Mathematical Models of the Cell And Cell Associated Objects

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780444527141 | 0444527141
Cover: Hardcover
Copyright: 7/11/2006

eBook

Available Instantly

Online: 1825 Days

Downloadable: Lifetime Access

*To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.

$270.00*

This book gives the reader a survey of hundreds results in the field of the cell and cell associated objects modeling. Applications to modeling in the areas of AIDS, cancers and life longevity are investigated in this book. - Introduces and proves fundamental properties of evolutionary systems on optimal distribution of their various resources on their internal and external functions - Gives detailed analysis of applications to modeling AIDS, cancers, and life longevity - Introducing and grounding the respective numerical algorithms and software - Detailed analysis of hundreds of scientific works in the field of mathematical modeling of the cell and cell associated objects

Preface

List of abbreviations

xviii

List of notations

xix

Introduction: Evolutionary Systems and Development Modeling

(1)

Evolutionary Systems (ES)

(6)

Artificial ES

(3)

Natural ES

(2)

Joined ES

(1)

Generalized Structure of ES

(1)

Generalized Structure of Two ES Interactions

(2)

Generalized Structure of CAO

(2)

On Development Modeling

(5)

Base simplest MM of development

(2)

Comparison with classical MM

(2)

A history, in short

(1)

Part 1: SURVEY OF MM OF CAO

(62)

General Methods of Inlet and Analysis of MM

(28)

Methods of Simplification of the Systems of Kinetic Equations

(2)

On the Qualitative Theory for the Systems of the Second Order

(9)

MM of cell cycles, I

(3)

MM of hyper-cycle

(1)

MM of cell excitable membranes

(2)

MM of Spatial Systems

(6)

MM of tumor angiogenesis

(2)

Mechanical models for mesenchymal morphogenesis

(1)

Possibility for Description of Biological Events on Molecular Level

(11)

MM of traffic through cell membranes

(1)

Passive transport

(1)

Active transport

(1)

On the problem of structure and protein folding

(1)

Simple kinetic MM in protein folding

(1)

Theories of reaction rates

(1)

Application to the protein folding without barriers

(1)

Physical model of DNA

(3)

MM of Enzyme Reactions

(14)

Method of Graphs

(2)

MM of Open Reactions with Substratum Inhibition

(1)

MM of Two-Substratum Reactions with Inhibition

(2)

On Multi-enzyme Systems

(4)

General notions

(1)

Simple MM of energetic metabolism

(3)

Effects of pH and T on the Reaction Rates

(2)

MM of Cell-to-Cell Interactions

(3)

MM of Kinetic Cellular Theory

(8)

Assumption 1

(1)

Assumption 2

(1)

Assumption 3

(2)

Assumption 4

(1)

Assumption 5

(1)

Assumption 6

(1)

Assumption 7

(2)

Assumption 8

(1)

Assumption 9

(1)

Assumption 10

(1)

Assumption 11

(1)

On Generalized Kinetic Models in Applied Sciences

(1)

Some Other MM

(10)

Delay Differential Equations

(1)

Mathematics in Population Biology

(3)

Some Problems and MM in Computational Biology and Bioinformatics

(3)

On the Theory Catastrophes

(3)

On the Respective Software

(1)

Part 2: MM OF DEVELOPMENT

(98)

Base MM

(20)

Base Minimal MM

(4)

More General MM

(3)

Additional MM

(1)

On Comparison with Well-Known MM

(1)

Methods for Estimation of MM Input Data

(2)

On the Problem of MM Completeness

(7)

Methods of CAO de- and aggregation

(1)

Detailing the CAO structure

(1)

Case of self-development of the indices α- and β-types

(2)

Case of the additional ``executive'' subsystem (E)

(1)

Case of the additional ``recreation'' subsystem (R)

(1)

Further factorization of the indices α- and β-types

(1)

On introduction of dimensionless relations

(1)

On using extreme concepts

(2)

Statement of the Modeling Problems

(3)

Examples of CAO and Their MM

101

(24)

On Hyper-Cycle, Origin of Life and DNA Code

101

(2)

Dehydration Synthesis and Hydrolysis

103

(1)

ATP Synthesis

104

(5)

Biosynthesis

109

(2)

On Pattern Formation

111

(2)

MM of Regulatory Processes in Cells

113

(12)

Biological background

113

(1)

Proteins turn genes on or off

113

(1)

Differentiated cells has a particular pattern of genes

114

(2)

Complex protein control transcription

116

(1)

RNA adds a cap and poly-A tail and removes non-coding segments

116

(1)

Multiple mechanisms control gene expression

117

(2)

Gene expression and cell-to-cell signaling

119

(1)

Signal-transduction pathways

119

(1)

MM of turning genes on or off

120

(2)

MM of DNA transcription and mRNA translation

122

(1)

MM of signal-transduction pathways

122

(1)

MM of molecular pumps

123

(2)

MM of the Cell

125

(26)

On Cell Biology

125

(9)

Molecular constituents of cells

125

(2)

Structure and functions of cells

127

(4)

On cell metabolism

131

(1)

On control of gene expression

132

(1)

Summing up

133

(1)

Base MM of a Cell

134

(6)

MM of cell structure and functions

135

(1)

MM of a cell with regard to its given spatial structure

136

(1)

MM of developing cell

137

(2)

MM of cell bio-field

139

(1)

On the Protein Folding Problem

140

(2)

