Table Of ContentContributors to Volume 210
Article numbers are in parentheses following the names of contributors.
Affiliations listed are current.
GARY K. ACKERS (19), Department of JULIEN S. DAVIS (17), Department of Biol-
Biochemistry and Molecular Biophysics, ogy and McCollum-Pratt Institute, The
Washington University School of Medi- Johns Hopkins University, Baltimore,
cine, St. Louis, Missouri 63110 Maryland 21218
MARCEL AMELOOT (12, 14), Research FRANS C. DE REVYRHCS (14), Department
Group of Physiology, Limburgs Universi- of Chemistry, Katholieke Universiteit
tair Centrum, B-3590 Diepenbeek, Bel- Leuven, B-3001 Heverlee, Belgium
gium
OCIRNE DI CERA (4), Department of
RONN ANDRIESSEN (14), Department of
Biochemistry and Molecular Biophysics,
Chemistry, Katholieke Universiteit
Washington University School of Medi-
Leuven, B-3001 Heverlee, Belgium
cine, St. Louis, Missouri 63110
DIVAD L. BAIN (19), Department of
YASDNIL M. FAUNT (1, 15), Biodynamics
Biochemistry and Molecular Biophysics,
Institute and Diabetes Center, Univer-
Washington University School of Medi-
sity of Virginia, Charlottesville, Virginia
cine, St. Louis, Missouri 01136
80922
~ELIKO *REZJAB (10), Department of Bio-
TREBREH R. NOSROVLAH (3, 28), Depart-
chemistry and Molecular Biology, Mayo
ment of Pathology, Henry Ford Hospital,
Clinic~Foundation, Rochester, Minnesota
Detroit, Michigan 20284
50955
YHTOROD BECKETT (19), Department of E. R. HENRY (8), Laboratory of Chemical
Physics, National Institute of Diabetes
Chemistry and Biochemistry, University
of Maryland, Baltimore, Maryland 21228 and Digestive and Kidney Diseases,
National Institutes of Health, Bethesda,
HPESOJ M. MEHCEEB (2, 23), Department of
Maryland 29802
Molecular Physiology and Biophysics,
Vanderbilt University School of Medi- NOTSERP HENSLEY (18), Macromolecular
cine, Nashville, Tennessee 37232 Sciences Department, SmithKline Bee-
L~ION BOENS (14), Department of Chemis- cham Pharmaceuticals, King of Prussia,
try, Katholieke Universiteit Leuven, Pennsylvania 60491
B-3001 Heverlee, Belgium J. HOFRICHTER (8), Laboratory of Chemi-
DAVID WAYNE BOLEN (22), Department of cal Physics, National Institute of Dia-
Chemistry and Biochemistry, Southern Il- betes and Digestive and Kidney Diseases,
linois University at Carbondale, Carbon- National Institutes of Health, Bethesda,
dale, Illinois 10926 Maryland 29802
E. E. BRUMBAUGH (25), Department of C. HUANG (25), Department of Biochemis-
Chemistry, Bridgewater College, Bridge- try, University of Virginia, Charlottes-
water, Virginia 22812 ville, Virginia 22908
PAUL BRIAN CONTINO (21), Department LEAHCIM L. JOHNSON (1, 5, 6, 7, ,51 26),
of Medicine~Thrombosis, Mount Sinai Department of Pharmacology, University
School of Medicine, New York, New York of Virginia, Charlottesville, Virginia
92001 80922
* On leave of absence from Rugjer Bogkovid Institute, Zagreb, Croatia.
