Journal ArticleDOI
Mathematical models for estimating mutation rates in cell populations
Kenny S. Crump,David G. Hoel +1 more
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A statistical analysis is given of the mutant accumulation method of estimating mutation rates, and Phenotypic delay, that is delay from the epoch at which a cell mutates until cells in resulting clone possess the property which distinguishes them from nonmutant cells, is determined.Abstract:
SUMMARY A number of mathematical models for cell populations in which mutations are occurring are studied and compared by viewing the models as filtered Poisson processes. Based upon these models, a statistical analysis is given of the mutant accumulation method of estimating mutation rates. Phenotypic delay, that is delay from the epoch at which a cell mutates until cells in resulting clone possess the property which distinguishes them from nonmutant cells, is incorporated into the models and its effect upon some estimation procedures is determined. A suggestion is also given for obtaining information about the duration of phenotypic delay.read more
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Branching processes in biology
Marek Kimmel,David E. Axelrod +1 more
TL;DR: This book provides a theoretical background of branching processes and discusses their biological applications and will be of interest to scientists who work in quantitative modeling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, cell biologists, molecular biologists, and bioinformaticians.
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Evolution of acquired resistance to anti-cancer therapy
Jasmine Foo,Franziska Michor +1 more
TL;DR: Recent advances towards elucidating the evolutionary dynamics of acquired drug resistance are reviewed and how evolutionary thinking can contribute to outstanding questions in the field is outlined.
Journal ArticleDOI
Progress of a half century in the study of the Luria–Delbrück distribution
TL;DR: This review article examines four most important formulations, focusing on important practical issues closely linked with the distribution of the number of mutants, including the probability generating functions, moments, computational methods and asymptotics.
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A model for the resistance of tumor cells to cancer chemotherapeutic agents
A.J. Coldman,J.H. Goldie +1 more
TL;DR: A mathematical model of tumor resistance to chemotherapy based on a stochastic process of change is presented and it is found that sequential alternation of drugs satisfies certain optimality criteria when both drugs are equally effective.
Book
Branching Process Models of Cancer
TL;DR: This chapter uses multitype branching processes with mutation to model cancer, with cancer progression, resistance to therapy, and metastasis in mind, and investigates the time of the first type k mutation and the growth of the number of type k cells.
References
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Journal ArticleDOI
Mutations of bacteria from virus sensitivity to virus resistance
Salvador E. Luria,Max Delbrück +1 more
TL;DR: This article reported Luria and Delbruck's breakthrough study in which they established that viruses do not induce mutations in bacteria, but that virus-resisting mutations are spontaneous.
Journal ArticleDOI
A mutational assay system using the thymidine kinase locus in mouse lymphoma cells
TL;DR: An estimate can be made of the relative mutagenicities of various treatments of the TK locus and the observed induced mutation rates with the spontaneous TK +/− → TK −/− mutation rate.
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Mutations of bacteria from virus sensitivity to virus resistance
Salvador E. Luria,Max Delbrück +1 more