Analytical And Numerical Approximation of Effective Diffusivities in The Cytoplasm of Biological Cells
This work addresses the challenge of simulating metabolism in mammalian cells with spatial distributions, offering a method to handle the complex geometric structure of the cytoplasm.
The authors propose a homogenization technique to compute effective diffusion constants in the cytoplasm of mammalian cells, using a two-step strategy combining analytic and numerical methods. The approach provides reasonable estimates of the homogenized diffusion constant, though the numerical algorithm is computationally expensive.
The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplasm has a very complex geometric structure which cannot be handled by standard discretization techniques. In the present paper we propose a homogenization technique for computing effective diffusion constants. This is accomplished by using a two-step strategy. The first step consists of an analytic homogenization from the smallest to an intermediate scale. The homogenization error is estimated by comparing the analytic diffusion constant with a numerical estimate obtained by using real cell geometries. The second step consists of a random homogenization. Since no analytical solution is known to this homogenization problem, a numerical approximation algorithm is proposed. Although rather expensive this algorithm provides a reasonable estimate of the homogenized diffusion constant.