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Analysis of Enzyme Kinetic Data

This page describes the book Analysis of Enzyme Kinetic Data by Athel Cornish-Bowden, published by Oxford University Press (1995): ISBN 0-19-854877-X

 Cover design

Publication details

Published by Oxford University Press, Oxford and New York, 1995

208 pages, 65 line illustrations

0-19-854878-8, hardback; 0-19-854877-X, paperback

This book is now out of print, and the publishers have no more copies left in stock.

The book can be downloaded

The text of the book may be downloaded from the web, as detailed below.

Availability

and amazon.co.uk

New copies of the book are no longer available through the web from amazon.com and amazon.co.uk. However, you may be able to locate a used copy from Amazon.

Download Chapters 1–7

The Theory part of the book, together with preliminary pages and bibliography, but not the practical part (see below), can be downloaded from this site as a PDF (Acrobat) file (large file: 5 megabytes). This file may be used, copied, circulated, etc. without restriction. However, I do ask that any published work in which it is used be acknowledged with an appropriate citation to the book as published. Although it was not practicable to maintain the exact layout and typography of the book (and there may be some minor variations in wording, as the file was prepared from the original files submitted to the publishers in 1994, not from the book itself), it does retain the original pagination, i.e. page numbers in the PDF file correspond exactly to pages of the book.

Version history.The present version is version 1.1, slightly changed on 19 October 2009 from the original prepared on 17 November 2004.

The main change, apart from updating my email address and my web site address, is that the front matter (general introduction to the web version, preface, contents list) was originally part of the same file as the book itself, but is now a separate file. This was not a deliberate choice but imposed by the fact that the parent file was writtten with software that is now obsolete, and from which I cannot produce a PDF file directly.

Chapters 8–11 of the book are not in the PDF file described above, as they are specifically related to the program Leonora, which must be regarded as obsolete, as it was written more than ten years ago for an operating system that has virtually disappeared. It can still be run as a DOS program under recent versions of Windows, but that is clearly not a choice that most users will find attractive.

What the reviewers thought

An American biochemist found that it induced him to think about the subject...

Should you buy this book for its essay on statistical analysis of rate data or for Leonora? Actually, both. My criticisms of the book are really arguments with Cornish-Bowden because he induced me to think about the subject.

Michael Silverberg in the Quarterly Review of Biology

... an Australian biochemist liked it quite a lot...

A valuable resource that bridges the gap between overly simple statistical texts and those which are incomprehensible to non-statisticians...

A valuable reference work and an effective, practical tool for analysis of experimental data. The description and synthesis of biochemical and statistical knowledge shows an insight that is not commonly found in experts from either discipline.


R. P. Learmonth in Biochemical Education

... whereas another Australian biochemist was less enthusiastic...

A book that is probably worth a read and might be a useful purchase for the novice

R. G. Duggleby in Trends in Biochemical Sciences

... not to mention a review that I didn’t see until long after it was published

This book will be useful for a biologist (working in a research or hospital laboratory) without any particular knowledge in mathematics other than the statistics acquired at the undergraduate level in biology. The student in biology will find here a very pedagogical presentation of classical enzyme kinetics, and the student in statistics will appreciate a concrete example of the application of least-squares methodology

J. Demongeot in the Bulletin of Mathematical Biology

Preface

This is a book that I have wanted to write (the first six chapters, at least) for many years, and, indeed, I made a start on an ancestral version during a sabbatical in 1977. However, it soon became clear that a short book on the theory of data analysis in enzymology would have very limited appeal, and for this and various other reasons the original project did not advance very far. The arrival of the personal computer has completely transformed the world of scientific computing, however, to the point where virtually every working scientist is now also a computer user. As a result, it has become quite feasible to incorporate all of the methods of analysis developed in the 1960s and 1970s into a single program and to present both the methods and the program in a single book.

The two principal parts of the book are largely independent of one another, with only a short link section (Chapter 7) between them: the first six chapters provide a theoretical account of statistical analysis of kinetic data for enzyme-catalysed reactions in the steady state; the last four describe Leonora, a program for analysing enzyme kinetic data on the IBM PC and compatible computers. Each of these parts can be read almost independently of the other, and each makes very little reference to the other. One may reasonably ask, therefore, why they have been bound between the same pair of covers and offered as a single book. The answer is that although they can be read in isolation from one another, that is far from being the best way to proceed.

Something that will strike anyone who pays more than passing attention to statistics journals is that the number of statistical methods that have been proposed for scientists and engineers to use is much larger than the number of such methods that are actually in use by scientists or engineers. This is less true of methods proposed in journals that are normally read by their potential users, but it is still true to some degree of methods of kinetic data analysis that one can find in the biochemical literature. It is one thing to be reasonably convinced by a research article that a new method is better than existing ones, but it is quite another to go out and use it in the laboratory if one has to develop it from nothing. The reason for adding the practical part of this book (and the accompanying software) to the theoretical part, therefore, is to provide the tools necessary for the reader to test and apply all of the theory.

This leaves unanswered, however, the complementary question of why the user of the software would want to be bothered with the theory. The reason is in the sort of program that Leonora is. It does not follow the philosophy of assuming that there is One True Way of analysing data that must be applied in all circumstances. On the contrary, it offers a great deal of choice to its users, though to avoid making use too difficult it makes its own (i.e. my) choices when others are not made. To make appropriate choices the user needs a theoretical point of reference. Moreover, when I started writing Leonora I intended it to permit use of virtually any method the user might wish to try, but in practice the number of possibilities is almost infinite, because the more choices allowed, the more sub-choices these imply, etc. Consequently Leonora does make some restrictions, but to know why these restrictions apply rather than others one again needs a point of reference.

