Branching processes in biology:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2002
|
| Schriftenreihe: | Interdisciplinary applied mathematics
19 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 179 - 195 |
| Beschreibung: | XVIII, 230 S. graph. Darst. |
| ISBN: | 038795340X |
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| 245 | 1 | 0 | |a Branching processes in biology |c Marek Kimmel ; David E. Axelrod |
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| 300 | |a XVIII, 230 S. |b graph. Darst. | ||
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| 500 | |a Literaturverz. S. 179 - 195 | ||
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Datensatz im Suchindex
| _version_ | 1804129336579588096 |
|---|---|
| adam_text | MAREK KIMMEL DAVID E. AXELROD BRANCHING PROCESSES IN BIOLOGY WITH 54
ILLUSTRATIONS SPRINGER CONTENTS PREFACE VII GUIDE TO APPLICATIONS, OR
HOW TO READ THIS BOOK XVII 1 MOTIVATING EXAMPLES AND OTHER PRELIMINARIES
1 1.1 SOME MOTIVATING EXAMPLES 1 1.2 APPLICATION: POLYMERASE CHAIN
REACTION AND BRANCHING PROCESSES 3 1.2.1 INTRODUCTION TO THE MECHANICS
OF PCR 3 1.2.2 MATHEMATICAL MODEL 5 1.2.3 GENEALOGICAL APPROACH 5 1.2.4
STATISTICAL ESTIMATION OF THE MUTATION RATE 7 1.2.5 MUTAGENIC PCR AND
ARTIFICIAL EVOLUTION 8 1.3 THE BRANCHING PROPERTY 9 1.4 PROBABILITY
GENERATING FUNCTIONS AND ANALYTICAL METHODS ... 11 1.5 CLASSIFICATIONS
OF THE BRANCHING PROCESSES 13 1.5.1 LIFETIME 13 1.5.2 TYPE SPACE 13
1.5.3 CRITICALITY 14 1.6 MODELING WITH BRANCHING PROCESSES 15 2
BIOLOGICAL BACKGROUND 19 2.1 GENOMES: CHANGES IN DNA AND CHROMOSOMES 19
2.1.1 GENOME 19 2.1.2 DNA AND GENES 19 2.1.3 MUTATION 20 2.1.4 NONCODING
SEQUENCES OF DNA 21 CONTENTS 2.1.5 REPEATED SEQUENCES OF DNA 21 2.1.6
GENE AMPLIFICATION 21 2.1.7 CHROMOSOMES 22 2.1.8 DNA REPLICATION 23
2.1.9 RECOMBINATION 24 2.2 CELLS: CELL CYCLE KINETICS AND CELL DIVISION
24 2.2.1 CELLS AS THE BASIC UNITS OF LIFE 24 2.2.2 CELL GROWTH AND
DIVISION 25 2.2.3 , CELL CYCLE KINETICS 27 2.3 CANCER: DRUG RESISTANCE
AND CHEMOTHERAPY 28 2.3.1 CANCER CELLS ARE IMMORTAL 28 2.3.2 TUMOR
HETEROGENEITY AND INSTABILITY 28 2.3.3 CELL CYCLE AND RESISTANCE TO
CHEMOTHERAPY 29 2.3.4 MUTATIONS IN CANCER CELLS 29 2.4 REFERENCES 29
2.4.1 TEXTBOOKS AND MONOGRAPHS IN BIOLOGY 30 2.4.2 MATHEMATICAL BIOLOGY
30 2.4.3 ARGUMENTS FOR MATHEMATICAL MODELING OF BIOLOGICAL PHENOMENA 31
THE GALTON-WATSON PROCESS 33 3.1 CONSTRUCTION, FUNCTIONAL EQUATION, AND
ELEMENTARY PROPERTIES 34 3.1.1 BACKWARD EQUATION 34 3.1.2 FORWARD
EQUATION 35 3.1.3 MOMENTS 36 3.1.4 THE LINEAR FRACTIONAL CASE 36 3.2
APPLICATION: CELL CYCLE MODEL WITH DEATH AND QUIESCENCE . . 37 3.2.1 THE
MATHEMATICAL MODEL 37 3.2.2 MODELING BIOLOGICAL DATA 39 3.3 EXTINCTION
AND CRITICALITY 42 3.4 APPLICATION: COMPLEXITY THRESHOLD IN THE
EVOLUTION OF EARLY LIFE 43 3.5 ASYMPTOTIC PROPERTIES 44 3.5.1
