Modeling and Simulation of spatial aspects in Systems Biology

Project in SBCancer, a part of the Helmholtz Alliance on Systems Biology

Colaboration partners: PD Dr. U. Klingmuller, Dr A. Pfeifer (DKFZ)
Quantitative mesurements of activation, localization and transport dynamics of several components of the Jak2/Stat5 pathway by immunoblotting and fluorescence microscopy (timelapse imaging, FRAP, FCS) in a fibroblast model system as well as primary erythroid cells

Project Members: E. Friedmann, R. Neumann

Mathematical Modeling
We model systems of Reaction Diffusion Equations to analyze the influence of different cell shapes to a signal transduction pathway and to find out how specific components of the pathway are transported. Our model describes the Jak2/Stat5 signaling pathway including diffusion for non-activated and activated Stat5 molecules in the cytoplasm. The model is considered in two different three-dimensional geometries, a CFUE- and fibroblast-like geometry with corresponding parameters determined by our collaborators through FSC, FRAP and immunoblotting measurements and via parameter estimation. The resulting system of equations is analyzed mathematically and the existence and uniqueness of the solution are proved.

Simulation with Gascoigne
Two- and three-dimensional meshes are generated for the two geometries in the software Gascoigne and with the commercial software ANSYS to obtain shapes satisfying the biological guidelines. Because of the complicated biological shapes, a very fine mesh is needed in the proximity of the boundaries. The fine mesh together with the small time step size because of the short diffusion time (some seconds) and the long reaction time until a steady state is reached (hours) leads to long computing times. Numerical algorithms are explored to reduce this long computing time. We use Implicit Euler and Crank-Nicholson time stepping method and discretization of the stationary equations by Q1, Q2 finite elements. The resulting linear system is solved with multigrid methods. We evaluate the total concentration distribution of the activated and non-activated Stat5 during time and the spatial concentration distribution in the cytoplasm (see figures).

Spatial distribution of the non-activated Stat5 concentration in the cytoplasm of a CFUE cell.

Spatial distribution of the non-activated Stat5 concentration in the cytoplasm of a fibroblast cell.