Not all of the methods Leonora offers are in my opinion good methods, and even if they were it would be reasonable to ask what is the point of offering so many. This comes back to the question of user choice: far too many programs of all kinds are written in the spirit of the One True Way, and when they tolerate different preferences from those of the programmer they may force them to be specified every time the program is used. In the case of enzyme kinetics some of the most widely used methods come into the category of bad methods, but the solution is not to forbid their use — if potential users don’t find the methods they find most natural they won’t continue to be users — but to try to persuade users that better methods exist that are just as convenient. The ideal, in my view, is not only to offer a choice, but also to offer users who don’t want to avail themselves of the choice a default method that will work well in most circumstances.

Anyone using Leonora to analyse results of research experiments will, in all likelihood, settle quite soon on one method of analysis and ignore the others. Not everyone is a resarcher, however, and for teaching the principles of data analysis there is a more obvious need for a program that will allow the use and comparison of many different methods. Leonora is intended to address this need.

I am grateful to Faculty of Sciences of the University of Chile for appointing me on two occasions to the visiting Chair set up in memory of the late Professor Hermann Niemeyer Fernández, and to the members of the Laboratory of Biochemistry in Santiago for providing me with the opportunity to do much of the work on this book there. Work on some of the methods described in the book benefitted greatly from collaborations with Robert Eisenthal and Laszlo Endrenyi, and I thank both of them for this. Finally, I thank Véronique Raphel for allowing me to use data from her doctoral thesis as the practical example around which Chapter 7 is written.

Contents

I. THEORY

1. Least-Squares Analysis: Basic Principles

1.1 The Statistical Approach to Data Analysis; 1.2 The Continuing Importance of Graphs; 1.3 True Values, Population Values, Observed Values and Estimates; 1.4 Variance; 1.5 Weighting; 1.6 Fitting the Straight Line; 1.7 Degrees of Freedom; 1.8 Choice of Dependent Variable

2. Fitting the Michaelis–Menten Equation by Least Squares

2.1 Linearization of the Michaelis–Menten Equation; 2.2 Corresponding Results for the Double-Reciprocal Plot; 2.3 Choosing the Proper Weights for the Rate; 2.4 Standard Errors of Michaelis–Menten Parameters

3. More than Two Parameters

3.1 The General Linear Model; 3.2 Standard Errors in the General Linear Model; 3.3 Application to Enzyme Inhibition and Other Kinetic Examples; 3.4 Comparing Models; 3.5 Additional Remarks about Residual Plots; 3.6 Use of Replicate Observations

4. Maximum Likelihood and Efficiency

4.1 The Theoretical Basis of Least Squares; 4.2 Minimum Variance; 4.3 The Normal Distribution; 4.4 How Normal is the Normal Distribution?; 4.5 Efficiency; 4.6 The Central Limit Theorem; 4.7 Review of Assumptions Implicit in Least Squares

5. Generalized Medians: Looking beyond Least Squares

5.1 Doing without Information on Distributions and Weights; 5.2 Median Estimate of the Slope of a Straight Line; 5.3 Confidence Limits for Median Slope Estimates; 5.4 Relationship between Least-squares and Median Estimates; 5.5 Median Estimates of Michaelis–Menten Parameters; 5.6. Least Absolutes Fitting

6. Robust Regression

6.1 Recognizing and Dealing with Outliers; 6.2 Biweight Regression; 6.3 Assessing Heteroscedasticity; 6.4 Worked Example of Robust Regression; 6.5 The Jackknife and Bootstrap; 6.6 Minimax Fitting; 6.7 Reading the Statistics Literature

II. INTERLUDE

7. Analysis of an Example

7.1 Introduction: Acylaminoacyl-peptidase; 7.2 Preliminary Examination of the Data; 7.3 Inhibition by Acetyl-L-alanine; 7.4 Inhibition by Acetyl-D-alanine; 7.5 Planning Future Experiments

III. PRACTICE

8. Leonora: a Program for Robust Regression of Enzyme Data

8.1 Introduction; 8.2 Typographical Conventions; 8.3 Installation on a Hard Disk; 8.4 Example 1: the Michaelis–Menten Equation; 8.5 Example 2: Competitive Inhibition; 8.6 Two-substrate Kinetics; 8.7 Example 3: pH-Dependence Data; 8.8 Fitting Other Equations; 8.9 Screen Layout; 8.10 Miscellaneous Points

9. Leonora Menus

9.1 Main Menu; 9.2 Data Menu; 9.3 Equation Menu; 9.4 Output Requirements Menu; 9.5 Calculations Menu; 9.6 Plotting Menu; 9.7 Graphical Menu; 9.8 Setting Defaults

10. Customizing Leonora

10.1 Introduction and Warning; 10.2 Editing a Menu; 10.3 Editing a Warning; 10.4 Editing Other Messages; 10.5 Editing Help Files; 10.6 Editing the Equation File

11. Use of Simulated Data

11.1 Introduction: Generation of Pseudo-Random Numbers; 11.2 Changing the Distribution of Pseudo-Random Numbers; 11.3 Simulating Leonora; 11.4 Entering Data; 11.5 Selecting Equations; 11.6 True Parameter Values, Error Parameters, Output; 11.7 Methods and Weights; 11.8 Results Screen; 11.9 Randomizer

References

Index

The topic of the book is covered in a briefer and more general fashion as Chapter 14 of Fundamentals of Enzyme Kinetics (3rd edn.; Chapter 12 in the 2nd edn.).