Source-linked AI summary
Maxwell's demon in biochemical signal transduction with feedback loop
Sosuke Ito, Takahiro Sagawa
TL;DR
The paper derives an information-based bound on entropy production for a subsystem using stochastic mutual-information quantities. It shows that the bound can become tight when information-thermodynamic dissipation vanishes under specified limiting conditions.
Problem
The paper examines how informational quantities bound entropy production in a feedback-linked stochastic system.
Method
The authors define stochastic mutual and conditional mutual information and use a Bayesian-network-based quantity Θ to bound the subsystem’s entropy production.
Results
The bound becomes tight when information-thermodynamic dissipation is zero, including the limit α → 0 and τ_a/τ_m → 0.
Takeaways & Limitations
The analysis identifies limiting conditions under which the information-thermodynamic entropy-production bound is achieved.
Takeaways & Limitations
The derivation assumes independent noise, expressed through factorization of the transition probability.
Abstract
from arXiv · showhide
Signal transduction in living cells is vital to maintain life itself, where information transfer in noisy environment plays a significant role. In a rather different context, the recent intensive researches of "Maxwell's demon" - a feedback controller that utilizes information of individual molecules - has led to a unified theory of information and thermodynamics. Here we combine these two streams of researches, and show that the second law of thermodynamics with information reveals the fundamental limit of the robustness of signal transduction against environmental fluctuations. Especially, we found that the degree of robustness is quantitatively characterized by an informational quantity called transfer entropy. Our information-thermodynamic approach is applicable to biological communication inside cells, in which there is no explicit channel coding in contrast to artificial communication. Our result would open up a novel biophysical approach to understand information processing in living systems on the basis of the fundamental information-thermodynamics link.
SUPPLEMENTARY INFORMATION
The supplementary information derives information-thermodynamic bounds for the coupled Langevin model, defines transfer entropy and related information quantities, and connects them to subsystem entropy production. It also identifies conditions under which the robustness bound becomes tight.
- Tight-bound limit: Equality in the robustness inequality is achieved in the limits α →0 and τ_a/τ_m →0, where information flow vanishes and a relaxes infinitely fast.These limits correspond to a nonworking feedback loop and infinitely rapid relaxation of subsystem a.
- Derivation of the information-thermodynamic inequality: The coupled Langevin model uses heat dissipation, conditional Shannon entropy, and transfer entropy to formulate an information-thermodynamic inequality for subsystem a.The derivation uses path probabilities, detailed fluctuation relations, and non-negativity of the Kullback–Leibler divergence.
- Transfer entropy: Transfer entropy is the directed information flow from a to m, defined through the conditional dependence of m_{t+dt} on a_t and m_t.The supplementary derivation expresses it as a conditional mutual-information quantity over an infinitesimal time interval.
- Bayesian-network formulation: A Bayesian-network representation of the Markov step gives an entropy-production bound involving mutual information, transfer entropy, and conditional mutual information.The stronger bound includes the conditional mutual-information term dI^B_tr, whereas the main text uses a weaker inequality focused on dI_tr.
- Comparison of bounds: The information-thermodynamic bound is tighter when the conditional mutual-information contribution is retained than when it is omitted.The main text focuses on transfer entropy for simplicity, using the weaker inequality.
Supplementary note 4 | Analytical calculation of the transfer entropy for the coupled linear Langevin system
This supplementary note analytically calculates transfer entropy for a coupled linear Langevin system under a Gaussian-distribution assumption. It then compares the resulting information-thermodynamic and conventional thermodynamic bounds for the E. coli chemotaxis model.
- Analytical transfer entropy: The note derives an analytical expression for transfer entropy in the coupled linear Langevin system.The derivation uses Gaussian conditional and joint path probabilities together with covariance and drift-matrix quantities.
- Analytical transfer entropy: The calculation assumes that the joint probability distribution of the coupled variables is Gaussian.The Gaussian assumption supports the covariance-based evaluation of the transfer entropy.
- Correlation structure: The correlation coefficient ρ_am between a_t and m_t is bounded by 1 and enters the covariance-based expression for the transfer entropy.For a Gaussian joint distribution, the factor 1 −(ρ_am)^2 can be rewritten using mutual information.
- Correlation structure: Strong correlation between the target and other systems makes the mutual-information contribution approach zero.The supplementary text states this implication when the mutual information I_am tends to zero.
- Bound comparison: The derived transfer entropy is used to compare the conventional thermodynamic bound with the information-thermodynamic bound in the stationary E. coli chemotaxis model.In the stationary state, the Shannon and conditional Shannon entropy changes vanish, allowing both bounds to be expressed through their respective heat or information-flow terms.
Figure of Merit
The supplementary figure-of-merit analysis evaluates information thermodynamics for several input-signal shapes and relates the Bayesian-network construction to the joint probability used in the formalism.
- Step function: The step-function figure uses the same parameters as main-text Fig. 2a.It is labeled as a figure of merit of information thermodynamics.
- Sinusoidal function: The sinusoidal-function figure uses the same parameters as main-text Fig. 2b.It is labeled as a figure of merit of information thermodynamics.
- Linear function: The linear-function figure uses the same parameters as main-text Fig. 2c.It is labeled as a figure of merit of information thermodynamics.
- Exponential decay: The exponential-decay figure uses the same parameters as main-text Fig. 2d.It is labeled as a figure of merit of information thermodynamics.
- Additional signal forms and Bayesian network: The square-wave and triangle-wave figures use the same parameters as main-text Figs. 2e and 2f, respectively.A separate Bayesian-network figure represents the joint probability associated with Eq. (2), with nodes as random variables and edges as causal relationships.