SUPERCRITICAL PROCESS 44 3.5.2 SUBCRITICAL PROCESS 46 3.5.3 CRITICAL
PROCESS 47 3.6 APPLICATION: GENE AMPLIFICATION 47 3.6.1 GENE
AMPLIFICATION AND DRUG RESISTANCE 48 3.6.2 GALTON-WATSON PROCESS MODEL
OF GENE AMPLIFICATION AND DEAMPLIFICATION 48 3.6.3 MATHEMATICAL MODEL OF
THE LOSS OF RESISTANCE 50 3.6.4 PROBABILITIES OF GENE AMPLIFICATION AND
DEAMPLIFICATION FROM MTX DATA 51 CONTENTS XIII 3.7 APPLICATION: ITERATED
GALTON-WATSON PROCESS AND EXPANSION OF DNA REPEATS 51 3.7.1 DYNAMICS OF
DNA REPEATS IN HUMAN PEDIGREES 52 3.7.2 DEFINITION OF THE PROCESS 52
3.7.3 EXAMPLE 54 3.7.4 PROPERTIES 55 3.8 APPLICATION: GALTON-WATSON
PROCESSES IN A RANDOM ENVIRONMENT AND MACROEVOLUTION 56 3.8.1 REDUCED
TREES FOR SUBCRITICAL GWBPRE 58 3.8.2 EVOLUTIONARY INTERPRETATION 59 3.9
OTHER WORKS AND APPLICATIONS 59 3.9.1 STOCHASTIC DEPENDENCE 59 3.9.2
PROCESS STATE DEPENDENCE 60 3.9.3 BISEXUAL GALTON-WATSON PROCESS 60
3.9.4 AGE OF THE PROCESS 60 3.9.5 FAMILY TREES AND SUBTREES 61 3.10
PROBLEMS 61 4 THE AGE-DEPENDENT PROCESS: THE MARKOV CASE 65 4.1
DIFFERENTIAL EQUATION FOR THE PGF AND ITS ELEMENTARY PROPERTIES 65 4.1.1
DEFINITION OF THE PROCESS 65 4.1.2 PROBABILITY OF EXTINCTION AND MOMENTS
67 4.2 APPLICATION: CLONAL RESISTANCE THEORY OF CANCER CELLS .... 68
4.2.1 SINGLE-MUTATION CASE 69 4.2.2 TWO-MUTATION CASE 73 4.3 GENEALOGIES
OF BRANCHING PROCESSES 76 4.3.1 NEAR-CRITICAL PROCESSES 77 4.4
APPLICATION: ESTIMATION OF THE AGE OF THE MITOCHONDRIAL EVE 80 4.4.1
POPULATION GENETIC MODEL 80 4.4.2 NUMERICAL ESTIMATES 82 4.5 OTHER WORKS
AND APPLICATIONS 83 4.6 PROBLEMS 84 5 THE BELLMAN-HARRIS PROCESS 87 5.1
INTEGRAL EQUATIONS FOR THE PGF AND BASIC PROPERTIES 87 5.2 RENEWAL
THEORY AND ASYMPTOTICS OF THE MOMENTS 89 5.2.1 BASICS OF THE RENEWAL
THEORY 89 5.2.2 THE MOMENTS 90 5.3 ASYMPTOTIC PROPERTIES OF THE PROCESS
IN THE SUPERCRITICAL CASE 91 5.4 APPLICATION: ANALYSIS OF THE
STATHMOKINETIC EXPERIMENT .... 91 5.4.1 AGE DISTRIBUTIONS 91 5.4.2 THE
STATHMOKINETIC EXPERIMENT 92 CONTENTS 5.4.3 MODEL 93 5.4.4 ESTIMATION 96
5.5 OTHER WORKS AND APPLICATIONS 97 5.5.1 CELL POPULATIONS 97 5.5.2
ESTIMATION OF CELL LIFETIMES 99 5.5.3 BIFURCATING AUTOREGRESSION 101 5.6
PROBLEMS 101 MULTITYPE PROCESSES 103 6.1 APPLICATION: TWO-STAGE
MUTATIONS AND FLUCTUATION ANALYSIS . . 103 6.1.1 LURIA-DELBRIICK MODEL
104 6.1.2 THE MARKOV BRANCHING PROCESS MODEL 106 6.1.3 THE GALTON-WATSON
PROCESS MODEL 107 6.1.4 THE GALTON-WATSON PROCESS MODEL WITH CELL DEATH
... 108 6.1.5 TWO-STAGE GALTON-WATSON PROCESS MODEL 109 6.1.6 THE
SINGLE-STAGE MODELS VERSUS DATA 110 6.1.7 THE TWO-STAGE MODEL VERSUS
DATA 112 6.2 THE POSITIVE REGULAR CASE OF THE MULTITYPE GALTON-WATSON
PROCESS 114 6.2.1 BASICS 115 6.2.2 POSITIVITY PROPERTIES 117 6.2.3
ASYMPTOTIC BEHAVIOR IN THE SUPERCRITICAL CASE 117 6.2.4 PROBABILITY OF
