Modelling Metabolism with Mathematica: 1st Edition (Hardback) book cover

Modelling Metabolism with Mathematica

1st Edition

By Peter Mulquiney, Philip W. Kuchel

CRC Press

328 pages | 48 B/W Illus.

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pub: 2003-05-14
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With the advent of sophisticated general programming environments like Mathematica, the task of developing new models of metabolism and visualizing their responses has become accessible to students of biochemistry and the life sciences in general. Modelling Metabolism with Mathematica presents the approaches, methods, tools, and algorithms for modelling the chemical-dynamics of metabolic pathways. The authors explain the concepts underpinning the deterministic theory of chemical and enzyme kinetics, present a graded series of computer models of metabolic pathways leading up to that of the human erythrocyte, and document a consistent set of rate equations and associated kinetic parameters.

The experimental and theoretical study of metabolism in mammalian cells has a long and fruitful history, but our understanding of cellular metabolism at the molecular level is far from complete. This book enables its readers to formulate their own models of time-dependent metabolic systems and aids them in the quest for the many fundamental and clinically relevant discoveries that remain to be made.

Table of Contents

Introduction to Chemical Kinetics and Numerical Integration

Aims and Objectives



Time Courses of Reactions

Numerical Integration of Differential Equations

Predictor Corrector Methods


Elements of Enzyme Kinetics

Kinetics of Enzymic Reactions

Enzyme Inhibition

Enzyme Mechanisms

Regulatory Enzymes

Basic Procedures for Simulating Metabolic Systems


Relationships between Unitary Rate Constants and Steady-State Parameters

Upper Limit of Values for Unitary Rate Constants

Realistic Enzyme Models

Deriving Expressions for Steady- State Parameters

Multiple Equilibria

pH Effects on Kinetic Parameters

A Simple Model of the Urea Cycle


Advanced Simulation of Metabolic Pathways


Simulating the Time Dependent Behaviour of Multienzyme Systems

Using Matrix Notation in Simulating Metabolic Pathways

Generating the Stoichiometry Matrix

Determining Steady- State Concentrations

Conservation Relations

Stability of a Steady State

When Cell Volume Changes with Time

Decomposition of N and Calculation of the Link Matrix (Optional)

Metabolic Control Analysis


Control Coefficients

Calculation of Control Coefficients by Numerical Perturbation

Elasticity Coefficients

Response Coefficients

Internal Response Coefficients


Parameter Estimation


Approaches to Parameter Estimation

Least Squares

Maximum a Posteriori (MAP)

Parameters in Rate Equations

Parameters in Systems of Differential Equations

Optimal Parameter

Variances of Parameters

Model of Erythrocyte Metabolism


Models of Erythrocyte Metabolism

Stoichiometry of Human Erythrocyte Metabolism

In Vivo Steady State of the Erythrocyte

Conservation of Mass Relationships

Simulating a Timecourse

Metabolic Control Analysis of Human Erythrocyte Metabolism


Normal In Vivo Steady State

Identifying Zero Fluxes

Flux Control Coefficients

Concentration Control Coefficients

Response Coefficients and Partitioned Responses

Elasticity Coefficients

Internal Response Coefficients

Concluding Remarks

Note: Each chapter contains Exercises and References.


Rate Equation Deriver

Metabolic Control Analysis Functions

Rate Equations for Enzymes of the Human Erythrocyte

Initial Conditions and External Parameters for the Erythrocyte Model

Equation List Describing the Erythrocyte Model of Chapters 7 and 8

Subject Categories

BISAC Subject Codes/Headings:
MEDICAL / Hematology
SCIENCE / Life Sciences / Biology / Molecular Biology