  The reliable detection of environmental molecules in the presence of noise is
an important cellular function, yet the underlying computational mechanisms are
not well understood. We introduce a model of two interacting sensors which
allows for the principled exploration of signal statistics, cooperation
strategies and the role of energy consumption in optimal sensing, quantified
through the mutual information between the signal and the sensors. Here we
report that in general the optimal sensing strategy depends both on the noise
level and the statistics of the signals. For joint, correlated signals, energy
consuming (nonequilibrium), asymmetric couplings result in maximum information
gain in the low-noise, high-signal-correlation limit. Surprisingly we also find
that energy consumption is not always required for optimal sensing. We
generalise our model to incorporate time integration of the sensor state by a
population of readout molecules, and demonstrate that sensor interaction and
energy consumption remain important for optimal sensing.
