Intracellular protein dynamics as a mathematical problem

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.

Computational Modelling of Cancer Development and Growth: Modelling at Multiple Scales and Multiscale Modelling

“…The inclusion of spatial terms rather than a delay equally leads to the necessary oscillations (e.g. Sturrock et al, 2011Sturrock et al, , 2012Szymańska et al, 2014;Lachowicz et al, 2016;Macnamara and Chaplain, 2016). Furthermore, Chaplain et al (2015) rigorously proved, for the Hes1 system, that molecular diffusion causes oscillations.…”

Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein

“…transport between the nucleus and the cytoplasm [15,16,17,19]. Some mathematical analysis of this model can be found in [4,8].…”