The Channel Capacity of Channelrhodopsin and Other Intensity-Driven Signal Transduction Receptors

Biological systems transduce signals from their surroundings through a myriad of pathways. In this paper, we describe signal transduction as a communication system: the signal transduction receptor acts as the receiver in this system, and can be modeled as a finite-state Markov chain with transition rates governed by the input signal. Using this general model, we give the mutual information under independent, identically distributed (IID) inputs in discrete time, and obtain the mutual information in the continuous-time limit. We show that the mutual information has a concise closed-form expression with clear physical significance. We also give a sufficient condition under which the Shannon capacity is achieved with IID inputs. We illustrate our results with three examples: 1) the light-gated Channelrhodopsin-2 (ChR2) receptor; 2) the ligand-gated nicotinic acetylcholine receptor; and 3) the ligand-gated calmodulin receptor. In particular, we show that the IID capacity of the ChR2 receptor is equal to its Shannon capacity. We finally discuss how the results change if only certain properties of each state can be observed, such as whether an ion channel is open or closed.

[1]  E. Bamberg,et al.  Channelrhodopsin-2, a directly light-gated cation-selective membrane channel , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Gabriel J. Lord,et al.  Stochastic Methods in Neuroscience , 2009 .

[3]  Sergio Verdú,et al.  On channel capacity per unit cost , 1990, IEEE Trans. Inf. Theory.

[4]  Michael Gastpar,et al.  To code, or not to code: lossy source-channel communication revisited , 2003, IEEE Trans. Inf. Theory.

[5]  C. W. Gardiner,et al.  Handbook of stochastic methods - for physics, chemistry and the natural sciences, Second Edition , 1986, Springer series in synergetics.

[6]  A. Means,et al.  Calmodulin: a prototypical calcium sensor. , 2000, Trends in cell biology.

[7]  Toby Berger,et al.  The capacity of finite-State Markov Channels With feedback , 2005, IEEE Transactions on Information Theory.

[8]  Andrew W. Eckford,et al.  Thermodynamic Properties of Molecular Communication , 2018, 2018 IEEE International Symposium on Information Theory (ISIT).

[9]  William Bialek,et al.  Information processing in living systems , 2014, 1412.8752.

[10]  Haim H. Permuter,et al.  Capacity of a POST Channel With and Without Feedback , 2014, IEEE Transactions on Information Theory.

[11]  Mohsen Sardari,et al.  Capacity of diffusion-based molecular communication with ligand receptors , 2011, 2011 IEEE Information Theory Workshop.

[12]  John L. Kelly,et al.  A new interpretation of information rate , 1956, IRE Trans. Inf. Theory.

[13]  T. Sejnowski,et al.  Calmodulin Activation by Calcium Transients in the Postsynaptic Density of Dendritic Spines , 2008, PloS one.

[14]  Andrew W. Eckford,et al.  Capacity of a simple intercellular signal transduction channel , 2013, 2013 IEEE International Symposium on Information Theory.

[15]  Massimiliano Pierobon,et al.  Noise Analysis in Ligand-Binding Reception for Molecular Communication in Nanonetworks , 2011, IEEE Transactions on Signal Processing.

[16]  Michael Z. Lin,et al.  Characterization of engineered channelrhodopsin variants with improved properties and kinetics. , 2009, Biophysical journal.

[17]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[18]  D. T. Yue,et al.  Calmodulin bifurcates the local Ca2+ signal that modulates P/Q-type Ca2+ channels , 2001, Nature.

[19]  Andrew W. Eckford,et al.  Shannon capacity of signal transduction for multiple independent receptors , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[20]  Maryam Farahnak-Ghazani,et al.  On the Capacity of Point-to-Point and Multiple-Access Molecular Communications With Ligand-Receptors , 2015, IEEE Transactions on Molecular, Biological and Multi-Scale Communications.

[21]  Michael Hucka,et al.  A Correction to the Review Titled "Rules for Modeling Signal-Transduction Systems" by W. S. Hlavacek et al. , 2006, Science's STKE.

[22]  S. Swain.  Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences , 1984 .

[23]  Christos K. Kourtellaris,et al.  Sequential Necessary and Sufficient Conditions for optimal channel input distributions of channels with memory and feedback , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[24]  A. Hawkes,et al.  On the stochastic properties of bursts of single ion channel openings and of clusters of bursts. , 1982, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[25]  Michael B. Yaffe,et al.  Data-driven modelling of signal-transduction networks , 2006, Nature Reviews Molecular Cell Biology.

[26]  Y. Kabanov.  The Capacity of a Channel of the Poisson Type , 1978 .

[27]  John E. Lisman,et al.  Calmodulin as a Direct Detector of Ca2+ Signals , 2011, Nature Neuroscience.

[28]  A. Destexhe,et al.  Stochastic Methods in Neuroscience , 2012 .

[29]  Hilary DeRemigio,et al.  Markov Chain Models of Ion Channels and Calcium Release Sites , 2009 .