vii
viii CONTRIBUTORS OT VOLUME 210
W. CURTIS JOHNSON, JR. (20), Department ENIREHTAC A. ROYER (23), School of Phar-
of Biochemistry and Biophysics, Oregon macy, University of Wisconsin-Madison,
State University, Corvallis, Oregon 13379 Madison, Wisconsin 60735
W. T. KATZ (29), Department of Biomedi- DLANOD F. SENEAR (22), Department of
cal Engineering, University of Virginia, Biochemistry and Molecular Biology,
Charlottesville, Virginia 80922 University of California, Irvine, Irvine,
California 71729
YAJ R. KNUTSON (16), Laboratory of Cell
Biology, National Heart, Lung and Blood MADELINE A. SHEA (19), Department of
Institute, National Institutes of Health, Biochemistry, University of Iowa College
Bethesda, Maryland 29802 of Medicine, Iowa City, Iowa 52242
ENOCH W. SMALL (ll), Department of
KENNETH S. KOBLAN (19), Department of
Chemistry and Biochemistry, Eastern
Biochemistry and Molecular Biophysics,
Washington University, Cheney, Wash-
Washington University School of Medi-
ington 40099
cine, St. Louis, Missouri 01136
ENNAEJ RUDZKI SMALL (24), Department of
WILLIAM R. LAWS (21), Department of Bio-
Chemistry and Biochemistry, Eastern
chemistry, Mount Sinai School of Medi-
Washington University, Cheney, Wash-
cine, New York, New York 92001
ington 40099
HENRY H. MANTSCH (9), Steacie Institute J. W. SNELL (29), Department of Biomedi-
for Molecular Sciences, National Re- cal Engineering, University of Virginia,
search Council of Canada, Ottawa, On- Charlottesville, Virginia 22908
tario K1A OR6, Canada
ELORAC J. SPANGLER (13), Center For Mo-
M. B. MERICKEL (29), Department of Bio- lecular Genetics, University of California,
medical Engineering, University of Vir- San Diego, La Jolla, California 39029
ginia, Charlottesville, Virginia 80922 MARTIN STRAUME (5, 7), Biocalorimetry
WEBB MILLER (27), Department of Com- Center, Department of Biology, The
puter Science and Institute of Molecu- Johns Hopkins University, Baltimore,
lar Evolutionary Genetics, Pennsylvania Maryland 81212
State University, University Park, Penn- VIVIANE VAN NED BERGH (14), Department
sylvania 20861 of Chemistry, Katholieke Universiteit
Leuven, B-3001 Heverlee, Belgium
SALGUOD J. MOFFATT (9), Steacie Institute
for Molecular Sciences, National Re- SENNAHOJ D. VELDHUIS (26), Departments
search Council of Canada, Ottawa, On- of Internal Medicine and Pharmacology,
tario KIA OR6, Canada University of Virginia Health Sciences
Center, and National Science Foundation
GLENN ENODRAN (18), Edvotek, Inc., West
Center for Biological Timing, Charlottes-
Bethesda, Maryland 20827
ville, Virginia 80922
WILLIAM R. NOSRAEP (27), Department of MERYL E. WASTNEY (18), Department of
Biochemistry, University of Virginia, Pediatrics, Georgetown University Medi-
Charlottesville, Virginia 22908 cal Center, Washington, D.C. 20007
NYLKNARF G. TSAGREDNERP (10), Depart- F. EUGENE YATES (30), Medical Monitoring
ment of Biochemistry and Molecular Biol- Unit, Department of Medicine, University
ogy, Mayo Clinic/Foundation, Rochester, of California, Los Angeles, Los Angeles,
Minnesota 50955 California 52009
Preface
In the past decade microcomputers have revolutionized biomedical
research. Almost every new scientific instrument is "computer con-
trolled." Almost every researcher has a personal computer easily avail-
able or is readily linked to a mainframe. The improvements in computer
software development and advances in methods of analysis have paral-
leled the computer hardware improvements.
It is clear that new ways of evaluating experimental data have en-
hanced the type of conclusions that may be drawn and have changed the
way in which experiments are conceived and done. The biochemical com-
munity must be aware of new developments in data analysis and com-
puter usage. The primary aim of this volume is to inform biomedical
researchers of the modern data analysis methods that have developed
concomitantly with computer hardware.
The process of collecting experimental data, analyzing the data, and
then publishing the data and results is not a one-way street. All methods
of data analysis make assumptions about the nature of the data. Specifi-
cally, they make assumptions about the types and magnitudes of the
experimental uncertainties contained within the data. A biomedical re-
searcher should carefully design the experimental data collection proce-
dures such that they are compatible with the desired method of data
analysis.
A common procedure used in the past for the analysis of nonlinear
systems was to rearrange the equation describing the process into a linear
form and then to use linear least-squares to determine slopes and inter-
cepts related to the parameters of interest. Typical examples include the
Lineweaver-Burk plot for analysis of Michaelis-Menton kinetic data and
the Scatchard plot for analysis of equilibrium binding data.
Consider a Scatchard plot as an example. The objective of this, and
many other types of plots, is to transform a set of experimental data into a
straight line form; in this case, a plot of the amount of bound ligand
divided by the free ligand (Y axis) as a function of bound ligand (X axis).
