BRANCHING PROCESSES IN BIOLOGY
CONTENTS MOTIVATING EXAMPLES AND OTHER PRELIMINARIES SOME MOTIVATING EXAMPLES APPLICATION: POLYMERASE CHAIN REACTION AND BRANCHING PROCESSES INTRODUCTION TO THE MECHANICS OF PCR MATHEMATICAL MODEL GENEALOGICAL APPROACH STATISTICAL ESTIMATION OF THE MUTATION RATE MUTAGENIC PCR AND ARTI?CIAL EVOLUTION THE BRANCHING PROPERTY PROBABILITY GENERATING FUNCTIONS AND ANALYTICAL METHODS CLASSI?CATIONS OF THE BRANCHING PROCESSES LIFETIME TYPE SPACE CRITICALITY MODELING WITH BRANCHING PROCESSES BIOLOGICAL BACKGROUND GENOMES: CHANGES IN DNA AND CHROMOSOMES GENOME DNA AND GENES MUTATION NONCODING SEQUENCES OF DNA REPEATED SEQUENCES OF DNA GENE AMPLI?CATION CHROMOSOMES DNA REPLICATION RECOMBINATION CELLS: CELL CYCLE KINETICS AND CELL DIVISION CELLS AS THE BASIC UNITS OF LIFE CELL GROWTH AND DIVISION CELL CYCLE KINETICS CANCER: DRUG RESISTANCE AND CHEMOTHERAPY CANCER CELLS ARE IMMORTAL TUMOR HETEROGENEITY AND INSTABILITY CELL CYCLE AND RESISTANCE TO CHEMOTHERAPY MUTATIONS IN CANCER CELLS TEXTBOOKS AND MONOGRAPHS IN BIOLOGY MATHEMATICAL BIOLOGY ARGUMENTS FOR MATHEMATICAL MODELING OF BIOLOGICAL PHENOMENA THE GALTON–WATSON PROCESS CONSTRUCTION, FUNCTIONAL EQUATION, AND ELEMENTARY PROPERTIES BACKWARD EQUATION FORWARD EQUATION MOMENTS THE LINEAR FRACTIONAL CASE APPLICATION: CELL CYCLE MODEL WITH DEATH AND QUIESCENCE THE MATHEMATICAL MODEL MODELING BIOLOGICAL DATA EXTINCTION AND CRITICALITY APPLICATION: COMPLEXITY THRESHOLD IN THE EVOLUTION OF EARLY LIFE ASYMPTOTIC PROPERTIES SUPERCRITICAL PROCESS SUBCRITICAL PROCESS CRITICAL PROCESS APPLICATION: GENE AMPLI?CATION GENE AMPLI?CATION AND DRUG RESISTANCE GALTON–WATSON PROCESS MODEL OF GENE AMPLI?CATION AND DEAMPLI?CATION MATHEMATICAL MODEL OF THE LOSS OF RESISTANCE PROBABILITIES OF GENE AMPLI?CATION AND DEAMPLI?CATION FROM MTX DATA APPLICATION: ITERATED GALTON–WATSON PROCESS AND EXPANSION OF DNA REPEATS DYNAMICS OF DNA REPEATS IN HUMAN PEDIGREES DE?NITION OF THE PROCESS EXAMPLE PROPERTIES APPLICATION: GALTON–WATSON PROCESSES IN A RANDOM ENVIRONMENT AND MACROEVOLUTION REDUCED TREES FOR SUBCRITICAL GWBPRE EVOLUTIONARY INTERPRETATION OTHER WORKS AND APPLICATIONS STOCHASTIC DEPENDENCE PROCESS STATE DEPENDENCE BISEXUAL GALTON–WATSON PROCESS AGE OF THE PROCESS FAMILY TREES AND SUBTREES PROBLEMS THE AGE-DEPENDENT PROCESS: THE MARKOV CASE DIFFERENTIAL EQUATION FOR THE PGF AND ITS ELEMENTARY PROPERTIES PROBABILITY OF EXTINCTION AND MOMENTS APPLICATION: CLONAL RESISTANCE THEORY OF CANCER CELLS SINGLE-MUTATION CASE TWO-MUTATION CASE GENEALOGIES OF BRANCHING PROCESSES “NEAR-CRITICAL” PROCESSES APPLICATION: ESTIMATION