Control of signal transduction cycles: general results and application to the Jak-Stat pathway

Signal transduction involves the transitions of proteins between inactive and active states that can be achieved by reversible phosphorylation, nucleo-cytoplasmic transport, and other processes. We consider a network of such state transitions governed by first-order kinetics and analyse how the reactions control the occupancy of the network states. First, a theorem is derived that relates concentration control coefficients and occupancy of the network states. Second, it is shown that the absolute value of each control coefficient is bounded by unity, so that the network does not exhibit ultrasensitive responses. Third, the signs of certain control coefficients are derived from the network topology. These results are applied to a mathematical model of the Jak/Stat1 signaling. This pathway has been thought to function as a continuous cycle of cytoplasmic activation, nuclear import, inactivation and re-export of Stat1 transcription factors, but the recent discovery of an apparently futile nucleo-cytoplasmic cycle of inactive Stat1 has yielded a more complex picture. We demonstrate here two consequences of shuttling: (1) homeostasis of unphosphorylated Stat1 in the cell nucleus and (2) enhanced stimulus sensitivity of the pathway, and discuss their functional implications.