  Escherichia coli bacteria respond to DNA damage by a highly orchestrated
series of events known as the SOS response, regulated by transcription factors,
protein-protein binding and active protein degradation. We present a dynamical
model of the UV-induced SOS response, incorporating mutagenesis by the
error-prone polymerase, Pol V. In our model, mutagenesis depends on a
combination of two key processes: damage counting by the replication forks and
a long term memory associated with the accumulation of UmuD'. Together, these
provide a tight regulation of mutagenesis resulting, we show, in a "digital"
turn-on and turn-off of Pol V. Our model provides a compact view of the
topology and design of the SOS network, pinpointing the specific functional
role of each of the regulatory processes. In particular, we suggest that the
recently observed second peak in the activity of promoters in the SOS regulon
(Friedman et al., 2005, PLoS Biol. 3, e238) is the result of a positive
feedback from Pol V to RecA filaments.
