Dynamics of cancer: mathematical foundations of oncology
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2014
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027192913&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVII, 514 S. Ill., graph. Darst. |
| ISBN: | 9789814566360 |
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| 245 | 1 | 0 | |a Dynamics of cancer |b mathematical foundations of oncology |c Dominik Wodarz & Natalia L. Komarova |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2014 | |
| 300 | |a XVII, 514 S. |b Ill., graph. Darst. | ||
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| 650 | 4 | |a Oncology |x Mathematics | |
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| adam_text | Contents
Preface vii
1. Teaching guide 1
1.1 How to use this book......................................... 1
1.2 A sample syllabus for a Mathematics course................... 2
1.3 A sample syllabus for a Biology course....................... 3
2. Cancer and somatic evolution 5
2.1 What is cancer?.............................................. 5
2.2 Basic cancer genetics........................................ 6
2.3 Multi-stage carcinogenesis and colon cancer.................. 8
2.4 Genetic instability......................................... 10
2.5 Barriers to cancer progression: importance of the micro-
environment ...................................................... 12
2.6 Cellular hierarchies in cancer ............................. 15
2.7 Genetic and epigenetic changes.............................. 15
2.8 Evolutionary theory and Darwinian selection ................ 17
3. Mathematical modeling of tumorigenesis 19
3.1 Ordinary differential equations ............................ 20
3.2 Extensions of ODE modeling.................................. 22
3.2.1 Optimal control..................................... 22
3.2.2 ODEs and cancer epidemiology........................ 23
3.3 Partial differential equations.............................. 23
3.4 Stochastic modeling ........................................ 25
3.5 Cellular automaton models .................................. 28
IX
x Dynamics of cancer: mathematical foundations of oncology
3.6 Hybrid and multiscale modeling.......................... 30
Basic growth dynamics and deterministic models 33
4. Single species growth 35
4.1 Exponential growth...................................... 35
4.2 Surface growth.......................................... 37
4.3 Sigmoidal growth........................................ 39
4.3.1 Logistic growth.................................. 39
4.3.2 Other sigmoidal laws ............................ 41
4.4 Atypical growth......................................... 43
4.5 Multistep growth........................................ 44
4.6 Conclusions............................................. 44
5. Two-species competition dynamics 47
5.1 Logistic growth of two species and the basic dynamics of
competition............................................. 47
5.2 Two-species dynamics: the axiomatic approach............ 50
5.3 Summary................................................. 55
6. Competition between genetically stable and unstable cells 57
6.1 Competition dynamics.................................... 58
6.2 Competition dynamics and cancer evolution............... 63
6.2.1 A quasispecies model............................. 63
6.2.2 Strong apoptosis................................. 71
6.2.3 Weak apoptosis .................................. 74
6.3 Overview of the insights obtained so far................ 76
6.4 Can competition be reversed by chemotherapy?............ 77
6.5 Summary................................................. 79
7. Chromosomal instability and tumor growth 81
7.1 The effect of chromosome loss on the generation of cancer 82
7.2 Calculating the optimal rate of chromosome loss ........ 84
7.3 The optimal rate of LOH: a time-dependent problem ... 89
7.3.1 Formulation of the time-dependent problem . ... 91
7.3.2 Mathematical apparatus ..................... 94
7.3.3 The optimal strategy for cancer.................. 98
7.4 The bigger picture..................................... 100
Contents xi
7.4.1 Does cancer solve an optimization problem? . . . 102
7.4.2 Summary.......................................... 102
8. Angiogenesis, inhibitors, promoters, and spatial growth 105
8.1 Model 1: Angiogenesis inhibition induces cell death .... 107
8.2 Model 2: Angiogenesis inhibition prevents tumor cell
division ................................................ 112
8.2.1 Linear stability analysis of the ODEs............ 113
8.2.2 Conclusions from the linear analysis............. 115
8.3 Spread of tumors across space............................ 115
8.3.1 Turing stability analysis........................ 116
8.3.2 Stationary periodic solutions.................... 119
8.3.3 Biological implications and numerical simulations 120
8.4 Somatic cancer evolution and progression................. 121
8.5 Summary and clinical implications........................ 127
Evolutionary dynamics and stochastic models 131
9. Evolutionary dynamics of tumor initiation through
oncogenes: the gain-of-function model 133
9.1 Introduction............................................. 133
9.2 Mutation-selection diagrams and the stochastic
Moran process............................................ 135
