Fitting a recurrent dynamical neural network to neural spiking data: tackling the sigmoidal gain function issues

This is a continuation of a recent study (Doruk RO, Zhang K. Fitting of dynamic recurrent neural networkmodels to sensory stimulus-response data. J Biol Phys 2018; 44: 449-469), where a continuous time dynamical recurrentneural network is fitted to neural spiking data. In this research, we address the issues arising from the inclusion ofsigmoidal gain function parameters to the estimation algorithm. The neural spiking data will be obtained from the samemodel as that of Doruk and Zhang, but we propose a different model for identification. This will also be a continuoustime recurrent neural network, but with generic sigmoidal gains. The simulation framework and estimation algorithmsare kept similar to that of Doruk and Zhang so that we can have a solid base to compare the results. We evaluatethe estimation performance in two different ways. First, we compare the firing rate responses of the original and theestimated model. We find that responses of both models to the same stimuli are similar. Secondly, we evaluate variationsof the standard deviations of the estimates against a number of samples and stimulus parameters. They show a similarpattern to that of Doruk and Zhang. We thus conclude that our model serves as a reasonable alternative provided thatfiring rate is the response of interest (to any stimulus).

PDF

___

[1] Doruk RO, Zhang K. Fitting of dynamic recurrent neural network models to sensory stimulus-response data. J Biol Phys 2018; 44: 449-469.
[2] Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol-London 1952; 117: 500. https://doi.org/10.1113.
[3] Morris C, Lecar H. Voltage oscillations in the barnacle giant muscle fiber. Biophys J 1981; 35: 193-213.
[4] Ermentrout B, Pascal M, Gutkin B. The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators. Neural Comput 2001; 13: 1285-1310.
[5] Booth V, Rinzel J, Kiehn O. Compartmental model of vertebrate motoneurons for Ca2+-dependent spiking and plateau potentials under pharmacological treatment. J Neurophysiol 1997; 78: 3371-3385.
[6] Koch C. Biophysics of Computation: Information Processing in Single Neurons. Oxford, UK: Oxford University Press, 2004.
[7] FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1961; 1: 445-466.
[8] Hindmarsh JL, Rose R. A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond B 1984; 221: 87-102.
[9] Rust NC, Schwartz O, Movshon JA, Simoncelli EP. Spatiotemporal elements of macaque v1 receptive fields. Neuron 2005; 46: 945-956.
[10] Hosoya T, Baccus SA, Meister M. Dynamic predictive coding by the retina. Nature 2005; 436: 71. https://doi.org/10.1016
[11] Mante V, Frazor RA, Bonin V, Geisler WS, Carandini M. Independence of luminance and contrast in natural scenes and in the early visual system. Nat Neurosci 2005; 8: 1690. https://doi.org/10.1038/nn1556.
[12] Borst A, Theunissen FE. Information theory and neural coding. Nat Neurosci 1999; 2: 947. https://doi.org/10.1038/14731.
[13] Barlow H. Possible principles underlying the transformation of sensory messages. In: Rosenblith W, editor. Sensory Communication. Cambridge, MA, USA: MIT Press, 1959, pp. 217-234.
[14] Fairhall AL, Lewen GD, Bialek W, van Steveninck RRR. Efficiency and ambiguity in an adaptive neural code. Nature 2001; 412: 787. https://doi.org/10.1038/35090500.
[15] Hassenstein B, Reichardt W. Systemtheoretische analyse der zeit-, reihenfolgen-und vorzeichenauswertung bei der bewegungsperzeption des rüsselkäfers chlorophanus. Z Naturforsch B 1956; 11: 513-524 (in German).
