................................... 168
6.13. Example: Infection of a Cell by a Virus.............................................................................. 169
7 NMR Measurement of Biomolecule Diffusion
Thomas Jue
7.1. Introduction......................................................................................................................... 181
7.2. Relaxation and Field Gradient Measurement of Diffusion.................................................. 182
7.3. Frequency Encoding of Spatial Position with Field Gradient............................................. 183
7.4. Phase Encoding by the Field Gradient................................................................................. 184
7.5. Diffusion and Pulsed Field Gradient Signal Intensity......................................................... 187
7.6. Fick’s Laws of Diffusion..................................................................................................... 188
7.7. Biomolecule Diffusion in the Cell....................................................................................... 189
7.8. Stimulated Echo and Biomolecule Diffusion in the Cell..................................................... 190
7.9. Myoglobin Function in the Cell........................................................................................... 190
7.10. Perfused Heart Model.......................................................................................................... 191
7.11. O Diffusion in Muscle Cell................................................................................................ 192
2
7.12. Translational Diffusion of Mb in Vitro............................................................................... 193
7.13. Translational Diffusion of Mb In Vivo................................................................................ 193
7.14. Mb Contribution to O transport in Vivo............................................................................. 193
2
7.15. Mb-Facilitated Diffusion and Myocardial Function............................................................ 195
7.16. Mb-Facilitated Diffusion and Skeletal Muscle Function..................................................... 195
7.17. Cytoplasmic Properties and Architecture............................................................................ 196
7.18. Summary............................................................................................................................. 196
Problem Solutions...................................................................................................... 201
Index............................................................................................................................ 233
C
ONTRIBUTORS
Tsung-Yu Chen (chap. 5) Michael J. Saxton (chap. 6)
Center for Neuroscience Department of Biochemistry
Department of Neurology & Molecular Medicine
University of California Davis University of California Davis
1544 Newton Court One Shields Avenue
Davis, CA 95618 USA Davis, CA 95616 USA
[email protected] [email protected]
William H. Fink (chap. 2) Rajiv R.P. Singh (chap. 1)
Department of Chemistry Department of Physics
University of California Davis University of California Davis
One Shields Avenue One Shields Avenue
Davis, CA 95616 USA Davis, CA 95616 USA
[email protected] [email protected]
Samantha Fore (chap. 4) Philippos Tsourkas (chap. 3)
Center for Biophotonics Department of Biomedical Engineering
Science and Technology University of California Davis
University of California, Davis One Shields Avenue
2700 Stockton Blvd., Suite 1400 Davis, CA 95616 USA
Sacramento, CA 95817 USA
[email protected] Eric Willgohs (chap. 3)
Department of Biomedical Engineering
Thomas Jue (chap. 7) University of California Davis
Department of Biochemistry One Shields Avenue
& Molecular Medicine Davis, CA 95616 USA
One Shields Avenue
University of California Davis Huawen Wu (chap. 4)
Davis, CA 95616 USA Department of Applied Science
[email protected] University of California, Davis
One Shields Avenue
Yu-Fung Lin (chap. 5) Davis, CA 95616 USA
Departments of Anesthesiology, [email protected]
& Physiology and Membrane Biology
University of California Davis Yin Yeh (chap. 4)
One Shields Avenue Department of Applied Science
Davis, CA 95616 USA University of California, Davis
One Shields Avenue
Subhadip Raychaudhuri (chap. 3) Davis, CA 95616 USA
Department of Biomedical [email protected]
Engineering
University of California Davis Jie Zheng (chap. 5)
One Shields Avenue Department of Physiology
Davis, CA 95616 USA & Membrane Biology
[email protected] University of California Davis
One Shields Avenue
Davis, CA 95616 USA
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