Inferring the Dynamics of “Hidden“ Neurons from Electrophysiological Recordings

Authors: Valeri A. Makarov, Nazareth P. Castellanos

Abstract:

Statistical analysis of electrophysiological recordings obtained under, e.g. tactile, stimulation frequently suggests participation in the network dynamics of experimentally unobserved “hidden" neurons. Such interneurons making synapses to experimentally recorded neurons may strongly alter their dynamical responses to the stimuli. We propose a mathematical method that formalizes this possibility and provides an algorithm for inferring on the presence and dynamics of hidden neurons based on fitting of the experimental data to spike trains generated by the network model. The model makes use of Integrate and Fire neurons “chemically" coupled through exponentially decaying synaptic currents. We test the method on simulated data and also provide an example of its application to the experimental recording from the Dorsal Column Nuclei neurons of the rat under tactile stimulation of a hind limb.

Keywords: Integrate and fire neuron, neural network models, spike trains.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1083471

References:

[1] G. P. Moore, D. P. Perkel, and J. P. Segundo,"Statistical analysis and functional interpretation of neural spike data". Annu Rev Physiol, vol. 28, pp. 493-522, 1966.
[2] D. H. Perkel, G. L. Gerstein, and G. P. Moore, "Neuronal spike trains and stochastic point processes. II Simultaneous spike train". Biophys J, vol. 7, pp. 419-440, 1967.
[3] E. R. Kandel, J. H. Schwartz, and T. M. Jessell, Principles of neural science. 4th ed. New York: McGraw-Hill, 2000.
[4] F. Panetsos, A. Nunez, and C. Avendano, "Electrophysiological effects of temporary differentiation on two characterized cell types in the nucleus gracilis of the rat". Eur J Neurosci, vol. 9, pp. 563-572, 1997
[5] F. Panetsos, A. Nunez, C. Avendano, "Sensory information processing in the dorsal column nuclei by neuronal oscillators". Neurosci, vol. 84, pp. 635-639, 1998.
[6] A. Nunez, F. Panetsos, and C. Avendao."Rhythmic neuronal interactions and synchronization in the rat dorsal column nuclei". Neurosci, vol. 100, pp. 599-609, 2000.
[7] G. Gerstein, P. Bedenbaugh, and M. Aertse, "Neuronal assemblies". IEEE Trans biomed engineering, vol. 36, no. 1, pp. 4-14, 1989.
[8] A. Aertsen and H. Preissl, Dynamics of activity and connectivity in physiological neural networks. In: Schuster H.G. Ed., New York: VCH. Nonlinear dynamics and neuronal networks, pp. 281-302, 1991.
[9] O. Sporns, G. Tonino, and G. M. Edelman, "Connectivity and complexity: the relationship between neuroanatomy and brain dynamics". Neural Network, vol. 13, pp. 909-922, 2000.
[10] V. A. Makarov, F. Panetsos, and O. De Feo, "A method for determining neural connectivity and inferring the underlying network dynamics using extracellular spike recordings". J Neurosci Methods, vol. 144, pp. 265- 279, 2005.
[11] N. Castellanos, V. A. Makarov, O. de Feo, A. Perez de Vargas, and F. Panetsos, "Identification of functional neural circuits from extracellular recordings using a novel mathematical method". Proc. of FENS, 2004.
[12] A. Pavlov, V. A. Makarov, I. Makarova, and F. Panetsos, "Sorting of neural spikes: When wavelet based methods outperform principal components analysis". Natural Computing, DOI 10.1007/s11047-006- 9014-8 (in press), 2006.
[13] R. Jolivet, T.J. Lewis, and W. Gerstner, "Generalized Integrate-and-Fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy". J Neurophysiol, vol. 92, pp. 959-976, 2004.
[14] R. B. Stein, "Some models of neuronal variability". Biophys J vol. 7, pp. 37-68, 1967.
[15] C. Koch and I. Segev, Methods in neuronal modelling: From ions to networks. MIT Press: Cambridge, Massachusetts, 1998.
[16] H. Motulsky and A. Christopoulos, Fitting models to biological data using linear and nonlinear regression: A practical guide to curve fitting.