MM of Cell Cycle, II

142

(4)

Biological background

142

(3)

The respective MM

145

(1)

MM of Morphogenesis

146

(5)

Biological background

146

(3)

The respective MM

149

(2)

MM of the Immune Network

151

(18)

Introduction

151

(1)

Cells of the Immune System

152

(5)

On the immune system

152

(2)

Properties of the immune network cells

154

(3)

Continuous MM

157

(6)

On the Classical and the New Approach

163

(3)

Some Results of Investigation

166

(1)

Conclusion

167

(2)

MM of Some Other CAO

169

(8)

Function of Special Cells

169

(1)

MM of Stem Cells

170

(2)

MM of Thymus and Spleen

172

(1)

MM of the Immune and Blood System Cells

173

(2)

MM of Endothelial Cells

175

(1)

Conclusion

175

(2)

Part 3: INTRODUCTION TO APPLICATIONS

177

(142)

AIDS

179

(22)

Introduction

179

(1)

Immune Status of an Organism

179

(2)

Viruses

181

(2)

Main properties of viruses

181

(1)

On retroviruses and HIV

181

(2)

Pattern of HIV infection

183

(1)

MM of Viruses

183

(9)

Base MM

183

(1)

MM of HIV

184

(1)

Qualitative investigation of MM of HIV

185

(3)

More complicated MM of HIV and its qualitative investigation

188

(1)

MM of HIV population

189

(1)

MM of HIV population inside of the host cell

189

(1)

MM of HIV free population

190

(2)

MM of AIDS

192

(8)

Qualitative investigation of MM of AIDS

196

(2)

On AIDS immune therapy

198

(2)

Conclusion

200

(1)

Cancers

201

(28)

On Study of a Cancer at the Molecular Level

201

(2)

MM of a Cancer Cell

203

(5)

Base MM of a cell at the start of proliferation

203

(1)

More complicated MM

204

(2)

MM of developing daughter cell

206

(1)

MM of a cancer cell bio-field

207

(1)

Qualitative Investigation of MM of a Cancer Cell

208

(5)

Investigation of MM (1)-(5)

208

(2)

Investigation of MM (6)-(8)

210

(2)

Investigation of MM (9), (10)

212

(1)

MM of a Cancer

213

(3)

Base MM of interaction of a cancer with host organism

216

(1)

Qualitative investigation of MM of a cancer

217

(7)

Investigation of MM (37)-(43)

217

(4)

Investigation of MM (44), (45)

221

(3)

On Immune Therapy of Cancers

224

(1)

On Gene Therapy of Cancers

225

(2)

Conclusion

227

(2)

On Life Longevity Problems

229

(8)

Clock of Cellular Aging

229

(2)

Error accumulation theory

229

(1)

Programmed dearth theory

229

(1)

Winding back the clock

230

(1)

Modeling of Cell Longevity Problems

231

(3)

Modeling of error accumulation

231

(1)

Modeling of programmed death

232

(1)

Modeling of winding back the clock

233

(1)

On Modeling of Organism Longevity Problems

234

(1)

Certain Perspectives

235

(2)

On MM of a Disease

237

(10)

Introduction

237

(1)

Conception of the Norm and Pathology

238

(1)

Norm Restoration Problems

239

(1)

On Optimization Problems

240

(1)

On the Problems of Individualization of MM

241

(1)

On MM of Doctor's Business

242

(5)

Appendix: Mathematics of Development

245

(2)

Investigation of Equations

247

(22)

Examples of Analytic Solutions

247

(2)

Existence and Uniqueness of Solutions

249

(10)

Cases of Non-Uniqueness of Solutions

259

(1)

On Stability of Solutions

260

(2)

Cases of Oscillating, Wave, and Some Other Solutions

262

(4)

Asymptotic Properties of Solutions

266

(1)

Some Additions and Remarks

267

(2)

Investigation of Optimization Problems

269

(24)

Preliminary Concepts and Results

269

(5)

Examples of Analytical Solutions

274

(2)

Existence and Uniqueness of Solutions

276

(4)

On Stability of Solutions

280

(3)

On Investigation of Solution Structure

283

(3)

Case of Non-Uniqueness of Solutions

286

(2)

Asymptotic Properties of Solutions

288

(2)

Additions and Remarks

290

(3)

Numerical Methods and Software

293

(26)

On the Solution with the Pre-Assigned Accuracy

293

(16)

Second kind of Volterra equations

293

(1)

Inherent errors

293

(4)

Method errors

297

(5)

Round-off errors

302

(1)

Analysis of the total errors

303

(1)

First kind of Volterra equations

304

(1)

Two main approaches

304

(1)

Quasi-solution method

305

(1)

Estimate of continuity modules for reciprocal operators

306

(1)

On regularization for linear equations

307

(2)

Reduction to Volterra-Type Equations

309

(4)

Mathematical programming problems

309

(3)

Some other problems

312

(1)

On Optimal Numerical Methods

313

(4)

Approximation of functions

313

(1)

On the solution of other applied problems

314

(3)

On Algorithms and Software

317

(2)

Summary

319

(2)

Bibliography

321

(8)

Index

329

(4)

About the Authors

333

Please wait while the item is added to your bag...

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Mathematical Models of the Cell And Cell Associated Objects

Summary

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Mathematical Models of the Cell And Cell Associated Objects

Summary

Table of Contents

Supplemental Materials

Digital License