For a ligand binding problem with a single class of noninteracting binding
sites this transformation will provide a straight line. The next step is to
"fit" a least-squares straight line to the transformed data points. The
slope of this line is related to the ligand binding affinity and the X-axis
intercept is the binding capacity. However, this approach makes an in-
valid assumption about the nature of the uncertainties contained in the
experimental data. Fitting a least-squares straight line to the transformed
xi
X PREFACE
data assumes that the experimental uncertainties follow a random distri-
bution and are parallel to the Y axis. However, in a Scatchard plot the
uncertainties are nearly parallel to the Y axis at low fractional saturations
and nearly parallel to the X axis at high fractional saturations. Conse-
quently, the use of a least-squares method is not valid for the analysis of
Scatchard plots. Note that this does not preclude the use of a Scatchard
plot to help a researcher visualize an experiment if the actual data analysis
is performed by another method.
So how can the data be analyzed? The best approach is to fit the
original data, without any transformations, by nonlinear least-squares.
For a more complete discussion of Scatchard plots refer to Klotz, 2,1
Munson and Rodbard, 4,3 and Johnson and Frasier. 5
So why was the Scatchard plot developed? The Scatchard plot was
developed in the 1940s before the availability of digital computers. Some
nonlinear least-squares techniques were available at the time, i.e., the
Gauss-Newton Method. 6 However, nonlinear least-squares techniques
require too many operations to be performed without a computer in a
reasonable length of time. At the time the Scatchard plot was the only
"show in town." Now that high-speed computers are available there is
no reason to attempt to analyze transformed data.
Almost every type of transformation "plot" to analyze experimental
data was developed because high-speed digital computers were not avail-
able to perform the correct calculation. Incidently, this includes a semilog
plot for the analysis of exponential decays. 5 These plots fail to meet the
statistical requirements of linear least-squares methods. This failure is
due to the required transformation of the data. The reason that these plots
are still used for the analysis of data is primarily due to a lack of informa-
tion about the available methods of data analysis. One purpose of this
volume is to provide this information to biomedical researchers.
"On the other side of the coin," many biomedical researchers have
learned to revere computers as oracles. They assume that if a computer
analyzed their data then the results must be correct. Computers are not
oracles! The results of any computer analysis are no better than the
computer programs used for the analysis. Data analysis computer pro-
grams are created by people who make assumptions about the nature of
t I. M. Klotz, Science 217, 1247 (1982).
2 I. M. Klotz, Science 220, 189 (1983).
3 p. j. Munson and D. Rodbard, Anal. Biochem. 107, 022 (1980).
4 p. j. Munson and D. Rodbard, Science ,1122 979 (1983).
s M. L. Johnson and S. G. Frasier, this series, Vol. 117, p. 301.
6 M. L. Johnson and L. M. Faunt, "Parameter estimation by least-squares methods," this
volume 1.
ECAFERP xi
the experimental data. They subsequently make assumptions about the
best method of analysis based on their assumptions about the experimen-
tal data. These assumptions may not be acceptable for your experimental
data. They also make compromises to save computer time and space in
the memory of the computer. Computer programmers can also make
mistakes. Thus, computer programs sometimes include unwarranted as-
sumptions and can make mistakes/
Consequently, biomedical researchers cannot simply insert data into a
computer and accept the results as gospel. Researchers must be aware of
the assumptions used by their data analysis programs. They must be
certain that they are using methods that are appropriate for their particu-
lar type of data. They need to validate their computer programs with real
and synthetic data to ascertain that the computer programs are producing
the results they expect. They should always question the results of a
computer analysis, i.e., do they have physical meaning? The purpose of
this volume is to help biomedical researchers meet these needs.
The chapters in this book are written for biomedical researchers by
biomedical researchers. The volume is divided into three basic categories.
First, basic methods such as nonlinear least-squares and maximum likeli-
hood are described. Second, specific examples of the use of some of these
methods are presented. The volume ends with introductory discussions
about methods that are currently being developed, such as neural net-
works and fractals.
We are grateful to Nathan O. Kaplan who recognized the importance
of data analysis in enzymology and conceived the idea for this volume.
