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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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Energetic costs of adaptation in an E. coli chemotaxis SAS.(A) Network representation of the nonequilibrium receptor model with five methylation and two activity states. Green arrows represent the addition/removal of methyl groups driven by the chemical fuel SAM. (B) Corresponding negative feedback topology, displaying the dissipative energy cycle (green arrow) sustained by adiabatic entropy production, due to the consumption of chemical fuel. (C) Energetics of nonequilibrium measurement in the chemotaxis pathway for a ligand concentration change of  (other parameters in Materials and Methods). The instantaneous change in ligand concentration performs chemical work on the cell, which increases its free energy  as the cell responds. To adapt, the bacterium has to provide excess work  from its own chemical reservoir, the fuel SAM.
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pcbi-1003974-g005: Energetic costs of adaptation in an E. coli chemotaxis SAS.(A) Network representation of the nonequilibrium receptor model with five methylation and two activity states. Green arrows represent the addition/removal of methyl groups driven by the chemical fuel SAM. (B) Corresponding negative feedback topology, displaying the dissipative energy cycle (green arrow) sustained by adiabatic entropy production, due to the consumption of chemical fuel. (C) Energetics of nonequilibrium measurement in the chemotaxis pathway for a ligand concentration change of (other parameters in Materials and Methods). The instantaneous change in ligand concentration performs chemical work on the cell, which increases its free energy as the cell responds. To adapt, the bacterium has to provide excess work from its own chemical reservoir, the fuel SAM.

Mentions: E. coli is a bacterium that can detect changes in the concentration of nearby ligands in order to perform chemotaxis: the act of swimming up a ligand attractor gradient. It is arguably the best studied example of a SAS. At a constant ligand concentration , chemoreceptors in E. coli – such as the one in Fig. 1C – have a fixed average activity, which through a phosphorylation cascade translates into a fixed switching rate of the bacterial flagellar motor. When changes, the activity of the receptor (which is a binary variable labeling two different receptor conformations) increases on a time-scale . On a longer time-scale , the methylesterase CheR and methyltransferase CheB alter the methylation level of the receptor in order to recover the adapted activity value. In this way, the methylation level (which ranges from none to four methyl groups for a single receptor) is a representation of the environment, acting as the long-term memory (see diagram in Fig. 5A). One important difference with the previous equilibrium model is that the chemotaxis pathway operates via a feedback. The memory is not regulated by the receptor's signal, but rather by the receptor's activity (see motif in Fig. 5B). The implication is that energy must constantly be dissipated to sustain the steady state [19], thus (9) and (10) are the appropriate tools for a thermodynamic analysis.


Thermodynamic costs of information processing in sensory adaptation.

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

Energetic costs of adaptation in an E. coli chemotaxis SAS.(A) Network representation of the nonequilibrium receptor model with five methylation and two activity states. Green arrows represent the addition/removal of methyl groups driven by the chemical fuel SAM. (B) Corresponding negative feedback topology, displaying the dissipative energy cycle (green arrow) sustained by adiabatic entropy production, due to the consumption of chemical fuel. (C) Energetics of nonequilibrium measurement in the chemotaxis pathway for a ligand concentration change of  (other parameters in Materials and Methods). The instantaneous change in ligand concentration performs chemical work on the cell, which increases its free energy  as the cell responds. To adapt, the bacterium has to provide excess work  from its own chemical reservoir, the fuel SAM.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003974-g005: Energetic costs of adaptation in an E. coli chemotaxis SAS.(A) Network representation of the nonequilibrium receptor model with five methylation and two activity states. Green arrows represent the addition/removal of methyl groups driven by the chemical fuel SAM. (B) Corresponding negative feedback topology, displaying the dissipative energy cycle (green arrow) sustained by adiabatic entropy production, due to the consumption of chemical fuel. (C) Energetics of nonequilibrium measurement in the chemotaxis pathway for a ligand concentration change of (other parameters in Materials and Methods). The instantaneous change in ligand concentration performs chemical work on the cell, which increases its free energy as the cell responds. To adapt, the bacterium has to provide excess work from its own chemical reservoir, the fuel SAM.
Mentions: E. coli is a bacterium that can detect changes in the concentration of nearby ligands in order to perform chemotaxis: the act of swimming up a ligand attractor gradient. It is arguably the best studied example of a SAS. At a constant ligand concentration , chemoreceptors in E. coli – such as the one in Fig. 1C – have a fixed average activity, which through a phosphorylation cascade translates into a fixed switching rate of the bacterial flagellar motor. When changes, the activity of the receptor (which is a binary variable labeling two different receptor conformations) increases on a time-scale . On a longer time-scale , the methylesterase CheR and methyltransferase CheB alter the methylation level of the receptor in order to recover the adapted activity value. In this way, the methylation level (which ranges from none to four methyl groups for a single receptor) is a representation of the environment, acting as the long-term memory (see diagram in Fig. 5A). One important difference with the previous equilibrium model is that the chemotaxis pathway operates via a feedback. The memory is not regulated by the receptor's signal, but rather by the receptor's activity (see motif in Fig. 5B). The implication is that energy must constantly be dissipated to sustain the steady state [19], thus (9) and (10) are the appropriate tools for a thermodynamic analysis.

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