# Numerical Analysis: Computational modeling of the mammalian cell

The project aims to develop realistic and computationally effective models of cellular metabolism. The detailed mathematical model of the cell dynamics is a coupled system of nonlinear reaction-diffusion partial differential equations. The quantitative properties of these equations differ considerably between different parts of the cell, e.g. cytoplasm and membranes. On the one hand, the typical dimension of the membranes is three orders of magnitude smaller than that of the cell. On the other hand, the aggregated volume of the membranes is comparable to the total volume of the cell. This is thus a typical multi-scale problem with the accompanying numerical multiple scale difficulty: A standard discretization must resolve the tiny structures (small scale) over the whole cell (large scale), giving rise to extremely expensive (if at all practically realizable) computational models. One way out is to derive effective quantities (diffusion coefficients, reactions constants etc.), which essentially removes the smallest scale, therefore allowing an efficient numerical approximation. These methods bypass the difficult mathematical derivation of precise models and directly compute the effective solution, without suffering from the high computational cost of using a full discretization. This will allow for the development of more realistic numerical models.

This project is carried out in collaboration with Karolinska Institutet, Institute for Environmental Medicine. Co-PIs there are Ralf Morgenstern, Kristian Dreij.