Spatial aspects in the SMAD signaling pathway

Abstract

Among other approaches, differential equations are used for a deterministic quantitative description of time-dependent biological processes. For intracellular systems, such as signaling pathways, most existing models are based on ordinary differential equations. These models describe temporal processes, while they neglect spatial aspects. We present a model for the SMAD signaling pathway, which gives a temporal and spatial description on the basis of reaction diffusion equations to answer the question whether cell geometry plays a role in signaling. In this article we simulate the ordinary differential equations as well as partial differential equations of parabolic type with suile numerical methods, the latter on different cell geometries. In addition to manual construction of idealized cells, we also construct meshes from microscopy images of real cells. The main focus of the paper is to compare the results of the model without and with spatial aspects to answer the addressed question. The results show that diffusion in the model can lead to significant intracellular gradients of signaling molecules and changes the level of response to the signal transduced by the signaling pathway. In particular, the extent of these observations depends on the geometry of the cell.

Appendix: Experimental procedures

Isolated primary mouse hepatocytes (Klingmüller et al. 2006) were seeded at a density of $4\times 10^4$ cells per well in collagen-coated 2-well Lab-Tek Chamber Slides. On the following day, cells were transiently transfected with GFP-SMAD2 expression plasmid with Lipofectamine 2000 reagent according to manufacturers protocol. After 16 hours of incubation, cells were stained for 15 min in 1:10,000 Hoechst 34580. Unbound dyes were removed by washing cells 3 times with cultivation medium. For reconstruction, imaging was performed (see Fig. 15) under cell culture conditions on a Zeiss 710 confocal microscope equipped with incubation chamber. Using a 63$\times$/1.40 Oil objective, Z-stack method in a 2-channel acquisition mode was applied: Hoechst-nucleus (excitation at 405 nm, and detection at 435–475 nm) and GFP-cytoplasm (excitation at 488 nm, and detection at 495–550 nm). The resulted voxel dimension is $x:y:z = 0.264\times 0.264\times 0.364~\mu$m$^3$.

Fig. 15

Left Hepatocyte expressing GFP-SMAD2 protein (green) and DNA is stained with Hoechst dye (blue). Right 3D shape of reconstructed image (color figure online)