OF THE AGE OF THE MITOCHONDRIAL EVE POPULATION GENETIC MODEL NUMERICAL ESTIMATES THE BELLMAN–HARRIS PROCESS INTEGRAL EQUATIONS FOR THE PGF AND BASIC PROPERTIES RENEWAL THEORY AND ASYMPTOTICS OF THE MOMENTS BASICS OF THE RENEWAL THEORY THE MOMENTS ASYMPTOTIC PROPERTIES OF THE PROCESS IN THE SUPERCRITICAL CASE APPLICATION: ANALYSIS OF THE STATHMOKINETIC EXPERIMENT AGE DISTRIBUTIONS THE STATHMOKINETIC EXPERIMENT MODEL ESTIMATION CELL POPULATIONS ESTIMATION OF CELL LIFETIMES BIFURCATING AUTOREGRESSION MULTITYPE PROCESSES APPLICATION: TWO-STAGE MUTATIONS AND FLUCTUATION ANALYSIS LURIA–DELBR¨UCK MODEL THE MARKOV BRANCHING PROCESS MODEL THE GALTON–WATSON PROCESS MODEL THE GALTON–WATSON PROCESS MODEL WITH CELL DEATH TWO-STAGE GALTON–WATSON PROCESS MODEL THE SINGLE-STAGE MODELS VERSUS DATA THE TWO-STAGE MODEL VERSUS DATA THE POSITIVE REGULAR CASE OF THE MULTITYPE GALTON–WATSON PROCESS BASICS POSITIVITY PROPERTIES ASYMPTOTIC BEHAVIOR IN THE SUPERCRITICAL CASE PROBABILITY OF EXTINCTION APPLICATION: A MODEL OF TWO CELL POPULATIONS APPLICATION: STOCHASTIC MODEL OF THE CELL CYCLE WITH CHEMOTHERAPY MODEL OF DRUG-PERTURBED STATHMOKINESIS MODEL PARAMETERS PREDICTION OF THE EFFECTS OF CONTINUOUS EXPOSURE TO THE DRUG RESULTS DISCUSSION APPLICATION: CELL SURFACE AGGREGATION PHENOMENA RELATIONSHIP BETWEEN THE GALTON–WATSON PROCESS AND THE AGGREGATION PROCESS PROGENY DISTRIBUTIONS ANTIGEN SIZE DISTRIBUTION ON A CELL SURFACE SAMPLING FORMULAS FOR THE MULTITYPE GALTON–WATSON PROCESS FORMULAS FOR MEAN AND VARIANCE THE MARKOV PROPERTY APPLICATION: DELETIONS IN MITOCHONDRIAL DNA APPLICATION: POLYMERASE CHAIN REACTION HEMOPOIESIS AND CLONAL CELL POPULATIONS MODELING IN VARYING ENVIRONMENTS BRANCHING PROCESSES WITH IN?NITELY MANY TYPES APPLICATION: STABLE GENE AMPLI?CATION ASSUMPTIONS PROBABILITY GENERATING FUNCTIONS AND EXPECTATIONS MODEL VERSUS DATA APPLICATION: MATHEMATICAL MODELING OF THE LOSS OF TELOMERE SEQUENCES STOCHASTIC MODEL BRANCHING PROCESS ANALYSIS IN THE MARKOV CASE FURTHER WORK ON TELOMERE MODELING BRANCHING RANDOM WALK WITH AN ABSORBING BARRIER APPLICATION: A MODEL OF UNSTABLE GENE AMPLI?CATION QUASISTATIONARITY IN A BRANCHING MODEL OF DIVISION-WITHIN-DIVISION QUASISTATIONARITY GALTON–WATSON AND BELLMAN–HARRIS PROCESSES WITH DENUMERABLY MANY TYPES AND BRANCHING RANDOM WALKS BIOLOGICAL MODELS WITH A DENUMERABLE IN?NITY OF TYPES APPLICATION: STRUCTURED CELL POPULATION MODELS A MODEL OF UNEQUAL DIVISION AND GROWTH REGULATION IN CELL COLONIES CELL CYCLE MODEL WITH CELL SIZE CONTROL, UNEQUAL DIVISION OF CELLS, AND TWO CELL TYPES APPLICATION: YULE’S EVOLUTIONARY PROCESS