Fitness Gain of Individually Sensed Information by Cells

Mutual information and its causal variant, directed information, have been widely used to quantitatively characterize the performance of biological sensing and information transduction. However, once coupled with selection in response to decision-making, the sensing signal could have more or less evolutionary value than its mutual or directed information. In this work, we show that an individually sensed signal always has a better fitness value, on average, than its mutual or directed information. The fitness gain, which satisfies fluctuation relations (FRs), is attributed to the selection of organisms in a population that obtain a better sensing signal by chance. A new quantity, similar to the coarse-grained entropy production in information thermodynamics, is introduced to quantify the total fitness gain from individual sensing, which also satisfies FRs. Using this quantity, the optimizing fitness gain of individual sensing is shown to be related to fidelity allocations for individual environmental histories. Our results are supplemented by numerical verifications of FRs, and a discussion on how this problem is linked to information encoding and decoding.

[1]  Ying Liu,et al.  The relationship between transfer entropy and directed information , 2012, 2012 IEEE Statistical Signal Processing Workshop (SSP).

[2]  R. Cheong,et al.  How Information Theory Handles Cell Signaling and Uncertainty , 2012, Science.

[3]  Shinya Kuroda,et al.  Robustness and Compensation of Information Transmission of Signaling Pathways , 2013, Science.

[4]  Carl T. Bergstrom,et al.  The fitness value of information , 2005, Oikos.

[5]  S. Leibler,et al.  A model for the generation and transmission of variations in evolution , 2013, Proceedings of the National Academy of Sciences.

[6]  S. Leibler,et al.  Individual histories and selection in heterogeneous populations , 2010, Proceedings of the National Academy of Sciences.

[7]  Yuki Sughiyama,et al.  Stochastic and information-thermodynamic structures of population dynamics in a fluctuating environment. , 2017, Physical review. E.

[8]  G. Iyengar,et al.  A lower bound on the free energy cost of molecular measurements , 2016 .

[9]  S. Leibler,et al.  Phenotypic Diversity, Population Growth, and Information in Fluctuating Environments , 2005, Science.

[10]  沙川 貴大,et al.  Thermodynamics of information processing in small systems , 2011 .

[11]  Yuki Sughiyama,et al.  Fluctuation Relations of Fitness and Information in Population Dynamics. , 2015, Physical review letters.

[12]  Y. Iwasa,et al.  Optimal Mixed Strategies in Stochastic Environments , 1995 .

[13]  Gerhard Kramer,et al.  Directed information for channels with feedback , 1998 .

[14]  W. Bialek,et al.  Information flow and optimization in transcriptional regulation , 2007, Proceedings of the National Academy of Sciences.

[15]  Tetsuya J Kobayashi,et al.  Theoretical aspects of cellular decision-making and information-processing. , 2012, Advances in experimental medicine and biology.

[16]  Tsvi Tlusty,et al.  Asymptotic Cellular Growth Rate as the Effective Information Utilization Rate , 2013 .

[17]  I. Nemenman,et al.  Information Transduction Capacity of Noisy Biochemical Signaling Networks , 2011, Science.

[18]  Andre C. Barato,et al.  Nonequilibrium sensing and its analogy to kinetic proofreading , 2015, 1502.02594.

[19]  Surya Ganguli,et al.  A universal tradeoff between power, precision and speed in physical communication , 2016, ArXiv.

[20]  Pierre Baldi,et al.  Autoencoders, Unsupervised Learning, and Deep Architectures , 2011, ICML Unsupervised and Transfer Learning.

[21]  Olivier Rivoire,et al.  Informations in Models of Evolutionary Dynamics , 2015, 1504.07761.

[22]  Clive G. Bowsher,et al.  Identifying sources of variation and the flow of information in biochemical networks , 2012, Proceedings of the National Academy of Sciences.

[23]  D. Stephens.  Variance and the Value of Information , 1989, The American Naturalist.

[24]  Thierry Mora,et al.  Transitions in optimal adaptive strategies for populations in fluctuating environments. , 2017, Physical review. E.

[25]  P. Swain,et al.  Strategies for cellular decision-making , 2009, Molecular systems biology.

[26]  Masahito Ueda,et al.  Nonequilibrium thermodynamics of feedback control. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Carl T. Bergstrom,et al.  Shannon information and biological fitness , 2004, Information Theory Workshop.

[28]  Marco Del Giudice,et al.  Thermodynamic limits to information harvesting by sensory systems , 2014, 1408.5128.

[29]  Thomas E. Ouldridge,et al.  The importance of thermodynamics for molecular systems, and the importance of molecular systems for thermodynamics , 2017, Natural Computing.

[30]  Haim H. Permuter,et al.  Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing , 2009, IEEE Transactions on Information Theory.

[31]  Tetsuya J Kobayashi,et al.  Implementation of dynamic Bayesian decision making by intracellular kinetics. , 2010, Physical review letters.

[32]  Pieter Rein Ten Wolde,et al.  Optimal resource allocation in cellular sensing systems , 2014, Proceedings of the National Academy of Sciences.

[33]  Clive G. Bowsher,et al.  Environmental sensing, information transfer, and cellular decision-making. , 2014, Current opinion in biotechnology.

[34]  Kazuyuki Aihara,et al.  Pathwise thermodynamic structure in population dynamics. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Stanislas Leibler,et al.  The Value of Information for Populations in Varying Environments , 2010, ArXiv.

[36]  F. Tostevin,et al.  Mutual information between input and output trajectories of biochemical networks. , 2009, Physical review letters.