Neuron modeling: estimating the parameters of a neuron model from neural spiking data
Neuron modeling: estimating the parameters of a neuron model from neural spiking data
We present a modeling study aiming at the estimation of the parameters of a single neuron model from neuralspiking data. The model receives a stimulus as input and provides the firing rate of the neuron as output. The neuralspiking data will be obtained from point process simulation. The resultant data will be used in parameter estimationbased on the inhomogeneous Poisson maximum likelihood method. The model will be stimulated by various forms ofstimuli, which are modeled by a Fourier series (FS), exponential functions, and radial basis functions (RBFs). Tabulatedresults presenting cases with different sample sizes (# of repeated trials), stimulus component sizes (FS and RBF),amplitudes, and frequency ranges (FS) will be presented to validate the approach and provide a means of comparison.The results showed that regardless of the stimulus type, the most effective parameter on the estimation performanceappears to be the sample size. In addition, the lowest variance of the estimates is obtained when a Fourier series stimulusis applied in the estimation.
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- Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and
excitation in nerve. J Physiol-London 1952; 117: 500-544.
- Morris C, Lecar H. Voltage oscillations in the barnacle giant muscle fiber. Biophys J 1981; 35: 193-213.
- FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1961; 1: 445-466.
- 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.
- 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: 1690-1697.
- Hosoya T, Baccus SA, Meister M. Dynamic predictive coding by the retina. Nature 2005; 436: 71-77.
- Rust NC, Schwartz O, Movshon JA, Simoncelli EP. Spatiotemporal elements of macaque v1 receptive fields. Neuron
2005; 46: 945-956.
- Adelson EH, Bergen JR. Spatiotemporal energy models for the perception of motion. J Opt Soc Am A 1985; 2:
284-299.
- Borst A, Theunissen FE. Information theory and neural coding. Nat Neurosci 1999; 2: 947-957.
- 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.
- Fairhall AL, Lewen GD, Bialek W, van Steveninck RRdR. Efficiency and ambiguity in an adaptive neural code.
Nature 2001; 412: 787-792.
- 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).
- 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.
- Ma J, Tang J. A review for dynamics in neuron and neuronal network. Nonlinear Dynam 2017; 89: 1569-1578.
- Linaro D, Storace M, Giugliano M. Accurate and fast simulation of channel noise in conductance-based model
neurons by diffusion approximation. PLoS Comput Biol 2011; 7: e1001102.
- White JA, Rubinstein JT, Kay AR. Channel noise in neurons. Trends Neurosci 2000; 23: 131-137
- Lv M, Wang C, Ren G, Ma J, Song X. Model of electrical activity in a neuron under magnetic flow effect. Nonlinear
Dynam 2016; 85: 1479-1490.
- Lv M, Ma J. Multiple modes of electrical activities in a new neuron model under electromagnetic radiation.
Neurocomputing 2016; 205: 375-381.
- Wu F, Wang C, Xu Y, Ma J. Model of electrical activity in cardiac tissue under electromagnetic induction. Sci
Rep-UK 2016; 6: 28.
- Wang Y, Ma J, Xu Y, Wu F, Zhou P. The electrical activity of neurons subject to electromagnetic induction and
Gaussian white noise. Int J Bifurcat Chaos 2017; 27: 1750030.
- Zhan F, Liu S. Response of electrical activity in an improved neuron model under electromagnetic radiation and
noise. Front Comput Neurosc 2017; 11: 107.
- Wu F, Wang C, Jin W, Ma J. Dynamical responses in a new neuron model subjected to electromagnetic induction
and phase noise. Physica A 2017; 469: 81-88.
- Chichilnisky E. A simple white noise analysis of neuronal light responses. Network-Comp Neural 2001; 12: 199-213.
- Paninski L. Estimation of entropy and mutual information. Neural Comput 2003; 15: 1191-1253.
- Sharpee TO, Sugihara H, Kurgansky AV, Rebrik SP, Stryker MP, Miller KD. Adaptive filtering enhances information
transmission in visual cortex. Nature 2006; 439: 936-942.
