Intracellular protein dynamics as a mathematical problem

Mirosław Lachowicz; Martin  Parisot; Zuzanna  Szymańska

doi:10.3934/dcdsb.2016060

Article Contents

2016, Volume 21, Issue 8: 2551-2566. Doi: 10.3934/dcdsb.2016060

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Intracellular protein dynamics as a mathematical problem

1.
Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa
2.
INRIA Paris, ANGE Project-Team, 75589 Paris Cedex 12
3.
ICM, University of Warsaw, ul. Pawińskiego 5a, 02-106 Warsaw

Received: September 30, 2015

Revised: January 31, 2016

Published: September 2016

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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.

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Mathematics Subject Classification: Primary: 35A01, 35K57, 35M13, 35Q92, 92B05, 92C37.

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