Modelling Metabolism with Mathematica

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Presents a comprehensive use of enzyme kinetics by simulation of complex systems Develops algorithm with Mathematica using its powerful numerical integration functions and excellent graphical output capabilities Introduces the basic procedures for representing metabolic systems as arrays of differential equations Develops matrix notation of differential rate equations, and methods for application Documents a consistent set of rate equations and associated kinetic parameters, valuable to readers involved with red cell enzymology Presents a graded series of computer models of various metabolic pathways leading up to that of human erythrocyte metabolism Equips readers with the information to formulate their own dynamic models of time-dependent metabolic systems By using the modelling process we can predict what will happen at specific points during the complex network of chemical reactions that take place in metabolism. The technology to predict or experiment with particular steps in metabolism has advanced greatly during the last decade and is used in a wide range of fields. This book presents the approaches, methods, tools, and algorithms for applying modelling methods to the Erythrocyte Metabolism using Mathematica. The authors, world experts in this field, use their talent to simulate the chemical-dynamics of metabolic pathways using computer methods. This book will be of particular interest to readers involved with red cell enzymology, as it documents a consistent set of rate equations and associated kinetic parameters are documented.

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Product Details

  • ISBN-13: 9780849314681
  • Publisher: Taylor & Francis
  • 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
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

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