## Control of Signal Transduction Cycles: General Results and Application to the Jak-Stat Pathway

Stephan Beirer (s.beirer@biologie.hu-berlin.de)

Thomas Höfer (thomas.hoefer@biologie.hu-berlin.de)

Theoretical Biophysics Department, Humboldt Universität Berlin, Invalidenstrasse 42, 10115 Berlin, Germany

### Abstract

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.

*Japanese Society for Bioinformatics*