  Multisite covalent modification of proteins is omnipresent in eukaryotic
cells. A well-known example is the mitogen-activated protein kinase (MAPK)
cascade, where in each layer of the cascade a protein is phosphorylated at two
sites. It has long been known that the response of a MAPK pathway strongly
depends on whether the enzymes that modify the protein act processively or
distributively: distributive mechanism, in which the enzyme molecules have to
release the substrate molecules in between the modification of the two sites,
can generate an ultrasensitive response and lead to hysteresis and bistability.
We study by Green's Function Reaction Dynamics, a stochastic scheme that makes
it possible to simulate biochemical networks at the particle level and in time
and space, a dual phosphorylation cycle in which the enzymes act according to a
distributive mechanism. We find that the response of this network can differ
dramatically from that predicted by a mean-field analysis based on the chemical
rate equations. In particular, rapid rebindings of the enzyme molecules to the
substrate molecules after modification of the first site can markedly speed up
the response, and lead to loss of ultrasensitivity and bistability. In essence,
rapid enzyme-substrate rebindings can turn a distributive mechanism into a
processive mechanism. We argue that slow ADP release by the enzymes can protect
the system against these rapid rebindings, thus enabling ultrasensitivity and
bistability.