9.3 Analysis................................................. 137
9.3.1 The method of differential equations............. 138
9.3.2 The probability of absorption.................... 139
9.4 Probability and timing of mutant fixation................ 140
9.4.1 The approximation of “almost absorbing’ states
and the growth of mutants........................ 143
9.4.2 Nearly-deterministic regime...................... 144
9.5 Summary.................................................. 145
10. Evolutionary dynamics of tumor initiation through
tumor-suppressor genes: the loss-of-function model and
stochastic tunneling 147
10.1 Introduction............................................. 147
10.2 Process description and the mutation-selection diagram . 148
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Dynamics of cancer: mathematical foundations of oncology
10.3 Three regimes: a two-step process, stochastic tunneling,
and a nearly-deterministic regime.......................
10.4 The transition matrix ...................................
10.5 Mathematical theory......................................
10.5.1 The Kolmogorov forward equation in the absence
of intermediate mutant fixation.................
10.5.2 The probability generating function.............
10.5.3 The method of characteristics and the Riccati
equation .......................................
10.5.4 Tunneling for disadvantageous, neutral, and
advantageous intermediate mutants...............
10.5.5 Genuine two-step process vs tunneling...........
10.5.6 Time-scales of the process......................
10.5.7 Neutral intermediate mutants ...................
10.5.8 Disadvantageous intermediate mutants ...........
10.5.9 Advantageous intermediate mutants...............
10.6 Dynamics of loss-of-function mutations...................
10.6.1 The genuine two-step processes..................
10.6.2 Tunneling.......................................
10.6.3 Nearly deterministic regime.....................
10.6.4 Disadvantageous, neutral and advantageous
intermediate mutants............................
10.6.5 The role of the population size.................
10.7 Summary..................................................
Microsatellite and chromosomal instability in sporadic
and familial colorectal cancers
11.1 Some biological facts about genetic instability in colon
cancer .................................................
11.2 A model for the initiation of sporadic colorectal cancers .
11.2.1 The first model of the APC gene inactivation: no
instabilities...................................
11.2.2 Colorectal cancer and chromosomal instability . .
11.3 Sporadic colorectal cancers, CIN and MSI.................
11.4 FAP......................................................
11.5 HNPCC....................................................
11.6 Summary..................................................
Evolutionary dynamics in hierarchical populations
Contents xiii
12.1 Introduction.............................................. 197
12.2 Types of stem cells divisions............................. 198
12.3 The set-up................................................ 200
12.4 Methodology .............................................. 202
12.4.1 Analysis of the Moran process..................... 202
12.4.2 Numerical simulations............................. 208
12.5 Generation of mutations in a hierarchical population . . . 210
12.5.1 Tunneling rates .................................. 210
12.5.2 Double-hit mutants are produced slower under
symmetric compared to asymmetric divisions ... 211
12.5.3 Comparison with the homogeneous model............. 213
12.5.4 The optimal fraction of stem cells................ 214
12.5.5 Do mutations in TA cells produce double-mutants? 216
12.6 Biological discussion..................................... 218
12.6.1 Symmetric divisions can have a cancer-delaying
effect............................................ 219
12.6.2 Can TA cells create double-hit mutants? .......... 221
12.6.3 Cancer stem cell hypothesis....................... 222
12.7 Summary................................................... 223
13. Spatial evolutionary dynamics of tumor initiation 225
13.1 Introduction.............................................. 225
13.2 ID spatial Moran process.................................. 226
13.3 Two-species dynamics...................................... 228
13.3.1 Preliminaries..................................... 228
13.3.2 Probability of mutant fixation.................... 229
13.4 Three-species dynamics ................................... 231
13.4.1 Calculating the tunneling rate by the doubly-
stochastic approximation.......................... 231
13.4.2 Limiting cases and the tunneling rate
approximations.................................... 234
13.4.3 When is tunneling important?...................... 236
13.5 Dynamics of mutant generation............................. 238
13.5.1 Gain-of-function mutations: a two-species
problem........................................... 238
13.5.2 Loss-of-function mutations: a three-species
problem........................................... 239
13.5.3 Definition of neutrality.......................... 241
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Dynamics of cancer: mathematical foundations of oncology
13.5.4 Three-species dynamic: a comparison with the
space-free model.................................