EXTINCTION 118 6.3 APPLICATION: A MODEL OF TWO CELL POPULATIONS 118 6.4
APPLICATION: STOCHASTIC MODEL OF THE CELL CYCLE WITH CHEMOTHERAPY 119
6.4.1 MODEL OF DRUG-PERTURBED STATHMOKINESIS 120 6.4.2 MODEL PARAMETERS
123 6.4.3 PREDICTION OF THE EFFECTS OF CONTINUOUS EXPOSURE TO THE DRUG
124 6.4.4 RESULTS 124 6.4.5 DISCUSSION 126 6.5 APPLICATION: CELL SURFACE
AGGREGATION PHENOMENA 127 6.5.1 RELATIONSHIP BETWEEN THE GALTON-WATSON
PROCESS AND THE AGGREGATION PROCESS 129 6.5.2 PROGENY DISTRIBUTIONS 130
6.5.3 ANTIGEN SIZE DISTRIBUTION ON A CELL SURFACE 130 6.6 SAMPLING
FORMULAS FOR THE MULTITYPE GALTON-WATSON PROCESS 132 6.6.1 FORMULAS FOR
MEAN AND VARIANCE 133 6.6.2 THE MARKOV PROPERTY 133 6.7 APPLICATION:
DELETIONS IN MITOCHONDRIAL DNA 134 6.8 APPLICATION: POLYMERASE CHAIN
REACTION 135 6.9 OTHER WORKS AND APPLICATIONS 137 6.9.1 HEMOPOIESIS AND
CLONAL CELL POPULATIONS -. 137 CONTENTS XV 6.9.2 GENE AMPLIFICATION 138
6.9.3 MODELING IN VARYING ENVIRONMENTS 139 7 BRANCHING PROCESSES WITH
INFINITELY MANY TYPES 141 7.1 APPLICATION: STABLE GENE AMPLIFICATION 141
7.1.1 ASSUMPTIONS 142 7.1.2 PROBABILITY GENERATING FUNCTIONS AND
EXPECTATIONS ... 144 7.1.3 MODEL VERSUS DATA 146 7.2 APPLICATION:
MATHEMATICAL MODELING OF THE LOSS OF TELOMERE SEQUENCES 147 7.2.1
STOCHASTIC MODEL 147 7.2.2 BRANCHING PROCESS 150 7.2.3 ANALYSIS IN THE
MARKOV CASE 151 7.2.4 MODEL VERSUS DATA 152 7.2.5 FURTHER WORK ON
TELOMERE MODELING 153 7.3 BRANCHING RANDOM WALK WITH AN ABSORBING
BARRIER 153 7.4 APPLICATION: A MODEL OF UNSTABLE GENE AMPLIFICATION 157
7.5 QUASISTATIONARITY IN A BRANCHING MODEL OF DIVISION-WITHIN-DIVISION
158 7.5.1 DEFINITION OF THE PROCESS 158 7.5.2 QUASISTATIONARITY 160
7.5.3 GENE AMPLIFICATION 161 7.6 GALTON-WATSON AND BELLMAN-HARRIS
PROCESSES WITH DENUMERABLY MANY TYPES AND BRANCHING RANDOM WALKS ... 162
7.6.1 BIOLOGICAL MODELS WITH A DENUMERABLE INFINITY OF TYPES 163 7.7
APPLICATION: STRUCTURED CELL POPULATION MODELS 164 7.7.1 A MODEL OF
UNEQUAL DIVISION AND GROWTH REGULATION IN CELL COLONIES 165 7.7.2 CELL
CYCLE MODEL WITH CELL SIZE CONTROL, UNEQUAL DIVISION OF CELLS, AND TWO
CELL TYPES 169 7.8 APPLICATION: YULE S EVOLUTIONARY PROCESS 175 8
REFERENCES 179 A MULTIVARIATE PROBABILITY GENERATING FUNCTIONS 197 B
PROBABILITY DISTRIBUTIONS FOR THE BELLMAN-HARRIS PROCESS 199 B.I
CONSTRUCTION 199 B.I.I THE FAMILIES 199 B.I.2 THE NUMBER OF OBJECTS AT
GIVEN TIME 200 B.I.3 PROBABILITY MEASURE 200 B.I.4 THE EMBEDDED
GALTON-WATSON PROCESS AND EXTINCTION PROBABILITY 201 XVI CONTENTS B.2
INTEGRAL EQUATION 202 B.2.1 DECOMPOSITION INTO SUBFAMILIES 202 B.2.2
GENERATING FUNCTIONS 202 B.2.3 UNIQUENESS OF F(S, T) AND FINITENESS OF
Z(T) 203 C GENERAL PROCESSES 205 C.I INTRODUCTION TO THE
JAGERS-CRUMP-MODE PROCESS 205 C.I.I DEFINITION OF THE GENERAL BRANCHING
PROCESS 205 C.1.2^ RANDOM CHARACTERISTICS AND BASIC DECOMPOSITION . . .
