  Sensory adaptation enables organisms to adjust their perception in a changing
environment. A paradigm is bacterial chemotaxis, where the output activity of
chemoreceptors is adapted to different baseline concentrations via receptor
methylation. The range of internal receptor states limits the stimulus
magnitude to which these systems can adapt. Here, we employ a highly idealized,
Langevin-equation based model to study how the finite range of state variables
affects the adaptation accuracy and the energy dissipation in individual and
coupled systems. Maintaining an adaptive state requires constant energy
dissipation. We show that the steady-state dissipation rate increases
approximately linearly with the adaptation accuracy for varying stimulus
magnitudes in the so-called perfect adaptation limit. This result complements
the well-known logarithmic cost-accuracy relationship for varying chemical
driving. Next, we study linearly coupled pairs of sensory units. We find that
the interaction reduces the dissipation rate per unit and affects the overall
cost-accuracy relationship. A coupling of the slow methylation variables
results in a better accuracy than a coupling of activities. Overall, the
findings highlight the significance of both the working range and collective
operation mode as crucial design factors that impact the accuracy and energy
expenditure of molecular adaptation networks.