LUDWIG BRAND
MICHAEL L. JOHNSON
METHODS IN ENZYMOLOGY
VOLUME I. Preparation and Assay of Enzymes
Edited by SIDNEY P. COLOWICK DNA NATHAN O. KAPLAN
VOLUME II. Preparation and Assay of Enzymes
Edited by SIDNEY P. COLOWICK DNA NATHAN O. KAPLAN
VOLUME III. Preparation and Assay of Substrates
Edited by SIDNEY P. COLOWlCK DNA NATHAN O. KAPLAN
VOLUME IV. Special Techniques for the Enzymologist
Edited yb SIDNEY P. COLOWlCK DNA NATHAN O. KAPLAN
VOLUME V. Preparation and Assay of Enzymes
Edited yb SIDNEY P. COLOWICK DNA NATHAN O. KAPLAN
VOLUME VI. Preparation and Assay of Enzymes )deunitnoC(
Preparation and Assay of Substrates
Special Techniques
Edited by SIDNEY P. COLOWICK DNA NATHAN O. KAPLAN
VOLUME VII. Cumulative Subject Index
Edited by SIDNEY P. COLOWICK DNA NATHAN O. KAPLAN
VOLUME VIII. Complex Carbohydrates
Edited by ELIZABETH F. NEUFELD DNA VICTOR GRUBSNIG
VOLUME IX. Carbohydrate Metabolism
Edited by WILLIS A. WOOD
VOLUME X. Oxidation and Phosphorylation
Edited by RONALD W. KOORBATSE DNA DRANYAM E. NAMLLUP
VOLUME XI. Enzyme Structure
Edited by C. H. W. HIRS
VOLUME XII. Nucleic Acids (Parts A and B)
Edited by LAWRENCE NAMSSORG DNA KIVIE EVADLOM
xiii
xiv SDOHTEM NI YGOLOMYZNE
VOLUME XlII. Citric Acid Cycle
Edited by J. M. LOWENSTEIN
VOLUME XIV. Lipids
Edited by J. M. LOWENSTEIN
VOLUME XV. Steroids and Terpenoids
Edited by RAYMOND B. NOTYALC
VOLUME XVI. Fast Reactions
Edited by KENNETH KUSTIN
VOLUME XVII. Metabolism of Amino Acids and Amines (Parts A and B)
Edited by HERBERT TABOR DNA CELIA WHITE ROBAT
VOLUME XVIII. Vitamins and Coenzymes (Parts A, B, and C)
Edited by DONALD B. MCCORMICK DNA LEMUEL D. WRIGHT
VOLUME XIX. Proteolytic Enzymes
Edited by GERTRUDE E. PERLMANN DNA LASZLO DNAROL
VOLUME XX. Nucleic Acids and Protein Synthesis (Part C)
Edited yb KIVIE MOLDAVE DNA LAWRENCE NAMSSORG
VOLUME XXI. Nucleic Acids (Part D)
Edited yb LAWRENCE NAMSSORG DNA KIVIE EVADLOM
EMULOV XXII. Enzyme Purification and Related Techniques
Edited by WILLIAM B. YBOKAJ
VOLUME XXIII. Photosynthesis (Part A)
Edited yb ANTHONY NAS PIETRO
VOLUME XXIV. Photosynthesis and Nitrogen Fixation (Part B)
Edited by ANTHONY NAS PIETRO
VOLUME XXV. Enzyme Structure (Part B)
Edited yb C. H. W. HIRS DNA SERGE N. TIMASHEFF
VOLUME XXVI. Enzyme Structure (Part C)
Edited by C. H. W. HIRS DNA SERGE N. TIMASHEFF
METHODS IN ENZYMOLOGY XV
VOLUME XXVII. Enzyme Structure (Part D)
Edited by C. H. W. HIRS DNA SERGE N. TIMASHEFF
VOLUME XXVIII. Complex Carbohydrates (Part B)
Edited by VICTOR GRUBSNIG
VOLUME XXIX. Nucleic Acids and Protein Synthesis (Part E)
Edited by LAWRENCE NAMSSORG DNA KIVIE EVADLOM
VOLUME XXX. Nucleic Acids and Protein Synthesis (Part F)
Edited by KIVIE MOLDAVE DNA LAWRENCE NAMSSORG
VOLUME XXXI. Biomembranes (Part A)
Edited by SIDNEY FLEISCHER DNA LESTER REKCAP
VOLUME XXXlI. Biomembranes (Part B)
Edited by SIDNEY FLEISCHER DNA LESTER REKCAP
VOLUME XXXIII. Cumulative Subject Index Volumes I-XXX
Edited by MARTHA G. DENNIS DNA EDWARD A. DENNIS
VOLUME XXXIV. Affinity Techniques (Enzyme Purification: Part B)
