Limits...
Thermodynamic costs of information processing in sensory adaptation.

Sartori P, Granger L, Lee CF, Horowitz JM - PLoS Comput. Biol. (2014)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Max Planck Institute for the Physics of Complex Systems, Dresden, Germany.

ABSTRACT
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.

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Thermodynamics of adaptation in an equilibrium SAS.(A) Energetic cost as a function of time given by the work  provided by the environment (red), free energy change of the system  (orange), and dissipated work  (black), compared to the measured information  (grey dashed), which gives the lower bound at every time. (B) Total entropic cost  (black) and decomposition in measurement  (gray) and erasure  (yellow). Parameters as in Fig. 3.
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pcbi-1003974-g004: Thermodynamics of adaptation in an equilibrium SAS.(A) Energetic cost as a function of time given by the work provided by the environment (red), free energy change of the system (orange), and dissipated work (black), compared to the measured information (grey dashed), which gives the lower bound at every time. (B) Total entropic cost (black) and decomposition in measurement (gray) and erasure (yellow). Parameters as in Fig. 3.

Mentions: Using again our equilibrium feedforward model as an example, we apply our formalism to investigate the costs of sensory adaptation. Since this model sustains its steady state at no energy cost, the ultimate limit lies in the sensing process itself. We see this immediately in Fig. 4 where we verify the inequalities in (4) and (7). Since in (1) is explicitly a function of the environmental signal , the sudden change in at does work on the system, which is captured in Fig. 4A by the initial jump in . This work is instantaneously converted into free energy and is then consumed as the system responds and adapts in order to measure. Thus, in this example the work to sense is supplied by the signal (the environment) itself and not the SAS, which is consistent with other equilibrium models of SAS [23]. Furthermore, Fig. 4B confirms that the erasure of information leads to an irreversible process with net entropy production. The bounds of (4) and (7) are not tightly met in our model, since we are sensing a sudden change in the signal that necessitates a dissipative response. Nonetheless, the total entropy production and energetic cost are on the order of the information erased and acquired. This indicates that these information theoretic bounds can be a limiting factor for the operation of adaptive systems. We now show that this is the case for E. coli chemotaxis, a fundamentally different system as it operates far from equilibrium.


Thermodynamic costs of information processing in sensory adaptation.

Sartori P, Granger L, Lee CF, Horowitz JM - PLoS Comput. Biol. (2014)

Thermodynamics of adaptation in an equilibrium SAS.(A) Energetic cost as a function of time given by the work  provided by the environment (red), free energy change of the system  (orange), and dissipated work  (black), compared to the measured information  (grey dashed), which gives the lower bound at every time. (B) Total entropic cost  (black) and decomposition in measurement  (gray) and erasure  (yellow). Parameters as in Fig. 3.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4263364&req=5

pcbi-1003974-g004: Thermodynamics of adaptation in an equilibrium SAS.(A) Energetic cost as a function of time given by the work provided by the environment (red), free energy change of the system (orange), and dissipated work (black), compared to the measured information (grey dashed), which gives the lower bound at every time. (B) Total entropic cost (black) and decomposition in measurement (gray) and erasure (yellow). Parameters as in Fig. 3.
Mentions: Using again our equilibrium feedforward model as an example, we apply our formalism to investigate the costs of sensory adaptation. Since this model sustains its steady state at no energy cost, the ultimate limit lies in the sensing process itself. We see this immediately in Fig. 4 where we verify the inequalities in (4) and (7). Since in (1) is explicitly a function of the environmental signal , the sudden change in at does work on the system, which is captured in Fig. 4A by the initial jump in . This work is instantaneously converted into free energy and is then consumed as the system responds and adapts in order to measure. Thus, in this example the work to sense is supplied by the signal (the environment) itself and not the SAS, which is consistent with other equilibrium models of SAS [23]. Furthermore, Fig. 4B confirms that the erasure of information leads to an irreversible process with net entropy production. The bounds of (4) and (7) are not tightly met in our model, since we are sensing a sudden change in the signal that necessitates a dissipative response. Nonetheless, the total entropy production and energetic cost are on the order of the information erased and acquired. This indicates that these information theoretic bounds can be a limiting factor for the operation of adaptive systems. We now show that this is the case for E. coli chemotaxis, a fundamentally different system as it operates far from equilibrium.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Max Planck Institute for the Physics of Complex Systems, Dresden, Germany.

ABSTRACT
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.

Show MeSH