  Bacteria communicate using secreted chemical signaling molecules called
autoinducers in a process known as quorum sensing. The quorum-sensing network
of the marine bacterium {\it Vibrio harveyi} employs three autoinducers, each
known to encode distinct ecological information. Yet how cells integrate and
interpret the information contained within the three autoinducer signals
remains a mystery. Here, we develop a new framework for analyzing signal
integration based on Information Theory and use it to analyze quorum sensing in
{\it V. harveyi}. We quantify how much the cells can learn about individual
autoinducers and explain the experimentally observed input-output relation of
the {\it V. harveyi} quorum-sensing circuit. Our results suggest that the need
to limit interference between input signals places strong constraints on the
architecture of bacterial signal-integration networks, and that bacteria likely
have evolved active strategies for minimizing this interference. Here we
analyze two such strategies: manipulation of autoinducer production and
feedback on receptor number ratios.
