Computational Biology Of Cancer: Lecture Notes And Mathematical Modeling

by Wodarz, Dominik; Komarova, Natalia L.

• ISBN13: 9789812560278
• ISBN10: 9812560270
• Format: Hardcover
• Copyright: 2005-01-24
• Publisher: World Scientific Pub Co Inc

Summary

- Provides an introduction to computational methods in cancer biology- Follows a multi-disciplinary approach

Table of Contents

Preface	vii
1. Cancer and somatic evolution	1	(12)
1.1 What is cancer?	1	(1)
1.2 Basic cancer genetics	2	(2)
1.3 Multi-stage carcinogenesis and colon cancer	4	(2)
1.4 Genetic instability	6	(2)
1.5 Barriers to cancer progression: importance of the microenvironment	8	(2)
1.6 Evolutionary theory and Darwinian selection	10	(3)
2. Mathematical modeling of tumorigenesis	13	(14)
2.1 Ordinary differential equations	14	(2)
2.2 Partial differential equations	16	(4)
2.3 Discrete, cellular automaton models	20	(2)
2.4 Stochastic modeling	22	(3)
2.5 Statistics and parameter fitting	25	(1)
2.6 Concluding remarks	26	(1)
3. Cancer initiation: one-hit and two-hit stochastic models	27	(26)
3.1 A one-hit model	28	(7)
3.1.1 Mutation-selection diagrams and the formulation of a stochastic process	28	(2)
3.1.2 Analysis of a one-hit process	30	(5)
3.2 A two-hit model	35	(10)
3.2.1 Process description	35	(1)
3.2.2 Two ways to acquire the second hit	36	(1)
3.2.3 The regime of tunneling	37	(7)
3.2.4 Genuine two-step processes	44	(1)
3.2.5 Summary of the two-hit model with a constant population	44	(1)
3.3 Modeling non-constant populations	45	(6)
3.3.1 Description of the model	45	(2)
3.3.2 A one-hit process	47	(1)
3.3.3 Three types of dynamics	48	(1)
3.3.4 Probability to create a mutant of type "C"	49	(1)
3.3.5 A two-hit process	49	(2)
3.4 Overview	51	(2)
4. Microsatellite and chromosomal instability in sporadic and familial cancers	53	(18)
4.1 Some biological facts about genetic instability in colon cancer	55	(1)
4.2 A model for the initiation of sporadic colorectal cancers	55	(5)
4.3 Sporadic colorectal cancers, CIN and MSI	60	(5)
4.4 FAP	65	(2)
4.5 HNPCC	67	(1)
4.6 Insights following from this analysis	68	(3)
5. Cellular origins of cancer	71	(16)
5.1 Stem cells, tissue renewal and cancer	73	(1)
5.2 The basic renewal model	74	(3)
5.3 Three scenarios	77	(1)
5.4 Mathematical analysis	78	(6)
5.5 Implications and data	84	(3)
6. Costs and benefits of chromosomal instability	87	(14)
6.1 The effect of chromosome loss on the generation of cancer	88	(2)
6.2 Calculating the optimal rate of chromosome loss	90	(5)
6.3 Why does CIN emerge?	95	(3)
6.4 The bigger picture	98	(3)
7. DNA damage and genetic instability	101	(26)
7.1 Competition dynamics	102	(5)
7.2 Competition dynamics and cancer evolution	107	(12)
7.2.1 A quasispecies model	107	(8)
7.2.2 Strong apoptosis	115	(3)
7.2.3 Weak apoptosis	118	(1)
7.3 Summary of mathematical results	119	(2)
7.4 Selection for genetic instability	121	(1)
7.5 Genetic instability and apoptosis	122	(2)
7.6 Can competition be reversed by chemotherapy?	124	(3)
8. Tissue aging and the development of cancer	127	(20)
8.1 What is aging?	128	(1)
8.2 Basic modeling assumptions	129	(1)
8.3 Modeling healthy tissue	130	(3)
8.4 Modeling tumor cell growth	133	(3)
8.5 Checkpoints and basic tumor growth	136	(3)
8.6 Tumor growth and the microenvironment	139	(2)
8.7 Theory and data	141	(6)
9. Basic models of tumor inhibition and promotion	147	(24)
9.1 Model 1: Angiogenesis inhibition induces cell death	149	(4)
9.2 Model 2: Angiogenesis inhibition prevents tumor cell division	153	(4)
9.2.1 Linear stability analysis of the ODEs	155	(1)
9.2.2 Conclusions from the linear analysis	156	(1)
9.3 Spread of tumors across space	157	(7)
9.3.1 Turing stability analysis	158	(3)
9.3.2 Stationary periodic solutions	161	(1)
9.3.3 Biological implications and numerical simulations	161	(3)
9.4 Somatic cancer evolution and progression	164	(4)
9.5 Clinical implications	168	(3)
10. Mechanisms of tumor neovascularization	171	(14)
10.1 Emergence of the concept of postnatal vasculogenesis	172	(1)
10.2 Relative importance of angiogenesis versus vasculogenesis	173	(1)
10.3 Mathematical models of tumor angiogenesis and vasculogenesis	174	(3)
10.4 Mathematical analysis	177	(3)
10.5 Applications	180	(6)
10.5.1 Dynamics of BM-derived EPCs	180	(1)
10.5.2 Re-evaluation of apparently contradictory experimental data	181	(1)
10.5.3 Tumor growth kinetics	182	(3)
11. Cancer and immune responses	185	(20)
11.1 Some facts about immune responses	186	(3)
11.2 The model	189	(3)
11.3 Method of model analysis	192	(1)
11.4 Properties of the model	192	(3)
11.5 Immunity versus tolerance	195	(1)
11.6 Cancer initiation	196	(2)
11.7 Tumor dormancy, evolution, and progression	198	(2)
11.8 Immunotherapy against cancers	200	(5)
12. Therapeutic approaches: viruses as anti-tumor weapons	205	(18)
12.1 Virus-induced killing of tumor cells	207	(5)
12.2 Effect of virus-specific CTL	212	(2)
12.3 Virus infection and the induction of tumor-specific CTL	214	(4)
12.4 Interactions between virus- and tumor-specific CTL	218	(1)
12.5 Treatment strategies	219	(2)
12.6 Evaluating viruses in culture	221	(2)
Appendix A Exact formula for total probability of double mutations	223	(4)
Bibliography	227	(20)
Index	247