Multisite protein phosphorylation and dephosphorylation are key cellular regulatory mechanisms but their system properties have been difficult to study in vivo and in vitro. Here we show by mathematical analysis that steady-state invariants enable the mechanism of the kinase or the phosphatase to be determined from steady-state measurements. Invariants exist when both enzymes act distributively (i.e., nonprocessively), making at most one modification in each molecular encounter. For instance, in the sequential case, in any experiment involving the same ingredients, the quantity [Si−1][Si+1]/[Si]2 always has the same value, where [Si] denotes the steady-state concentration of the i-th phospho-form. For a two-site substrate, if either enzyme exhibits processivity, so that more than one modification can be made in each molecular encounter, the degree of processivity can be estimated from changes in this invariant. We discuss the experimental and theoretical challenges in extending these results.
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