The Interplay of Common Noise and Finite Pulses on Biological Neurons

Afifurrahman; Mohd Hafiz Mohd; Farah Aini Abdullah

doi:10.5614/cbms.2023.6.2.5

Authors

Afifurrahman Department of Mathematics, Universitas Islam Negeri Mataram, Mataram 83116, Indonesia
Mohd Hafiz Mohd School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia
Farah Aini Abdullah School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia

DOI:

https://doi.org/10.5614/cbms.2023.6.2.5

Keywords:

finite pulses, inter-spike interval, LIF neuron, stochastic process, synchronization

Abstract

The response of neurons is highly sensitive to the stimulus. The stimulus can be associated with a direct injection in vitro experimentation (e.g., time dependent and independent inputs); or post-synaptic potentials resulting from the interaction of many neurons. A typical incoming stimulus resembles a noise which in principle can be described as a random variable. In computational neuroscience, the noise has been extensively studied for different setups. In this study, we investigate the effect of noisy inputs in a minimal network of two identical leaky integrate-and-fire (LIF) neurons interacting with finite pulses. In particular, we consider a Gaussian white noise as a standard function for stochastic modelling of neurons, while taking into account the pulse width as an elementary component for the signal transmission. By exploring the role of noise and finite pulses, the two neurons show a synchronous spiking behaviour characterized by fluctuations in the interspike intervals. Above some critical values the synchronous regime collapses onto asynchronous dynamics. The abrupt change in such dynamics is accompanied by a hysteresis, i.e., the coexistence of synchronous and asynchronous firing behaviour.

References

Afifurrahman, Ullner, E. and Politi, A., Collective dynamics in the presence of finite width pulses, Chaos: an interdisciplinary journal of nonlinear sciences, 31(4), p. 043135, 2021.

Afifurrahman, Neuronal dynamics: from complexity to simplicity, Jurnal Teori dan Aplikasi Matematika, 7(2), pp. 310-323, 2023.

Barrett, K.E., Barman, S.M., Boitano, S. and Reckelfhoff, J.F., Ganong?s Medical Physiology Examination and Board Review, McGraw-Hill USA, 2017.

Beeman, D., Hodgkin-Huxley model, Encyclopedia of Computational Neuroscience, Springer New York, pp. 1-13, 2014.

Chirwa, S.S. and Sastry, B.R., Asynchronous synaptic responses in hippocampal CA1 neurons during synaptic long-term potentiation, Neuroscience Letter, 89(3), pp. 355-360, 1988.

Chaplin, T.A., Allitt, B.J., Hagan, M.A., Price, N.S.C., Rajan, R., Rosa, M.G.P. and Lui, L.L., Sensitivity of neurons in the middle temporal area of marmoset monkeys to random dot motion, Journal of Neurophysiology, 118(3), pp. 1567-1580, 2017.

Durstewitz, D. and Gabriel, T., Dynamical Basis of Irregular Spiking in NMDA-Driven Prefrontal Cortex Neurons, Cerebral Cortex, 17(4), pp. 894-908, 2007.

Ermentrout, G.B., Galan, R.F. and Urban, N.N., Reliability, synchrony and noise, Trends Neuroscience, 31(8), pp. 428-434, 2018.

Faisal, A.A., Selen, L.P.J. and Wolpert, D.M., Noise in the nervous system, Nature Review Neuroscience, 9(4), pp. 292-303, 2008.

Fedosejevs, C.S. and Schneider, M.F., Sharp, localized phase transitions in single neuronal cells, Proceedings of the National Academy of Sciences, 119(8), pp. 1-6, 2022.

Gerstner, W., Kistler, W.M., Naud, R. and Paninski, L., Neuronal dynamics: from single neurons to networks and model of cognition, Cambridge University Press, 2014.

Gray, C.M., Konig, P., Engel A.K. and Singer, W., Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties, Nature, 338(6213), pp. 334-337, 1989.

Kaltenbrunner, A., Gomez, V., and Lopez, V., Phase Transition and Hysteresis in an Ensemble of Stochastic Spiking Neurons, Neural Computation, 19(11), pp. 3011-3050, 2007.

Kim, D.J., Yogendrakumar, V., Chiang, J., Ty Edna, Wang, Z.J. and MacKeown, M.J., Noisy Galvanic Vestibular Stimulation Modulates the Amplitude of EEG Synchrony Patterns, Plos One, 8(7), pp.1-10, 2013.

Laffargue, T., Tailleur, J. and Wijland, F.v., Lyapunov exponents of stochastic systems-from micro to macro, Journal of Statistical Mechanics: Theory and Experiment, 3, p. 034001, 2016.

McDonnell, M. and Ward, L., The benefits of noise in neural systems: bridging theory and experiment, Nature Review Neuroscience, 12(7), pp. 415-425, 2011.

Mishra, D., Yadav, A., Ray, S. and Kalra, P.K., Effects of noise on the dynamics of biological neuron models, In: Abraham, A., Dote, Y., Furuhashi, T., K?oppen, M., Ohuchi, A., Ohsawa, Y. (eds.), Soft Computing as Transdisciplinary Science and Technology, Springer, 29, pp. 61-69, 2005.

Ostojic, S., Interspike interval distributions of spiking neurons driven by fluctuating inputs, Journal of Neurophysiology, 106(1), pp. 361-373, 2011.

Politi, A. and Luccioli, S., Dynamics of Networks of Leaky-Integrate and Fire Neurons, Network Science, Estrada, E., Fox, M., Higham, D.J., Oppo, G.L., Springer London, 2010.

