Simulation of cell behavior: normal and abnormal growth

Bulletin of Mathematical Biology
E J Davison

Abstract

A mathematical model simulating a cell growing in a culture medium is obtained. Using this model, various behavioral patterns of the cell are obtained under different types of disturbances, in particular when (i) a Mg2+ deficiency experiment and, (ii) a split-dose ionizing radiation experiment are carried out, (iii) when disturbances on the rate constants of the biochemical reactions taking place in the nucleus of the cell are applied, and (iv) when the cell's interior components are perturbed. The cell model results obtained agree well with experimental results for the Mg2+ and split dose experiments, and explain the mechanism of the split dose radiation experiment without the need to introduce additional axioms (e.g. healing processes) into the dynamics of the cell. Conditions are obtained which cause the cell to behave in a rapidly growing 'tumor-like' mode; it is shown that once the cell moves into this 'tumor-like; mode, its behavior is irreversible, i.e. if a disturbance of opposite type is then applied to the 'tumor cell, the cell will not revert back to its original normal behavior.

References

Feb 15, 1968·The New England Journal of Medicine·J B Little
Nov 1, 1964·Journal of Theoretical Biology·W G Yeisley, E C Pollard
Mar 9, 1967·The New England Journal of Medicine·J R Warner, R Soeiro
Mar 30, 1967·The New England Journal of Medicine·G Medoff, M N Swartz
Dec 1, 1970·The American Journal of Physiology·N E DiamantE J Davison
Jan 1, 1964·Journal of Theoretical Biology·F Heinmets

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Citations

Feb 5, 1988·Biotechnology and Bioengineering·A Joshi, B O Palsson
Apr 1, 1981·Mathematical Biosciences·A BertuzziM A Giovenco

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