Background: In order for signals generated at the plasma membrane to reach intracellular targets, activated messengers, such as G proteins and phosphoproteins, must diffuse through the cytoplasm. If the deactivators of these messengers, GTPase activating proteins (GAPs) and phosphatases, respectively, are sufficiently active in the cytoplasm, then the signal could in principle decay before reaching the target and a stable spatial gradient in phosphostate would be generated. Recent experiments document the existence of such gradients in living cells and suggest a role for them in mitotic spindle morphogenesis and cell migration. However, how such systems behave theoretically when embedded in a cell of varying size or shape has not been considered. Results: Here we use a simple mathematical model to explore the theoretical consequences of a plasma membrane bound activator (i.e., guanine nucleotide exchange factor, GEF, or kinase) and a cytoplasmic deactivator (i.e., GAP or phosphatase), and we find that as a model cell grows, the substrate becomes progressively dephosphorylated as a result of decreased proximity to the activator. Conversely, as a cell spreads and flattens, the substrate becomes globally phosphorylated because of increased proximity of the substrate to the activator. Similarly, in the leading edge of polarized cells and in protrusions such as lamellipodia or filopodia, the substrate is highly phosphorylated. As a specific test of the model, we found that the experimentally observed preferential activation of the G protein Cdc42 in the periphery of fibroblasts that was recently reported is consistent with model predictions. Conclusions: We conclude that cell-signaling pathways can theoretically be turned on and off, both locally and globally, in response to alterations in cell size and shape.
Bibliographical noteFunding Information:
The authors thank L. Hodgson and K. Hahn for providing their original MeroCBD fibroblast data, B. Earnshaw and J. Howard for helpful comments, V. Barocas for technical assistance with the finite element modeling and helpful discussions, and the Minnesota Supercomputing Institute for providing computing resources. This article is dedicated to the memory of Raymond A. Odde, P.E. The work was supported partially by a grant from the National Science Foundation (BES-0119481) and from the National Institutes of Health (GM-71522).