Quantitative understanding of cell signaling: the importance of membrane organization

Abstract

Systems biology modeling of signal transduction pathways traditionally employs ordinary differential equations, deterministic models based on the assumptions of spatial homogeneity. However, this can be a poor approximation for certain aspects of signal transduction, especially its initial steps: the cell membrane exhibits significant spatial organization, with diffusion rates approximately two orders of magnitude slower than those in the cytosol. Thus, to unravel the complexities of signaling pathways, quantitative models must consider spatial organization as an important feature of cell signaling. Furthermore, spatial separation limits the number of molecules that can physically interact, requiring stochastic simulation methods that account for individual molecules. Herein, we discuss the need for mathematical models and experiments that appreciate the importance of spatial organization in the membrane.

Figure 1

Classes of mathematical models for biochemical processes in cells and their applicability and assumptions. Well-mixed systems: The underlying biochemical processes with cells are stochastic transformations. However, a deterministic mathematical description may be applicable depending on the number of molecules N of each molecular species in the volume (or area) of interest. This number must be large (N≫1) for a deterministic approach to provide an accurate representation. Basically, the expected stochastic fluctuations of the molecule number (ΔN, the magnitude of intrinsic fluctuations is on the order of N^1/2) must be small relative to the absolute number for a deterministic description to be an acceptable assumption. Spatially heterogeneous systems: The well-mixed assumption implies that there is no significant spatial heterogeneity in the system. If this is not true but there are well-defined spatial regions that are homogeneous, then a compartment-based model may be used instead of a fully spatial model.

Figure 2

Electron micrograph of a membrane sheet as prepared by Wilson et al [75]. The figure shows colocalization of the formyl peptide receptor (FPR)(5 nm) and FcεRI (10 nm) within 1 min of simultaneous addition of their ligands.

Figure 3

Membrane organization of a subset of signaling proteins in the FcεRI (High-affinity IgE receptor) cascade, based on immunogold labeling experiments. This figure features new added complications that must be addressed by systems biology. Abbreviations used: PLCγ2 (Phospholipase C-γ2), PLCγ (Phospholipase C-γ), LAT (linker for activation of T cells), Syk (Spleen Tyrosine Kinase), Lyn (Yamaguchi sarcoma viral related oncogene homolog – a Src family tyrosine kinase), Gab2 (Grb2 associated binding protein 2), PI3K (Phosphoinositide 3-Kinase).