The effect of cellular differentiation on the development of permanent drug resistance
type: Item
instance of: scholarly article
title: The effect of cellular differentiation on the development of permanent drug resistance
zbMATH Open document ID: 0576.92009
DOI: 10.1016/0025-5564(85)90054-9
author: Andrew J. Coldman
author: James H. Goldie
author: Vincent Ng
published in: Mathematical Biosciences
publication date: 1985-01-01T00:00:00Z
review text: Birth and death processes are applied to modeling of development of spontaneous drug resistance of tumor stem cells. It is supposed that new stem cells are produced at a rate b, while the existing stem cells differentiate (leave the system) at rate d. Resistance to drug is caused by a single mutation occuring at a rate \(\alpha\). Cell death is not considered. The authors carefully investigate the Kolmogorov equations of the process to find expected values and extinction probabilities yielded by the model. It is found that cell differentiation increases the rate of development of single drug resistance, although this is balanced by an increased likelihood that such resistant cells sooner leave the stem cell population. Situation changes if resistance to two drugs is considered; then the probability that doubly resistant cells persist, is proportional to the rate of cell differentiation. A discussion of the validity of assumptions used, is provided.
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 60J85
zbMATH DE Number: 3922425
zbMATH Keywords: development of permanent drug resistance
zbMATH Keywords: compartment model
zbMATH Keywords: growth
zbMATH Keywords: of human tumors
zbMATH Keywords: Birth and death processes
zbMATH Keywords: spontaneous drug resistance of tumor stem cells
zbMATH Keywords: mutation
zbMATH Keywords: Kolmogorov equations
zbMATH Keywords: expected values
zbMATH Keywords: extinction probabilities
zbMATH Keywords: cell differentiation
zbMATH Keywords: single drug resistance
zbMATH Keywords: doubly resistant cells
MaRDI profile type: Publication
full work available at URL: 0025-5564(85)90054-9
OpenAlex ID: W2022562134
cites work: A STOCHASTIC MODEL OF STEM CELL PROLIFERATION, BASED ON THE GROWTH OF SPLEEN COLONY-FORMING CELLS
cites work: A model for the resistance of tumor cells to cancer chemotherapeutic agents
cites work: Partial differential equations. 4th ed
cites work: On the distribution of the number of mutants at the hypoxanthine-quanine phosphoribosal transferase locus in Chinese hamster ovary cells
description: scientific article; zbMATH DE number 3922425