Output Stream of Binding Neuron with Threshold 2 Stimulated with Renewal Process

Authors

  • O.V. Shchur Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine, Institute of Experimental Medicine

DOI:

https://doi.org/10.15407/ujpe68.3.170

Keywords:

binding neuron, Poisson process, renewal process, interspike interval, probability density function, moments of a distribution

Abstract

Information is transmitted between neurons in a brain via typical electrical impulses, which are called spikes. Since the activity of biological neurons is random, the statistics of neuronal activity, namely, the time intervals between neuron-generated consecutive spikes, is studied. A neuron transforms a random stream of input impulses into another stream, the output one. The input stream is described in this paper as a renewal point process. As a neuronal model, a binding neuron with threshold 2 is considered. A relationship between the Laplace transforms of the probability density functions of the interspike intervals in the input stream of impulses and the output stream generated as a response to this stimulus has been obtained. The derived relationship enables the determination of the probability density function and all of its moments. The resulting formulas are applied to the case where the input process is the Erlang one. In the considered case, the dependence of the regularity of the neuronal activity on the input stream parameters and the physical parameters of the neuron model is found.

References

R. Brette. Philosophy of the spike: Rate-based vs. spikebased theories of the brain. Front. Syst. Neurosci. 9, 151 (2015).

https://doi.org/10.3389/fnsys.2015.00151

G. Maimon, J.A. Assad. Beyond Poisson: Increased spiketime regularity across primate parietal cortex. Neuron 62, 426 (2009).

https://doi.org/10.1016/j.neuron.2009.03.021

S. Shinomoto et al. Relating neuronal firing patterns to functional differentiation of cerebral cortex. PLoS Comput. Biol. 5, e1000433 (2009).

https://doi.org/10.1371/journal.pcbi.1000433

D.H. Johnson. Point process models of single-neuron discharges. J. Comput. Neurosci. 3, 275 (1996).

https://doi.org/10.1007/BF00161089

A.K. Vidybida. Inhibition as binding controller at the single neuron level. BioSystems 48, 263 (1998).

https://doi.org/10.1016/S0303-2647(98)00073-2

O.K. Vidybida. Output stream of a binding neuron. Ukr. Math. J. 59, 1819 (2007).

https://doi.org/10.1007/s11253-008-0028-5

D. Cox. Renewal Theory. 1st Edition (Methuen and Co., 1962) [ISBN: 978-0412205705].

A.K. Dhawale, M.A. Smith, B.P. Olveczky. The role of variability in motor learning. Annu. Rev. Neurosci. 40, 479 (2017).

https://doi.org/10.1146/annurev-neuro-072116-031548

A. Compte, C. Constantinidis, J. Tegn'er, S. Raghavachari, M.V. Chafee, P.S. Goldman-Rakic, Xiao-Jing Wang. Temporally irregular mnemonic persistent activity in prefrontal neurons of monkeys during a delayed response task. J. Neurophysiol. 90, 3441 (2003).

https://doi.org/10.1152/jn.00949.2002

V. Arunachalam, R. Akhavan-Tabatabaei, C. Lopez. Results on a binding neuron model and their implications for modified hourglass model for neuronal network. Comput. Math. Methods Med. 2013, 374878 (2013).

https://doi.org/10.1155/2013/374878

A. Vidybida. Relation between firing statistics of spiking neuron with instantaneous feedback and without feedback. Fluct. Noise Lett. 14, 1550034 (2015).

https://doi.org/10.1142/S0219477515500340

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

https://doi.org/10.1007/s00422-006-0068-6

A.K. Vidybida. Output stream of binding neuron with instantaneous feedback. Eur. Phys. J. B 65, 577 (2008).

https://doi.org/10.1140/epjb/e2008-00360-1

P. Lansky, L. Sacerdote, C. Zucca. The Gamma renewal process as an output of the diffusion leaky integrate-andfire neuronal model. Biol. Cybern. 110, 193 (2016).

https://doi.org/10.1007/s00422-016-0690-x

O. Shchur, A. Vidybida. Distribution of interspike intervals of a neuron with inhibitory autapse stimulated with a renewal process. Fluct. Noise Lett. 22, 2350003 (2023).

https://doi.org/10.1142/S0219477523500037

A.K. Vidybida. Output stream of leaky integrate-and-fire neuron without diffusion approximation. J. Stat. Phys. 166, 267 (2017).

https://doi.org/10.1007/s10955-016-1698-2

A.K. Vidybida, O.V. Shchur. Moment-generating function of output stream of leaky integrate-and-fire neuron. Ukr. J. Phys. 66, 254 (2021).

https://doi.org/10.15407/ujpe66.3.254

K. Kravchuk. Leaky integrate-and-fire neuron under Poisson stimulation. In: Proceedings of the 2016 II International Young Scientists Forum on Applied Physics and Engineering (YSF), Kharkiv, Ukraine, October 10-14 (IEEE, 2016), p. 203.

https://doi.org/10.1109/YSF.2016.7753837

Published

2023-05-11

How to Cite

Shchur, O. (2023). Output Stream of Binding Neuron with Threshold 2 Stimulated with Renewal Process. Ukrainian Journal of Physics, 68(3), 170. https://doi.org/10.15407/ujpe68.3.170

Issue

Section

Physics of liquids and liquid systems, biophysics and medical physics