13.6 Outlook.................................................
Complex tumor dynamics in space
14.1 Introduction.............................................
14.2 Complex traits and fitness valleys......................
14.3 The Moran process.......................................
14.3.1 Spatial restriction accelerates evolution........
14.3.2 Dependence on parameters.........................
14.4 The contact process ....................................
14.4.1 The steady-state density of cells................
14.4.2 Complex effects of spatial restriction...........
14.4.3 Parameter dependencies...........................
14.5 Advantageous intermediate mutants ......................
14.6 Summary and discussion..................................
Stochastic modeling of cancer growth, treatment, and
resistance generation
15.1 Introduction.............................................
15.2 The basic model of cancer growth and generation of
mutations................................................
15.2.1 The concept: a birth-death process with
mutations........................................
15.2.2 Summary of all the probabilities.................
15.2.3 Stochastic description: the example of one
mutation.........................................
15.2.4 The probability generating function description . .
15.2.5 The method of characteristics ...................
15.3 Application to cancer treatment and generation of
resistance...............................................
15.3.1 The framework....................................
15.3.2 Treatment regimes................................
15.3.3 Probability of extinction and treatment success . .
15.3.4 Symmetric coefficients...........................
15.4 Example: the case of two drugs..........................
15.4.1 Equations for the moments........................
15.4.2 Equations for the characteristics................
Contents
xv
15.5 Mutant production before and during treatment............. 291
15.5.1 General theory..................................... 291
15.5.2 The case of one drug ........................... 294
15.5.3 The case of two drugs........................... 297
15.6 Outlook................................................... 299
16. Evolutionary dynamics of drug resistance in chronic
myeloid leukemia 301
16.1 Biology of CML............................................ 302
16.2 Therapy and targeted small molecule inhibitors............ 302
16.3 The computational framework............................... 305
16.4 When do resistant cells emerge?........................... 307
16.5 Cancer turnover and the evolution of resistance........... 308
16.6 Combination therapy and the prevention of resistance . . 309
16.7 Parameters and CML........................................ 312
16.8 Tumor architecture and tumor stem cells................... 314
16.9 Short-term versus long-term treatment strategies.......... 317
16.10 Cross-resistance and combination therapy................. 319
16.11 Combination versus cyclic sequential treatment........... 324
16.12 Summary.................................................. 328
Advanced topics 331
17. Evolutionary dynamics of stem-cell driven tumor growth 333
17.1 The model................................................. 334
17.2 Evolutionary dynamics in ODE models....................... 336
17.3 Evolutionary dynamics in a stochastic, spatial model . . . 339
17.4 Predicted versus observed tumor growth patterns........... 340
17.5 The order of phenotypic transitions....................... 342
17.6 Summary................................................... 345
18. Tumor growth kinetics and disease progression 347
18.1 Cell death and mutant generation.......................... 349
18.2 Does PCD protect against cancer?.......................... 353
18.3 Cell turnover and pathology............................... 356
18.4 Conclusions............................................... 357
19. Epigenetic changes and the rate of DNA methylation 359
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Dynamics of cancer: mathematical foundations of oncology
19.1 De novo méthylation kinetics in CIMP and non-CIMP cells
following déméthylation..................................
