Mathematical Modeling of Biological Systems

This two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout both works are mathematical and computational approaches to examine central problems in the life sciences, ranging from the organizational principles of individual cells to the dynamics of large populations. Volume I covers a number of areas, including: * Cellular Biophysics * Regulatory Networks * Developmental Biology * Biomedical Applications * Data Analysis and Model Validation Volume II examines a diverse range of subjects, including: * Epidemiology * Evolution and Ecology * Immunology * Neural Systems and the Brain * Innovative Mathematical Methods Both volumes will be excellent reference texts for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.

Preface	p. v
Cellular Biophysics	p. 1
Multiparticle Direct Simulation of Photosynthetic Electron Transport Processes	p. 3
Selective Regulation of Protein Activity by Complex Ca2+ Oscillations: A Theoretical Study	p. 11
Phase Separation in Eukaryotic Directional Sensing	p. 23
Protein Domains of GTPases on Membranes: Do They Rely on Turing's Mechanism?	p. 33
In Vitro Tubulogenesis of Endothelial Cells: Analysis of a Bifurcation Process Controlled by a Mechanical Switch	p. 47
Nonexponential Time Distributions in Biocatalytic Systems: Mass Service Replacing Mass Action	p. 59
Regulatory Networks	p. 69
A Stochastic Model of Gene Regulation Using the Chemical Master Equation	p. 71
Piecewise-Linear Models of Genetic Regulatory Networks: Analysis of the Carbon Starvation Response in Escherichia coli	p. 83
Predicting Gene Expression from Combined Expression and Promoter Profile Similarity with Application to Missing Value Imputation	p. 97
Chemical Organizations in the Central Sugar Metabolism of Escherichia coli	p. 105
Transition Networks: A Unifying Theme for Molecular Simulation and Computer Science	p. 121
Development	p. 139
Pigmentation Pattern Formation in Butterfly Wings: Global Patterns on Fore- and Hindwing	p. 141
Agent-Based Model for Developmental Pattern Formation with Multiscale Dynamics and Varying Cell Geometry	p. 149
Bacterial Swarming Driven by Rod Shape	p. 163
Stability Properties of Some Tissue-Growth Models	p. 175
A Modified Backward Euler Scheme for Advection-Reaction-Deiffusion Systems	p. 183
Biomedical Applications	p. 191
Fractional Transport of Cancer Cells Due to Self-Entrapment by Fission	p. 193
Mathematical Modelling of Vascular Tumour Growth and Implications for Therapy	p. 205
A Stochastic Model of Glioblastoma Invasion	p. 217
Morphology of Tumor Vasculature: A Theoretical Model	p. 225
A Mathematical Model of the Cell Cycle and Its Circadian Control	p. 239
Bone Turnover Cycle Model with a Torus-Like Steady State	p. 253
Modelling the Early Stages of Atherosclerosis	p. 263
Magnetic Nanoparticles for In Vivo Applications: A Numerical Modeling Study	p. 275
Fluid Transport in Peritoneal Dialysis: A Mathematical Model and Numerical Solutions	p. 281
Relevance of Intracellular Replication to the Evolution of Chagas' Disease	p. 289
A Finite Volume Spatial Discretisation for Taxis-Diffusion-Reaction Systems with Axi-Symmetry: Application to Fracture Healing	p. 299
Information Content Toward a Neonatal Disease Severity Score System	p. 313
Data Analysis and Model Validation	p. 321
Statistical Analysis and Physical Modelling of Oligonucleotide Microarrays	p. 323
Validation of Human Alternative Splice Forms Using the EASED Platform and Multiple Splice Site Discriminating Features	p. 337
Gaussian Mixture Decomposition of Time-Course DNA Microarray Data	p. 351
SVD Analysis of Gene Expression Data	p. 361
Index	p. 373
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Mathematical Modeling of Biological Systems

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