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Thermodynamic Costs of Information Processing in Sensory Adaptation

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      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.

      Author Summary

      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.

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      Most cited references 21

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      Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
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            Author and article information

            [1 ]Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
            [2 ]Departamento de Física Atómica, Molecular y Nuclear and GISC, Universidad Complutense de Madrid, Madrid, Spain
            [3 ]Department of Bioengineering, Imperial College London, London, United Kingdom
            [4 ]Department of Physics, University of Massachusetts at Boston, Boston, Massachusetts, United States of America
            University of Michigan, United States of America
            Author notes

            The authors have declared that no competing interests exist.

            Conceived and designed the experiments: PS LG CFL JMH. Performed the experiments: PS LG CFL JMH. Analyzed the data: PS LG CFL JMH. Contributed reagents/materials/analysis tools: PS LG CFL JMH. Wrote the paper: PS LG CFL JMH.

            Role: Editor
            PLoS Comput Biol
            PLoS Comput. Biol
            PLoS Computational Biology
            Public Library of Science (San Francisco, USA )
            December 2014
            11 December 2014
            : 10
            : 12
            25503948 4263364 PCOMPBIOL-D-14-00608 10.1371/journal.pcbi.1003974

            This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

            Pages: 9
            This work was partially supported by a Max Planck society ( scholarship to PS and LG, by grant ENFASIS (Spanish government: to LG and JMH, and by Army Research Office ( MURI grant W911NF-11-1-0268 to JMH. The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.
            Research Article
            Biology and Life Sciences
            Biophysics Theory
            Physical Sciences
            Custom metadata
            The authors confirm that all data underlying the findings are fully available without restriction. All relevant data are within the paper and its Supporting Information files.

            Quantitative & Systems biology


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