Analysis of parameter changes of a neuronal network model using transfer entropy

Abstract

Understanding the dynamics of coupled neurons is one of the fundamental problems in the analysis of neuronal model dynamics. The transfer entropy (TE) method is one of the primary analyses to explore the information flow between the neuronal populations. We perform the TE analysis on the two-neuron conductance-based Hodgkin-Huxley (HH) neuronal network to analyze how their connectivity changes due to conductances. We find that the information flow due to underlying synaptic connectivity changes direction by changing conductances individually and/or simultaneously as a result of TE analysis through numerical simulations.

Keywords

• Hodgkin-Huxley Network
• Parameter Analysis
• Transfer Entropy

References

1. 1. Pournaki, A., Merfort, L., Ruiz, J., Kouvaris, N. E., Hövel, P., & Hizanidis, J., Synchronization patterns in modular neuronal networks: A case study of C. elegans. Frontiers in Applied Mathematics and Statistics, 2019.
2. 2. Zhou, Y., Qiu, L., Wang, H., & Chen, X., Induction of activity synchronization among primed hippocampal neurons out of random dynamics is key for trace memory formation and retrieval. The FASEB Journal, 2019. 34(3): p. 3658-3676.
3. 3. Nikitin, D., Omelchenko, I., Zakharova, A., Avetyan, M., Fradkov, A. L., & Schöll, E., Complex partial synchronization patterns in networks of delay-coupled neurons. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2019. 377(2153) 20180128, p. 1-19.
4. 4. Gray, C. M., König, P., Engel, A. K., & Singer, W., Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature, 1989. 338(6213): p. 334-337.
5. 5. Leiberg, S., Lutzenberger, W., & Kaiser, J.,. Effects of memory load on cortical oscillatory activity during auditory pattern working memory. Brain Research, 2006. 1120(1): p. 131-140.
6. 6. Fernando, C., & Sojakka, S., Pattern recognition in a bucket. Advances in Artificial Life, ECAL 2003. p. 588-597.
7. 7. Timofeev, I., Bazhenov, M., Seigneur, J., & Sejnowski, T., Neuronal synchronization and Thalamocortical rhythms during sleep, wake, and epilepsy. Jasper's Basic Mechanisms of the Epilepsies, 2012 p. 157-175.
8. 8. Timme, N. M., & Lapish, C., A tutorial for information theory in neuroscience. Eneuro. ENEURO, 2018. 5(3), https://doi.org/10.1523/eneuro.0052-18. 2018.

9. 9. Gençağa, D., Şengül Ayan, S., Farnoudkia, H., & Okuyucu, S., Statistical approaches for the analysis of dependency among neurons under noise. Entropy, 2020. 22(4): 387.
10. 10. Jæger, K. H., Wall, S., & Tveito, A., Detecting undetectables: Can conductances of action potential models be changed without appreciable change in the transmembrane potential?. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019. 29(7): 073102.
11. 11. Liu, Z., Golowasch, J., Marder, E., & Abbott, L. F., A model Neuron with activity-dependent conductances regulated by multiple calcium sensors. The Journal of Neuroscience, 1998. 18(7): p. 309-2320.
12. 12. Fernandez, F. R., & White, J. A., Reduction of spike Afterdepolarization by increased leak conductance alters Interspike interval variability. Journal of Neuroscience, 2009. 29(4): p. 973-986.
13. 13. Şengül Ayan, S., Sırcan, A. K., Abewa, M., Kurt, A., Dalaman, U., & Yaraş, N., Mathematical model of the ventricular action potential and effects of isoproterenol-induced cardiac hypertrophy in rats. European Biophysics Journal, 2020. 49(5): p. 323-342.
14. 14. Duncan, P. J., Sengul, S., Tabak, J., Ruth, P., Bertram, R., & Shipston, M. J., Large conductance ca2+-activated K+channels (BK) promote secretagogue-induced transition from spiking to bursting in murine anterior pituitary corticotrophs. The Journal of Physiology, 2014. 593(5): p. 1197-211.
15. 15. Patel, A. X., & Burdakov, D., Mechanisms of gain control by voltage-gated channels in intrinsically-firing neurons. Plos One, 2015. 10(3), e0115431.
16. 16. Gençağa, D., & Ayan, S. Ş., Effects of neuronal noise on neural communication. Proceedings of The 39th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, 2019. 33(1): p. 2.
17. 17. Lane, B. J., Samarth, P., Ransdell, J. L., Nair, S. S., & Schulz, D. J., Synergistic plasticity of intrinsic conductance and electrical coupling restores synchrony in an intact motor network. eLife, 2016. 5. https://doi.org/10.7554/elife.16879.
18. 18. Cover, T. M., Thomas, J. A., Information theory and portfolio theory. Elements of Information Theory, 2005. p:613-656. USA: John Wiley & Sons, Inc.
19. 19. Schreiber, T., Measuring information transfer. Physical Review Letters, 2000. 85(2): p. 461-464.
20. 20. Scott, D. W., Multivariate density estimation. 2012, USA: Wiley Series in Probability and Statistics.
21. 21. Gençağa, D., Transfer entropy. Entropy, 2018. 20(4): p. 288. https://doi.org/10.3390/e20040288.
22. 22. Hodgkin, A. L., & Huxley, A. F., A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 1952. 117(4): p.500-544.
23. 23. Dhanya E, Pradhan, N., Sunitha R, & Sreedevi, A., Modelling and implementation of two coupled Hodgkin-Huxley Neuron model. 2015 International Conference on Computing and Network Communications (CoCoNet).
24. 24. Ermentrout, B., Simulating, analyzing, and animating dynamical systems. 2002, USA: Society for Industrial and Applied Mathematics.
25. 25. Şengül, S., Clewley, R., Bertram, R., & Tabak, J., Determining the contributions of divisive and subtractive feedback in the Hodgkin-Huxley model. Journal of Computational Neuroscience, 2014. 37(3): p. 403-415.
26. 26. Bezanilla, F., Rojas, E., & Taylor, R. E., Sodium and potassium conductance changes during a membrane action potential. The Journal of Physiology, 1970. 211(3): p. 729-751.