Abstract
The present paper provides a mathematical analysis of the model of intracellular protein dynamics proposed in [14]. The model describes protein and mRNA transport inside a cell and takes into account diffusion in the nucleus and cytoplasm as well as active transport of protein molecules along microtubules in the cytoplasm. The model is a complex system of nonlinear PDEs with appropriate boundary conditions. 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 the existence and uniqueness result for the model in arbitrary space dimension. The model may be adapted to other signaling pathways.
Highlights
Mathematical modeling of intracellular proteins dynamics is one of the most commonly undertaken challenges in mathematical biology
The nucleus is separated from the cytoplasm by a membrane, which is called the nuclear envelope that is denoted by Γn
Some of the proteins are needed in the nucleus in order to regulate the process of mRNA production
Summary
Mathematical modeling of intracellular proteins dynamics is one of the most commonly undertaken challenges in mathematical biology. This follows from our belief that increased knowledge about these processes will allow us to better understand the functioning of a cell, especially if it is distorted, as it is in the case of many diseases like cancer. We show a well–posedness of a model of intracellular transport processes generalizing the system presented in [1] to the case of N couples mRNA/protein. The mathematical analysis is perform for an arbitrary space dimension and with non-linear parameters satisfying classical mathematical properties To our knowledge, this is the first work that in multidimensional case deals with rigorous mathematical analysis of the model of intracellular protein dynamics including active transport along microtubules.
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