- Haykin S. Neural Netwoks: A Comprehensive Foundation. 2nd ed. Upper Saddle River, NJ, USA: Prentice Hall,
2004.
- Funahashi Ki, Nakamura Y. Approximation of dynamical systems by continuous time recurrent neural networks.
Neural Networks 1993; 6: 801-806.
- Miller KD, Fumarola F. Mathematical equivalence of two common forms of firing rate models of neural networks.
Neural Comput 2012; 24: 25-31.
- DiMattina C, Zhang K. Adaptive stimulus optimization for sensory systems neuroscience. Front Neural Circuit
2013; 7: 101.
- DiMattina C, Zhang K. Active data collection for efficient estimation and comparison of nonlinear neural models.
Neural Comput 2011; 23: 2242-2288.
- DiMattina C, Zhang K. How to modify a neural network gradually without changing its input-output functionality.
Neural Comput 2010; 22: 1-47.
- Doruk RO, Zhang K. Fitting of dynamic recurrent neural network models to sensory stimulus-response data. J Biol
Phys 2018; 44: 449-469.
- Wang C, Guo S, Xu Y, Ma J, Tang J, Alzahrani F, Hobiny A. Formation of autapse connected to neuron and its
biological function. Complexity 2017; 2017: 5436737.
- Guo S, Wang C, Ma J, Jin W. Transmission of blocked electric pulses in a cable neuron model by using an electric
field. Neurocomputing 2016; 216: 627-637.
- Xu Y, Ying H, Jia Y, Ma J, Hayat T. Autaptic regulation of electrical activities in neuron under electromagnetic
induction. Sci Rep-UK 2017; 7: 43452.
- Ren G, Zhou P, Ma J, Cai N, Alsaedi A, Ahmad B. Dynamical response of electrical activities in digital neuron
circuit driven by autapse. Int J Bifurcat Chaos 2017; 27: 1750187.
- Jia B. Negative Feedback Mediated by Fast Inhibitory Autapse Enhances Neuronal Oscillations Near a Hopf
Bifurcation Point. Int J Bifurcat Chaos 2018; 28: 1850030.
- Dayan P, Abbott LF. Theoretical Neuroscience. 1st ed. Cambridge, MA, USA: MIT Press, 2001.
- Shadlen MN, Newsome WT. Noise, neural codes and cortical organization. Curr Opin Neurobiol 1994; 4: 569-579.
- Eden UT. Point process models for neural spike trains. In: Mitra P, editor. Neural Signal Processing: Quantitative
Analysis of Neural Activity. Washington, DC, USA: Society for Neuroscience, 2008. pp. 45-51.
- Myung IJ. Tutorial on maximum likelihood estimation. J Math Psychol 2003; 47: 90-100.
- Kollias S, Anastassiou D. An adaptive least squares algorithm for the efficient training of artificial neural networks.
IEEE T Circuits Syst 1989; 36: 1092-1101.
- Parlitz U, Junge L, Kocarev L. Synchronization-based parameter estimation from time series. Phys Rev E 1996;
54: 6253-6259.
- Wang CN, Ma J, Jin WY. Identification of parameters with different orders of magnitude in chaotic systems.
Dynam Syst 2012; 27: 253-270.
- Lynch EP, Houghton CJ. Parameter estimation of neuron models using in-vitro and in-vivo electrophysiological
data. Front Neuroinform 2015; 9: 10.
- Kreuz T, Chicharro D, Houghton C, Andrzejak RG, Mormann F. Monitoring spike train synchrony. J Neurophysiol
2012; 109: 1457-1472.
- van Rossum M. A novel spike distance. Neural Comput 2001; 13: 751-763.
- Houghton C, Kreuz T. On the efficient calculation of van Rossum distances. Network-Comp Neural 2012; 23: 48-58.
- Hindmarsh JL, Rose R. A model of neuronal bursting using three coupled first order differential equations. P R
Soc B 1984; 221: 87-102.
- Crawford JD. Introduction to bifurcation theory. Rev Mod Phys 1991; 63: 991-103