Biological sensory systems react to changes in their surroundings. They are characterized by fast response and slow adaptation to varying environmental cues. Insofar as sensory adaptive systems map environmental changes to changes of their internal degrees of freedom, they can be regarded as computational devices manipulating information. Landauer established that information is ultimately physical, and its manipulation subject to the entropic and energetic bounds of thermodynamics. Thus the fundamental costs of biological sensory adaptation can be elucidated by tracking how the information the system has about its environment is altered. These bounds are particularly relevant for small organisms, which unlike everyday computers, operate at very low energies. In this paper, we establish a general framework for the thermodynamics of information processing in sensing. With it, we quantify how during sensory adaptation information about the past is erased, while information about the present is gathered. This process produces entropy larger than the amount of old information erased and has an energetic cost bounded by the amount of new information written to memory. We apply these principles to the E. coli's chemotaxis pathway during binary ligand concentration changes. In this regime, we quantify the amount of information stored by each methyl group and show that receptors consume energy in the range of the information-theoretic minimum. Our work provides a basis for further inquiries into more complex phenomena, such as gradient sensing and frequency response.
The ability to process information is a ubiquitous feature of living organisms. Indeed, in order to survive, every living being, from the smallest bacterium to the biggest mammal, has to gather and process information about its surrounding environment. In the same way as our everyday computers need power to function, biological sensors need energy in order to gather and process this sensory information. How much energy do living organisms have to spend in order to get information about their environment? In this paper, we show that the minimum energy required for a biological sensor to detect a change in some environmental signal is proportional to the amount of information processed during that event. In order to know how far a real biological sensor operates from this minimum, we apply our predictions to chemo-sensing in the bacterium Escherichia Coli and find that the theoretical minimum corresponds to a sizable portion of the energy spent by the bacterium.