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Quantum counting: Operator methods for discrete population dynamics with applications to cell division

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journal contribution
posted on 2017-07-06, 15:29 authored by T. R. Robinson, E. Haven, A. M. Fry
The set of natural numbers may be identified with the spectrum of eigenvalues of an operator (quantum counting), and the dynamical equations of populations of discrete, countable items may be formulated using operator methods. These equations take the form of time dependent operator equations, involving Hamiltonian operators, from which the statistical time dependence of population numbers may be determined. The quantum operator method is illustrated by a novel approach to cell population dynamics. This involves Hamiltonians that mimic the process of stimulated cell division. We evaluate two different models, one in which the stimuli are expended in the division process and one in which the stimuli act as true catalysts. While the former model exhibits only bounded cell population variations, the latter exhibits two distinct regimes; one has bounded population fluctuations about a mean level and in the other, the population can undergo growth to levels that are orders of magnitude above threshold levels, through an instability that could be interpreted as a cancerous growth phase.

Funding

AMF is funded by Worldwide Cancer Research.

History

Citation

Progress in Biophysics and Molecular Biology, 2017

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Physics and Astronomy

Version

  • AM (Accepted Manuscript)

Published in

Progress in Biophysics and Molecular Biology

Publisher

Elsevier

issn

0079-6107

Acceptance date

2017-07-04

Copyright date

2017

Available date

2018-06-26

Publisher version

http://www.sciencedirect.com/science/article/pii/S0079610716301754

Notes

The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.

Language

en

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