  Push-pull 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 push-pull 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 push-pull
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.
