Spatial gradients in kinase cascade regulation.

The spatiotemporal kinetics of proteins and other substrates regulate cell fate and signaling. In this study, we consider a reaction-diffusion model of interaction of membrane receptors with a two-step kinase cascade. The receptors activate the 'up-stream' kinase, which may diffuse over cell volume and activate the 'down-stream' kinase, which is also diffusing. Both kinase species and receptors are inactivated by uniformly distributed phosphatases. The positive feedback, key to the considered dynamics, arises since the up-stream kinase activates the receptors. Such a mutual interaction is characteristic for immune cell receptors. Based on the proposed model, we demonstrated that cell sensitivity (measured as a critical value of phosphatase activity at which cell maybe activated) increases with decreasing motility of receptor-interacting kinases and with increasing polarity of receptors distribution. These two effects are cooperating, the effect of receptors localisation close to one pole of the cell grows with the decreasing kinase diffusion and vanishes in the infinite diffusion limit. As the cell sensitivity increases with decreasing diffusion of receptor-interacting kinase, the overall activity of the down-stream kinase increases with its diffusion. In conclusion, the analysis of the proposed model shows that, for the fixed substrate interaction rates, spatial distribution of the surface receptors together with the motility of intracellular kinases control cell signalling and sensitivity to extracellular signals. The increase of the cell sensitivity can be achieved by (i) localisation of receptors in a small subdomain of the cell membrane, (ii) lowering the motility of receptor-interacting kinase, (iii) increasing the motility of down-stream kinases which distribute the signal over the whole cell.