Pietras, B., Pulse shape and voltage-dependent synchronization in spiking neuron networks, 2023, unpublished.

Protachevicz, P.R., Bonin, C.A., Larosz, K.C., Caldas, I.L. and Batista, A.M., Large coefficient of variation of inter-spike intervals induced by noise current in the resonate-and-fire model neuron, Cognitive Neurodynamics, 16(6), pp. 1461-1470, 2022.

Scharfman, H.E., The Neurobiology, Current Neurology and Neuroscience Reports, 7(4), pp. 348-354, 2007.

Sherwood, W.E., FitzHugh-Nagumo Model, Encyclopedia of Computational Neuroscience, Jaeger, D. and Jung, R., Springer New York, pp. 1-11, 2014.

Stiefel, K.M., Englitz, B. and Sejnowski, T.J., Origin of intrinsic irregular firing in cortical interneurons, Proceedings of the National Academy of Sciences, 110(19), pp. 7886-7891, 2013.

Schwalger, T., Fisch, K., Benda, J. and Lindner, B., How Noisy Adaptation of Neurons Shapes Interspike Interval Histogram and Correlations, Plos Computational Biology, 6(12), pp. 1-25, 2010.

Shi, Xhi, Wang, Qingyun and Lu, Qishao, Firing synchronization and temporal order in noisy neuronal networks, Cognitive Neurodynamics, 2(3), pp. 195-206, 2008.

Zirkle, J. and Rubchinsky, L.L., Noise effect on the temporal pattern of neural synchrony, Neural Networks, 141, pp. 30-39, 2021.

Bayram, M., Partal, T. and Orucova Buyukoz, G., Numerical methods for simulation of stochastic differential equations. Advances in Difference Equations, 17, pp. 1-10, 2018.

Gabbiani, F. and Cox, Steven J., Quantification of Spike Train Variability in Mathematics for Neuroscientists, pp. 237-249, Academic Press, London, 2010.

Dumont, G., Henry, J. and Tarniceriu, C. O., Noisy threshold in neuronal models: connections with the noisy leaky integrateand-fire model, J. Math. Biol., 73(6-7), pp. 1413-1436, 2016.

Afifurrahman, Ullner, E. and Politi, A., Stability of synchronous states in sparse neuronal networks, Nonlinear Dynamics, 102(2), pp. 733-743, 2020.

Protachevicz, P. R., Hansen, M., Iarosz, K. C., Caldas, I. L., Batista, A. M. and Kurths, J., Emergence of Neuronal Synchronisation in Coupled Areas, Frontiers in Computational Neuroscience, 15, p. 663408, 2021.

Liu, C., Liu, X. and Liu, S., Bifurcation analysis of a Morris-Lecar neuron model, Biol Cybern, 108, pp. 75-84, 2014.

Gerstein, G. L. and Kiang, N. Y. -S., An approach to the quantitative analysis of Electropyhsiological Data from single neurons, Biophys J., 1(1), pp. 15-28, 1960.

Christodoulou, C. and Bugmann, G., Coefficient of variation vs. mean interspike interval curves: What do they tell us about the brain?, Neurocomputing, 38(40), pp. 1141-1149, 2001.

Rong, S., Zhang, P., He, C., Li, Y., Li, X., Li, R., Nie, K., Huang, S., Wang, L., Wang, L. and Zhang, Y., Abnormal neural activity in different frequency bands in Parkinson?s disease with mild cognitive impairment, Frontiers in Aging Neuroscience, 13, p. 709998, 2021.

Wu, L., Zhan, Q., Liu, Q., Xie, S., Tian, S., Xie, L. and Wu, W., Abnormal Regional Spontaneous Neural Activity and Functional Connectivity in Unmedicated Patients with Narcolepsy Type 1: A Resting-State fMRI Study, International Journal of Environmental Research and Public Health, 19(23), p. 15482, 2022.

Taube, J. S., Interspike Interval Analyses Reveal Irregular Firing Patterns at Short, But Not Long, Intervals in Rat Head Direction Cells, Journal of Neurophysiology, 104(3), pp. 1635-1648, 2010.

Peng, X. and Lin, W., Complex dynamics of noise-perturbed excitatory-inhibitory neural networks with intra-correlative and inter-independent connections, Frontiers in Physiology, 13, p. 915511, 2022.

Pirozzi, E., Colored noise and a stochastic fractional model for correlated inputs and adaptation in neuronal firing, Biol Cybern, 112, pp. 25-39, 2018.

Thieu, T. K. T. and Melnik, R., Effects of noise on leaky integrate-and-fire neuron models for neuromorphic computing applications, In: Gervasi, O., Murgante, B., Hendrix, E.M.T., Taniar, D., Apduhan, B.O. (eds) Computational Science and Its Applications - ICCSA 2022, Lecture Notes in Computer Science, Springer, p. 13375, 2022.

Leng, S. and Aihara, K., Common stochastic inputs induce neuronal transient synchronization with partial reset, Neural Networks, 128, pp. 13-21, 2020.

Burkitt, A. N., A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input, Biol Cybern, 95(1), pp. 1-19, 2006.

Burkitt, A. N., A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties, Biol Cybern, 95(2), pp. 97-112, 2006.

Zhang, X. and Hedwig, B., Response properties of spiking and non-spiking brain neurons mirror pulse interval selectivity, Frontiers in Cellular Neuroscience, 16, p. 1010740, 2022.

Serletis, D., Complexity in neuronal noise depends on network interconnectivity, Ann Biomed Eng, 39(6), pp. 1768-1778, 2011.