[16] Schneidman E, Freedman B, Segev I. Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comput 1998; 10: 1679-1703.
[17] Haykin S. Neural Networks and Learning Machines. 3rd ed. Upper Saddle River, NJ, USA: Pearson, 2009.
[18] Arulampalam G, Bouzerdoum A. A generalized feedforward neural network architecture for classification and regression. Neural Networks 2003; 16: 561-568.
[19] Funahashi KI, Nakamura Y. Approximation of dynamical systems by continuous time recurrent neural networks. Neural Networks 1993; 6: 801-806.
[20] Guo DQ, Chen MM, Perc M, Wu SD, Xia C, Zhang YS, Xu P, Xia Y, Yao DZ. Firing regulation of fastspiking interneurons by autaptic inhibition. Europhys Lett 2016; 2016: 114. https://dx.doi.org/10.1209/0295- 5075/114/30001.
[21] Guo DQ, Wu SD, Chen MM, Perc M, Zhang YS, Ma JL, Cui Y, Xu P, Xia Y, Yao DZ. Regulation of irregular neuronal firing by autaptic transmission. Sci Rep 2016; 6: 26096. https://dx.doi.org/10.1038/srep26096.
[22] Yilmaz E, Ozer M, Baysal V, Perc M. Autapse-induced multiple coherence resonance in single neurons and neuronal networks. Sci Rep 2016; 6: 30914. https://dx.doi.org/10.1038/srep30914.
[23] Schäfer AM, Zimmermann HG. Recurrent neural networks are universal approximators. In: International Conference on Artificial Neural Networks. pp. 632-640.
[24] Gosak M, Markovic R, Dolensek J, Rupnik MS, Marhl M, Stozer A, Perc M. Network science of biological systems at different scales: a review. Phys Life Rev 2018; 24: 118-135. .
[25] Jalili M, Perc M. Information cascades in complex networks. J Complex Networks 2017; 5: 665-693. .
[26] Rieke F, Warland D, Bialek W. Coding efficiency and information rates in sensory neurons. Europhys Lett 1993; 22: 151. https://doi.org/10.1209/0295-5075/22/2/013.
[27] Herz AV, Gollisch T, Machens CK, Jaeger D. Modeling single-neuron dynamics and computations: a balance of detail and abstraction. Science 2006; 314: 80-85.
[28] Ozer M, Uzuntarla M, Perc M, Graham LJ. Spike latency and jitter of neuronal membrane patches with stochastic Hodgkin-Huxley channels. J Theor Biol 2009; 261: 83-92. https://dx.doi.org/10.1016/j.jtbi.2009.07.006.
[29] Uzun R, Ozer M, Perc M. Can scale-freeness offset delayed signal detection in neuronal networks? Europhys Lett 2014; 2014: 105. https://dx.doi.org/10.1209/0295-5075/105/60002.
[30] Shadlen MN, Newsome WT. Noise, neural codes and cortical organization. Curr Opin Neurol 1994; 4: 569-579.
[31] Myung IJ. Tutorial on maximum likelihood estimation. J Math Psychol 2003; 47: 90-100.
[32] Hsiao T. Identification of time-varying autoregressive systems using maximum a posteriori estimation. IEEE T Signal Process 2008; 56: 3497-3509.
[33] DiMattina C, Zhang K. Active data collection for efficient estimation and comparison of nonlinear neural models. Neural Comput 2011; 23: 2242-2288.
[34] DiMattina C, Zhang K. Adaptive stimulus optimization for sensory systems neuroscience. Front Neural Circuit 2013; 7: 101. https://doi.org/10.3389/fncir.2013.00101.
[35] Doruk O, Zhang K. An attempt to fit all parameters of a dynamical recurrent neural network from sensory neural spiking data. PeerJ Preprints 2018; 6: e27015v1. https://dx.doi.org/10.7287/peerj.preprints.27015v1.
[36] Lewis PA, Shedler GS. Simulation of nonhomogeneous Poisson processes by thinning. Nav Res Logist Q 1979; 26: 403-413.
[37] Eden UT. Point process models for neural spike trains. Neural Signal Processing: Quantitative Analysis of Neural Activity 2008; 2008: 45–51.
[38] Klein RW, Roberts SD. A time-varying Poisson arrival process generator. Simulation 1984; 43: 193-195.