Intracellular protein dynamics as a mathematical problem

Abstract : In this paper we undertake a mathematical analysis of a model of intracellular protein dynamics , i.e. protein and mRNA transport inside a cell, proposed by Szymanska at al. in 2014. The model takes into account diffusive transport in the nucleus and cytoplasm, as well as active transport of protein molecules along microtubules in the cytoplasm. The model reproduces, at least in numerical simulations, the oscillatory changes in protein concentration observed in the experimental data. To our knowledge this is the first paper that, in the multidimensional case, deals with a rigorous mathematical analysis of a model of intracellular dynamics with active transport on microtubules. In particular, in the present paper we prove well-posedness of the model in any space dimension. The model is a complex system of nonlinear PDEs with specific boundary conditions. It may be adapted to other signaling pathways.
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Mirosław Lachowicz, Martin Parisot, Zuzanna Szymańska. Intracellular protein dynamics as a mathematical problem. Discrete and Continuous Dynamical Systems - Series B (DCDS-B), American Institute of Mathematical Sciences, 2016. 〈hal-01152399〉

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