Time-dependent subpopulation induction in heterogeneous tumors
type: Item
instance of: scholarly article
title: Time-dependent subpopulation induction in heterogeneous tumors
zbMATH Open document ID: 0656.92005
DOI: 10.1007/BF02460096
author: Seth Michelson
author: John T. Leith
author: István Győri
published in: Bulletin of Mathematical Biology
publication date: 1988-01-01T00:00:00Z
review text: Time-dependent induction of clonal heterogeneity in the neoplastic micro- environment is analysed within the context of a competitive ecology. A model that describes a constant source for clonal emergence was analysed by the last two authors, \textit{B. E. Miller} and \textit{A. S. Glicksman}, J. Theor. Biol. 128, 233-346 as an extension of a model proposed by \textit{B. Jansson} and \textit{L. Revesz} [Math. Biosci. 19, 131-154 (1974; Zbl 0272.92005)]. The extended model has been termed the JRE Model. This paper extends these analyses to time-dependent emergence rates which may represent induction in the presence of a cytotoxic agent. If the analysis is constrained to the tumor microenvironment, and if the emergent subpopulation is drug resistant, then the model may describe the induction and emergence of drug resistant subclones in a growing neoplasm. Asymptotic closed form solutions are derived for a class of emergence rate functions which decay asymptotically to a constant mutation rate. This underlying mutation rate may represent spontaneous mutation to the resistant phenotype, and has been analysed stochastically. The asymptotic solutions to the time-dependent model approach the steady state solution for the JRE Model which represents the dynamics observed in the presence of a constant, spontaneous mutation rate. The clinical and biological implications of these results are discussed.
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 4072759
zbMATH Keywords: drug resistance in tumors
zbMATH Keywords: cytotoxicity
zbMATH Keywords: Time-dependent induction of clonal heterogeneity
zbMATH Keywords: neoplastic micro-environment
zbMATH Keywords: JRE Model
zbMATH Keywords: cytotoxic agent
zbMATH Keywords: tumor microenvironment
zbMATH Keywords: drug resistant subclones
zbMATH Keywords: growing neoplasm
zbMATH Keywords: Asymptotic closed form solutions
zbMATH Keywords: emergence rate functions
zbMATH Keywords: mutation rate
Wikidata QID: Q52579469
MaRDI profile type: Publication
cites work: The effect of cellular differentiation on the development of permanent drug resistance
cites work: A branching-process model for heterogeneous cell populations
cites work: Analysis of the growth of tumor cell populations
full work available at URL: https://doi.org/10.1007/bf02460096
OpenAlex ID: W2037464275
description: scientific article; zbMATH DE number 4072759