Pushpull networks are ubiquitous in signal transduction pathways in both prokaryotic and eukaryotic cells. They allow cells
to strongly amplify signals via the mechanism of zero-order ultrasensitivity. In a pushpull network, two antagonistic enzymes control the activity of a protein by covalent modification. These enzymes are often uniformly distributed in the cytoplasm. They can, however, also be colocalized in space; for instance, near the pole of the cell. Moreover, it is increasingly recognized that these enzymes can also be spatially separated, leading to gradients of the active form of the messenger protein. Here, we investigate the consequences of the spatial distributions of the enzymes for the
amplification properties of pushpull networks. Our calculations reveal that enzyme
localization by itself can have a dramatic effect on the gain. The gain is maximized when the two enzymes are either uniformly distributed or colocalized in one region in the cell. Depending on the diffusion constants, however, the sharpness of the response can be strongly reduced when the enzymes are spatially separated. We discuss how our predictions could be tested experimentally.