Keywords:
Mathematics.
;
Electronic books.
Type of Medium:
Online Resource
Pages:
1 online resource (254 pages)
Edition:
1st ed.
ISBN:
9783540324157
Series Statement:
Lecture Notes in Mathematics Series ; v.1872
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=5579176
DDC:
510
Language:
English
Note:
Intro -- Modeling the Cell Division Cycle -- Baltazar D. Aguda -- 1 Introduction -- 2 Basic Biology of the Cell Division Cycle: Chromosome Cycle and Growth Cycle -- 3 The Molecular Regulators of the Cell Cycle: CDKs and APC -- 4 The Key Molecular Pathways -- 5 From Qualitative Network and Mechanisms to Dynamical Equations -- 6 Mammalian Cell Cycle and Checkpoints -- 7 Coupling Between the Cell Cycle and Apoptosis -- 8 Conclusions and Future Directions -- References -- Angiogenesis-A Biochemical/Mathematical Perspective -- Howard A. Levine and Marit Nilsen-Hamilton -- 1 Introduction -- 2 What is Angiogenesis? -- 3 What are the Key Events in Angiogenesis? -- 4 What are the Chemical and Cellular Contributions to Capillary Structure? -- 5 Interaction of Endothelial Cells with Their Environment -- 6 What are the Extracellular Events Leading to Vascularization? -- 7 Soluble Proteins that Modify the ECM and Influence EC Function: Proteases and Protease Inhibitors -- 8 Growth and Angiogenesis Factors: Factors that Stimulate Angiogenesis -- 9 Inhibitors of Angiogenesis -- 10 Cellular Events that Characterize Angiogenesis -- 11 Intracellular Signals (Signal Transduction) that Regulate Cellular Events -- 12 How does one Model These Events Mathematically? -- 13 Vocabulary -- References -- Mathematical Modelling of Proteolysisand Cancer Cell Invasion of Tissue -- Georgios Lolas -- 1 Introduction -- 2 Mathematical Modelling of Solid Tumour Growth and Invasion -- 3 Biological Background -- 4 The Mathematical Model of Proteolysisand Cancer Cell Invasion of Tissue -- 5 Numerical Simulation Results -- 6 Discussion -- References -- Mathematical Modelling of Spatio-temporal Phenomena in Tumour Immunology -- Mark Chaplain and Anastasios Matzavinos -- 1 Introduction -- 2 Tumour Immunology.
,
3 Modelling the Spatio-temporal Response of Cytotoxic T-lymphocytes to a Solid Tumour -- 4 Discussion and Conclusions -- References -- Control Theory Approach to Cancer Chemotherapy: Benefiting from Phase Dependence and Overcoming Drug Resistance -- Marek Kimmel and Andrzej Swierniak -- 1 Introduction -- 2 Modeling the Cell Cycle -- 3 Control Problems with Cell-Cycle-Phase Dependence -- 4 Evolution of Resistance by Gene Amplification -- 5 Control Under Evolving Resistance -- 6 Remarks on Estimation of Parameters -- 7 Discussion -- References -- Cancer Models and Their Mathematical Analysis -- Avner Friedman -- 1 Introduction -- 2 Introduction to Tumors -- 3 Three Types of Cells -- 4 Two Types of Cells -- 4 Proliferating Cells -- 5 Tumors with Necrotic Core -- 6 Cancer Therapy -- 7 Concluding Remarks -- References.
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