Edited by WILLIAM B. YBOKAJ DNA MEIR WILCHEK
VOLUME XXXV. Lipids (Part B)
Edited by JOHN M. LOWENSTEIN
VOLUME XXXVI. Hormone Action (Part A: Steroid Hormones)
Edited by BERT W. O'MALLEY DNA JOEL G. NAMDRAH
VOLUME XXXVII. Hormone Action (Part B: Peptide Hormones)
Edited by BERT W. O'MALLEY DNA JOEL G. NAMDRAH
VOLUME XXXVIII. Hormone Action (Part C: Cyclic Nucleotides)
Edited yb JOEL G. HARDMAN DNA BERT W. O'MALLEY
EMULOV XXXlX. Hormone Action (Part D: Isolated Cells, Tissues, and
Organ Systems)
Edited by JOEL G. HARDMAN DNA BERT W. O'MALLEY
EMULOV XL. Hormone Action (Part E: Nuclear Structure and Function)
Edited by BERT W. O'MALLEY DNA JOEL G. NAMDRAH
xvi SDOHTEM IN YGOLOMYZNE
VOLUME XLI. Carbohydrate Metabolism (Part )B
Edited by W. A. WOOD
VOLUME XLII. Carbohydrate Metabolism (Part C)
Edited yb W. A. WOOD
VOLUME XLIII. Antibiotics
Edited yb JOHN H. HASH
VOLUME XLIV. Immobilized Enzymes
Edited yb KLAUS HCABSOM
VOLUME XLV. Proteolytic Enzymes (Part )B
Edited yb LORAND LASZLO
EMULOV XLVI. Affinity Labeling
Edited by WILLIAM B. YBOKAJ DNA MEIR KEHCL1W
VOLUME XLVII. Enzyme Structure (Part E)
Edited yb C. H. W. HIRS DNA SERGE N. TIMASHEFF
VOLUME XLVIII. Enzyme Structure (Part F)
Edited yb C. H. W. HIRS DNA SERGE N. FFEHSAMIT
VOLUME XLIX. Enzyme Structure (Part G)
Edited yb C. H. W. HIRS DNA SERGE N. TIMASHEFF
VOLUME L. Complex Carbohydrates (Part C)
Edited yb VICTOR GRUBSN1G
VOLUME LI. Purine and Pyrimidine Nucleotide Metabolism
Edited by PATRICIA A. HOFFEE DNA MARY ELLEN SENOJ
VOLUME LII. Biomembranes (Part C: Biological Oxidations)
Edited by SIDNEY FLEISCHER DNA LESTER REKCAP
VOLUME LIII. Biomembranes (Part D: Biological Oxidations)
Edited by SIDNEY FLEISCHER AND LESTER PACKER
VOLUME LIV. Biomembranes (Part E: Biological Oxidations)
Edited yb SIDNEY FLEISCHER DNA LESTER REKCAP
xvii
METHODS IN ENZYMOLOGY
VOLUME LV. Biomembranes (Part F: Bioenergetics)
Edited by SIDNEY FLEISCHER DNA LESTER REKCAP
VOLUME LVI. Biomembranes (Part G: Bioenergetics)
Edited by SIDNEY FLEISCHER DNA LESTER REKCAP
VOLUME LVII. Bioluminescence and Chemiluminescence
Edited by MARLENE A. DELUCA
VOLUME LVIII. Cell Culture
Edited by WILLIAM B. YBOKAJ DNA ARI NATSAP
VOLUME LIX. Nucleic Acids and Protein Synthesis (Part G)
Edited by KIVIE MOLDAVE DNA LAWRENCE NAMSSORG
VOLUME LX. Nucleic Acids and Protein Synthesis (Part H)
Edited by KIVIE MOLDAVE DNA LAWRENCE NAMSSORG
VOLUME 61. Enzyme Structure (Part H)
Edited by C. H. W. HIRS DNA SERGE N. TIMASHEFF
VOLUME 62. Vitamins and Coenzymes (Part )D
Edited by DONALD B. MCCORMICK DNA LEMUEL D. WRIGHT
VOLUME 63. Enzyme Kinetics and Mechanism (Part A: Initial Rate and
Inhibitor Methods)
Edited by DANIEL L. PURICH
VOLUME 64. Enzyme Kinetics and Mechanism (Part B: Isotopic Probes
and Complex Enzyme Systems)
Edited by DANIEL L. PURICH
VOLUME 65. Nucleic Acids (Part )1
Edited by LAWRENCE NAMSSORG DNA KIVIE EVADLOM
VOLUME 66. Vitamins and Coenzymes (Part )E
Edited by DONALD B. MCCORMICK DNA LEMUEL D. WRIGHT
VOLUME 67. Vitamins and Coenzymes (Part F)
Edited by DONALD B. MCCORMICK DNA LEMUEL D. WRIGHT