19.2 Quantifying the de novo méthylation kinetics.............
19.3 Interpreting the results with the help of a mathematical
model....................................................
19.4 De novo méthylation kinetics in highly methylated cells .
19.5 Importance of experimental verification .................
19.6 Summary..................................................
Telomeres and cancer protection
20.1 Lineages and replication limits .........................
20.2 Model analysis ..........................................
20.2.1 Population turnover and replication capacity:
analytical results...............................
20.2.2 Agent-based model ...............................
20.2.3 Decrease in the replication capacity of stem cells .
20.3 Tissue architecture and the development of cancer . . . .
20.4 Theory and observed tissue architecture..................
20.5 Summary..................................................
Gene therapy and oncolytic virus therapy
21.1 A basic ordinary differential equation model.............
21.1.1 Non-replicating viruses..........................
21.1.2 Replicating viruses..............................
21.2 Different mathematical formulations and the robustness of
results..................................................
21.3 A spatially explicit model of oncolytic virus dynamics . .
21.3.1 Initial virus growth patterns....................
21.3.2 Growth patterns and the extinction of cells . . . .
21.4 Experimentally observed patterns of virus spread.........
21.5 Conclusions..............................................
Immune responses, tumor growth, and therapy
22.1 Some facts about immune responses .......................
22.2 The model................................................
22.3 Properties of equilibria and parameter dependencies . . .
22.4 Immunity versus tolerance................................
22.5 Cancer initiation........................................
Contents xvii
22.6 Tumor dormancy, evolution, and progression............. 443
22.7 Immunotherapy against cancers ......................... 446
22.8 Case study: immune responses and the treatment for
chronic myeloid leukemia............................... 449
22.9 Role of immunity and resistance in driving treatment
dynamics .............................................. 452
22.10 Possible role of immune stimulation for long-term
remission ............................................. 456
22.11 Summary............................................... 457
23. Towards higher complexities: social interactions 459
23.1 Microenvironment ...................................... 459
23.2 Cooperation and division of labor...................... 460
23.3 Conclusion............................................. 462
Bibliography 463
Index 511
|
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| id | DE-604.BV041746423 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:54:07Z |
| institution | BVB |
| isbn | 9789814566360 |
| language | English |
| lccn | 013033157 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027192913 |
| oclc_num | 884287388 |
| open_access_boolean | |
| owner | DE-703 DE-83 DE-739 |
| owner_facet | DE-703 DE-83 DE-739 |
| physical | XVII, 514 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | World Scientific |
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| spellingShingle | Wodarz, Dominik Komarova, Natalia L. Dynamics of cancer mathematical foundations of oncology Datenverarbeitung Mathematik Oncology Mathematics Cancer Treatment Data processing Computational biology Onkologie (DE-588)4075658-0 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4075658-0 (DE-588)4155620-3 |
| title | Dynamics of cancer mathematical foundations of oncology |
| title_auth | Dynamics of cancer mathematical foundations of oncology |
| title_exact_search | Dynamics of cancer mathematical foundations of oncology |
| title_full | Dynamics of cancer mathematical foundations of oncology Dominik Wodarz & Natalia L. Komarova |
| title_fullStr | Dynamics of cancer mathematical foundations of oncology Dominik Wodarz & Natalia L. Komarova |
| title_full_unstemmed | Dynamics of cancer mathematical foundations of oncology Dominik Wodarz & Natalia L. Komarova |
| title_short | Dynamics of cancer |
| title_sort | dynamics of cancer mathematical foundations of oncology |
| title_sub | mathematical foundations of oncology |
| topic | Datenverarbeitung Mathematik Oncology Mathematics Cancer Treatment Data processing Computational biology Onkologie (DE-588)4075658-0 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Datenverarbeitung Mathematik Oncology Mathematics Cancer Treatment Data processing Computational biology Onkologie Mathematische Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027192913&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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