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Superdiffusive dynamics of cancer cells

Sergei Fedotov, School of Mathematics, The University of Manchester, UK


We have been motivated by experiments (C. T. Mierke et al, J. Cell Sci. (2011) 124 , 369) showing non-Markovian subballistic superdiffusive dynamics of cancer cells. Our main challenge was to implement a death process into a non-Markovian transport processes governed by the anomalously persistent random walks. We model the inhibition of cell proliferation due to anticancer therapeutic agents by the random death process with the constant rate. We show that the death process leads to the transition from an intermediate superdiffusive regime to asymptotically normal diffusion transport regime. In another words, the death process leads to not just the inhibition of cell proliferation but also to the inhibition of cell transport ('death inhibited transport') by tempering superdiffusive process. This comes about from the nontrivial interaction between non-Markovian superdiffusion and random death process. We derived non-Markovian master equations for the cell densities with the generalized switching terms involving the tempered fractional material derivatives. We find the upper and lower bounds for the stationary profiles corresponding to the ballistic transport and diffusion with the death rate dependent diffusion coefficient. Monte Carlo simulations confirm these bounds.

Format: Oral communication

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