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Modeling Uniaxial Nonuniform Cell Proliferation
Alexander Lai De Oliveira1, Benjamin J Binder2
1School of Mathematical Sciences, University of Adelaide, Adelaide, SA, 5005, Australia.
Abstract:
Growth in biological systems occurs as a consequence of cell proliferation fueled by a nutrient supply. In general, the nutrient gradient of the system will be nonconstant, resulting in biased cell proliferation. We develop a uniaxial discrete cellular automaton with biased cell proliferation using a probability distribution which reflects the nutrient gradient of the system. An explicit probability mass function for the displacement of any tracked cell under the cellular automaton model is derived and verified against averaged simulation results; this displacement distribution has applications in predicting cell trajectories and evolution of expected site occupancies.
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