Modelling Metabolism with Mathematica

Published:
May 14, 2003 by CRC Press - 328 Pages
Author(s):
Peter Mulquiney, University of Sydney, Australia; Philip W. Kuchel, University of Sydney, Australia

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$209.95
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ISBN 9780849314681
Cat# 1468
 

Features

  • Uses Mathematica to dynamically simulate simple, intermediate, and complex systems in enzyme kinetics
  • Allows hands-on learning of the necessary Mathematica procedures for numerically solving the differential equations of enzyme kinetics
  • Introduces the basic procedures for representing metabolic systems as arrays of differential equations
  • Explains the matrix notation of differential rate equations and describes advanced methods for simulating metabolic pathways
  • Provides numerous worked examples to emphasize or extend the basic concepts discussed in the text
  • Devotes an entire chapter to metabolic control analysis
  • Documents a consistent set of rate equations and associated kinetic parameters, valuable to readers involved with red cell enzymology

    • Summary

    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
    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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