Modelling Metabolism with Mathematica

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Overview

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.

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Product Details

  • ISBN-13: 9780849314681
  • Publisher: CRC Press
  • Publication date: 5/28/2003
  • Pages: 328
  • Product dimensions: 6.40 (w) x 9.30 (h) x 1.00 (d)

Table of Contents

Introduction to Chemical Kinetics and Numerical Integration
Aims and Objectives
Complexity
Definitions
Time Courses of Reactions
Numerical Integration of Differential Equations
Predictor Corrector Methods
Conclusions

Elements of Enzyme Kinetics
Kinetics of Enzymic Reactions
Enzyme Inhibition
Enzyme Mechanisms
Regulatory Enzymes

Basic Procedures for Simulating Metabolic Systems
Introduction
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
Conclusions

Advanced Simulation of Metabolic Pathways
Introduction
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
Introduction
Control Coefficients
Calculation of Control Coefficients by Numerical Perturbation
Elasticity Coefficients
Response Coefficients
Internal Response Coefficients
Conclusions

Parameter Estimation
Introduction
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

Introduction
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

Introduction
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.

Appendices
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

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