. 206 C.I.3 EXPECTATIONS, MALTHUSIAN PARAMETER, AND EXPONENTIAL GROWTH
207 C.I.4 ABSTRACT TYPE SPACES AND COMPOSITION OF THE PROCESS . . 208
C.2 APPLICATION: ALEXANDERSSON S CELL POPULATION MODEL USING A GENERAL
BRANCHING PROCESS 210 C.2.1 THE MODEL 211 C.2.2 EXISTENCE OF THE STABLE
BIRTH SIZE DISTRIBUTION 212 C.2.3 ASYMPTOTICS OF THE CELL MODEL 213 D
GLOSSARIES 215 D.I BIOLOGICAL GLOSSARY FOR MATHEMATICIANS 215 D.2
MATHEMATICAL GLOSSARY FOR BIOLOGISTS 219 INDEX 227
|
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| id | DE-604.BV014556854 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:03:31Z |
| institution | BVB |
| isbn | 038795340X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009898647 |
| oclc_num | 54533819 |
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| owner | DE-29T DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| owner_facet | DE-29T DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| physical | XVIII, 230 S. graph. Darst. |
| publishDate | 2002 |
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| publisher | Springer |
| record_format | marc |
| series | Interdisciplinary applied mathematics |
| series2 | Interdisciplinary applied mathematics |
| spelling | Kimmel, Marek Verfasser aut Branching processes in biology Marek Kimmel ; David E. Axelrod New York [u.a.] Springer 2002 XVIII, 230 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Interdisciplinary applied mathematics 19 Literaturverz. S. 179 - 195 Mathematisches Modell Biology Mathematical models Branching processes Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Biologie (DE-588)4006851-1 gnd rswk-swf Biologie (DE-588)4006851-1 s Verzweigung Mathematik (DE-588)4078889-1 s DE-604 Axelrod, David E. Verfasser aut Interdisciplinary applied mathematics 19 (DE-604)BV004216726 19 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009898647&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kimmel, Marek Axelrod, David E. Branching processes in biology Interdisciplinary applied mathematics Mathematisches Modell Biology Mathematical models Branching processes Verzweigung Mathematik (DE-588)4078889-1 gnd Biologie (DE-588)4006851-1 gnd |
| subject_GND | (DE-588)4078889-1 (DE-588)4006851-1 |
| title | Branching processes in biology |
| title_auth | Branching processes in biology |
| title_exact_search | Branching processes in biology |
| title_full | Branching processes in biology Marek Kimmel ; David E. Axelrod |
| title_fullStr | Branching processes in biology Marek Kimmel ; David E. Axelrod |
| title_full_unstemmed | Branching processes in biology Marek Kimmel ; David E. Axelrod |
| title_short | Branching processes in biology |
| title_sort | branching processes in biology |
| topic | Mathematisches Modell Biology Mathematical models Branching processes Verzweigung Mathematik (DE-588)4078889-1 gnd Biologie (DE-588)4006851-1 gnd |
| topic_facet | Mathematisches Modell Biology Mathematical models Branching processes Verzweigung Mathematik Biologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009898647&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004216726 |
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