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Mathematical Models of the Cell and Cell Associated Objects, Volume 206 [Kõva köide]

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  • Formaat: Hardback, 354 pages, kõrgus x laius: 229x152 mm, kaal: 680 g
  • Sari: Mathematics in Science & Engineering
  • Ilmumisaeg: 10-May-2006
  • Kirjastus: Elsevier Science Ltd
  • ISBN-10: 0444527141
  • ISBN-13: 9780444527141
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Mathematical Models of the Cell and Cell Associated Objects, Volume 206Suurem pilt
  • Formaat: Hardback, 354 pages, kõrgus x laius: 229x152 mm, kaal: 680 g
  • Sari: Mathematics in Science & Engineering
  • Ilmumisaeg: 10-May-2006
  • Kirjastus: Elsevier Science Ltd
  • ISBN-10: 0444527141
  • ISBN-13: 9780444527141
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780444527141.html
Märksõnad:
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

The book contains five main parts: Introduction: Evolutionary System and Development Modelling; Part I: A Survey of MM of CAO (cell associated objects); Part II: MM (mathematical models) of Development; Part III: Introduction to Applications; Appendix: Mathematics of Development.



The part I gives the reader a survey of hundreds results in the field of the cell and cell associated objects modelling, which are not easy accessible. The original four parts of the book have no analogy in the literature, except the previous book of the first author 'Model Development and Optimization', KAP, 1999, and the book 'Mathematical Modeling in Economics, Ecology and the Environment', KAP, 1999, by N. Hritonenko, Yu. Yatsenko (Yu. Yatsenko is a pupil of the first author of the cell book).



The present book is different from the previous mainly by much more profound investigation of such a complicated object as the cell and by much more detailed description of applications to modelling AIDS, cancers, and life longevity.



Key features:



- Inlet novel class of non-linear mathematical models based on the general theory of evolutionary systems and their development .

- Introducing and proving fundamental properties of evolutionary systems on optimal distribution of their various resources on their internal and external functions.

- Proof of effective applicability of that class of models to complicated objects such as the cell and the immune network .

- Detailed modelling complicated processes such as the cell cycle, protein folding, immune network response, etc.

- Detailed analysis of applications to modelling 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 modelling of the cell and cell associated objects.

Key features:



- Inlet novel class of non-linear mathematical models based on the general theory of evolutionary systems and their development .

- Introducing and proving fundamental properties of evolutionary systems on optimal distribution of their various resources on their internal and external functions.

- Proof of effective applicability of that class of models to complicated objects such as the cell and the immune network .

- Detailed modelling complicated processes such as the cell cycle, protein folding, immune network response, etc.

- Detailed analysis of applications to modelling 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 modelling of the cell and cell associated objects.

Preface xv
List of abbreviations
xviii
List of notations
xix
Introduction: Evolutionary Systems and Development Modeling 1(1)
Evolutionary Systems (ES)
1(6)
Artificial ES
1(3)
Natural ES
4(2)
Joined ES
6(1)
Generalized Structure of ES
7(1)
Generalized Structure of Two ES Interactions
8(2)
Generalized Structure of CAO
10(2)
On Development Modeling
12(5)
Base simplest MM of development
12(2)
Comparison with classical MM
14(2)
A history, in short
16(1)
Part 1: SURVEY OF MM OF CAO
17(62)
General Methods of Inlet and Analysis of MM
19(28)
Methods of Simplification of the Systems of Kinetic Equations
19(2)
On the Qualitative Theory for the Systems of the Second Order
21(9)
MM of cell cycles, I
24(3)
MM of hyper-cycle
27(1)
MM of cell excitable membranes
28(2)
MM of Spatial Systems
30(6)
MM of tumor angiogenesis
33(2)
Mechanical models for mesenchymal morphogenesis
35(1)
Possibility for Description of Biological Events on Molecular Level
36(11)
MM of traffic through cell membranes
39(1)
Passive transport
39(1)
Active transport
40(1)
On the problem of structure and protein folding
41(1)
Simple kinetic MM in protein folding
42(1)
Theories of reaction rates
42(1)
Application to the protein folding without barriers
43(1)
Physical model of DNA
44(3)
MM of Enzyme Reactions
47(14)
Method of Graphs
47(2)
MM of Open Reactions with Substratum Inhibition
49(1)
MM of Two-Substratum Reactions with Inhibition
50(2)
On Multi-enzyme Systems
52(4)
General notions
52(1)
Simple MM of energetic metabolism
53(3)
Effects of pH and T on the Reaction Rates
56(2)
MM of Cell-to-Cell Interactions
58(3)
MM of Kinetic Cellular Theory
61(8)
Assumption 1
61(1)
Assumption 2
61(1)
Assumption 3
61(2)
Assumption 4
63(1)
Assumption 5
63(1)
Assumption 6
63(1)
Assumption 7
64(2)
Assumption 8
66(1)
Assumption 9
66(1)
Assumption 10
67(1)
Assumption 11
67(1)
On Generalized Kinetic Models in Applied Sciences
68(1)
Some Other MM
69(10)
Delay Differential Equations
69(1)
Mathematics in Population Biology
69(3)
Some Problems and MM in Computational Biology and Bioinformatics
72(3)
On the Theory Catastrophes
75(3)
On the Respective Software
78(1)
Part 2: MM OF DEVELOPMENT
79(98)
Base MM
81(20)
Base Minimal MM
81(4)
More General MM
85(3)
Additional MM
88(1)
On Comparison with Well-Known MM
89(1)
Methods for Estimation of MM Input Data
89(2)
On the Problem of MM Completeness
91(7)
Methods of CAO de- and aggregation
92(1)
Detailing the CAO structure
92(1)
Case of self-development of the indices α- and β-types
92(2)
Case of the additional ``executive'' subsystem (E)
94(1)
Case of the additional ``recreation'' subsystem (R)
95(1)
Further factorization of the indices α- and β-types
96(1)
On introduction of dimensionless relations
96(1)
On using extreme concepts
96(2)
Statement of the Modeling Problems
98(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