Diffusion control of protein phosphorylation in signal transduction pathways

Multiple signalling proteins are phosphorylated and dephosphorylated at separate cellular locations, which potentially causes spatial gradients of phospho-proteins within the cell. We have derived relationships that enable us to estimate the extent to which a protein kinase, a phosphatase and the diffusion of signalling proteins control the protein phosphorylation flux and the phospho-protein gradient. Two different cellular geometries were analysed: (1) the kinase is located on one planar membrane and the phosphatase on a second parallel planar membrane, and (2) the kinase is located on the plasma membrane of a spherical cell and the phosphatase is distributed homogeneously in the cytoplasm. We demonstrate that the control contribution of protein diffusion is potentially significant, given the measured rates for protein kinases, phosphatases and diffusion. If the distance between the membranes is 1 mu m or greater, the control by diffusion can reach 33 % or more, with the rest of the control (67 %) shared by the kinase and the phosphatase. At distances of less than 0.1 mu m, diffusion does not limit protein phosphorylation. For a spherical cell of radius 10 mu m, a protein diffusion coefficient of 10(-8) cm(2 .) s(-1) and rate constants for the kinase and the phosphatase of approx. 1 s(-1), control over the phosphorylation flux resides mainly with the phosphatase and protein diffusion, with approximately equal contributions of each of these. The ratio of phospho-protein concentrations at the cell membrane and the cell centre (the dynamic compartmentation of the phospho-protein) is shown to be controlled by the rates of the protein phosphatase and of diffusion. The kinase can contribute significantly to the control of the absolute value of the phosphoprotein gradient.