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Sensory adaptation enables organisms to adjust their perception in a changingenvironment. A paradigm is bacterial chemotaxis, where the output activity ofchemoreceptors is adapted to different baseline concentrations via receptormethylation. The range of internal receptor states limits the stimulusmagnitude to which these systems can adapt. Here, we employ a highly idealized,Langevin-equation based model to study how the finite range of state variablesaffects the adaptation accuracy and the energy dissipation in individual andcoupled systems. Maintaining an adaptive state requires constant energydissipation. We show that the steady-state dissipation rate increasesapproximately linearly with the adaptation accuracy for varying stimulusmagnitudes in the so-called perfect adaptation limit. This result complementsthe well-known logarithmic cost-accuracy relationship for varying chemicaldriving. Next, we study linearly coupled pairs of sensory units. We find thatthe interaction reduces the dissipation rate per unit and affects the overallcost-accuracy relationship. A coupling of the slow methylation variablesresults in a better accuracy than a coupling of activities. Overall, thefindings highlight the significance of both the working range and collectiveoperation mode as crucial design factors that impact the accuracy and energyexpenditure of molecular adaptation networks.

Sensory adaptation in a continuum model of bacterial chemotaxis -- working range, cost-accuracy relation, and coupled systems