Enzyme Mathematics (eBook)

Front Cover 1
Enzyme Mathematics 4
Copyright Page 5
TABLE OF CONTENTS 12
Preface 11
Chapter 1 - Diffusion and Reaction in an Enzyme Membrane 16
1.1 - Motivation for Studying Artificial Enzyme Membranes 16
1.2 - Enzyme Kinetics 17
1.4 - Simple Irreversible Monoenzymatic Reactions 24
1.5 - Numerical Solution 31
1.6 - Mathematical Methods 36
References 47
Chapter 2 - Glucose Pump 50
2.1 - Description 50
2.2 - Modeling 53
2.3 - Numerical Simulations 58
2.4 - Mathematical Analysis 59
References 70
Chapter 3 - Multiple Steady States and Hysteresis 72
3.1 - The Zero-dimensional System 74
3.2 - The One-dimensional System 79
3.3 - Kubicek Method of Continuation 89
3.4 - Mathematical Analysis of the S-shaped Curve 94
3.5 - Stability 113
3.6 - Justification of the Quasi-steady-state Hypothesis 117
References 124
Chapter 4 - Assemblages of Cells and Bifurcations 126
4.1 - Multiple Cell Assemblages 129
4.2 - Two Cell Assemblage 130
4.3 - Nonisolated Solutions and Bifurcation 133
4.4 - Numerical Analysis of Bifurcations (2,3] ) 146
4.5 - Imperfections 151
References 158
Chapter 5 - The Uricase System and Pattern Formation 160
5.1 - Presentation of the Uricase System 164
5.2 - Stability of the Trivial Steady State 170
5.3 - Bifurcation from the Trivial Steady State 175
5.4 - Numerical Exploration of the Steady States 178
References 183
Chapter 6 - Pattern Formation in a Monoenzyme Membrane 184
6.1 - Pattern Formation in Fruitfly Drosophila Imaginal Disks 187
6.2 - Description of the S-A System 194
6.3 - Linear Stability Analysis of the Spatially Uniform Steady State uo = (s,a) 198
6.4 - Bifurcation Analysis 203
6.5 - Numerical Methods and Results 211
6.6 - Mathematical Technical Details 237
References 251
Chapter 7 - Oscillations and Wave Front Propagation 256
7.1 - Papain System 257
7.2 - Uricase System 263
7.3 - Wave Front Propagation in the s-a System 267
References 273