A method for determining neural connectivity and inferring the underlying network dynamics using extracellular spike recordings

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In the present paper we propose a novel method for the identification and modeling of neural networks using extracellular spike recordings. We create a deterministic model of the effective network, whose dynamic behavior fits experimental data. The network obtained by our method includes explicit mathematical models of each of the spiking neurons and a description of the effective connectivity between them. Such a model allows us to study the properties of the neuron ensemble independently from the original data. It also permits to infer properties of the ensemble that cannot be directly obtained from the observed spike trains. The performance of the method is tested with spike trains artificially generated by a number of different neural networks. (c) 2004 Elsevier B.V. All rights reserved.
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Aertsen A, Preissl H. Dynamics of activity and connectivity in physiological neuronal networks. In: Schuster HG, editor. Nonlinear dynamics and neuronal networks. New York: VCH; 1991. p. 281–302. Brillinger DR, Bryant HL, Segundo JP. Identification of synaptic interactions. Biol Cybern 1976;22:213–28. Cizek P. Robust estimation in nonlinear regression models. Sonderforschungsbereich 2001;373:25 Humboldt Universitaet Berlin. Dahlhaus R, Eichler M, Sandkühler J. Identification of synaptic connections in neural ensembles by graphical models. J Neurosci Meth 1997;77:93–107. Eichler M, Dahlhaus R, Sandkühler J. Partial correlation analysis for the identification of synaptic connections. Biol Cybern 2003;89:289–302. Ermentrout GB. Asymptotic behavior of stationary homogeneous neuronal nets. Lecture notes in biomath. Berlin, New York: Springer; 1982 p. 45. Ermentrout GB. Type I membranes, phase resetting curves, and synchrony. Neural Comput 1996;8:979–1001. FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1961;1:445–66. Gerstner W. Time structure of the activity in neural network models. Phys Rev E 1995;51:738–48. Getting PA. Reconstruction of small neural networks. In: Koch C, Segev I, editors. Methods in neuronal modeling: from synapses to networks. A Bradford Book. Cambridge: MIT Press; 1989. p. 171–94. Granger CWJ. Investigating causal relations by econometric models and cross-spectral methods. Econometrica 1969;37:424–38. Harris KD, Henze DA, Csicsvari J, Hirase H, Buzsaki G. Accuracy of tetrode spike separation as determined by simultaneous intracellular and extracellular measurements. J Neurophysiol 2000;84:401–14. Hindmarsh JL, Rose RM. A model of neuronal bursting using three coupled first order differential equations. Proc R Soc London B 1984;221:87–102. Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 1952;117:500–44. Horwitz B. The elusive concept of brain connectivity. NeuroImage 2003;19:466–70. Izhikevich EM. Simple model of spiking neurons. IEEE Trans Neural Netw 2003;14:1569–72. Izhikevich EM. Which model to use for cortical spiking neurons? IEEE Trans Neural Netw 2004;15:1063–70. Jolivet R, Lewis TJ, Gerstner W. Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy. J Neurophysiol 2004;92:959–76. Kaminski M, Ding M, Truccolo W, Bressler S. Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance. Biol Cybern 2001;85:145–57. Kandel ER, Schwartz JH, Jessell TM. Principles of neural science. 4th ed. New York: McGraw-Hill; 2000. Korzeniewska A, Manczak M, Kaminski M, Blinowska K, Kasicki S. Determination of information flow direction among brain structures by a modified directed transfer function (dDTF) method. J Neurosci Meth 2003;125:195–207. Makarov VA. Identification of Neural Connectivity and Modeling (INCAM) package is available at:, 2004. Moore GP, Perkel DP, Segundo JP. Statistical analysis and functional interpretation of neural spike data. Annu Rev Physiol 1966;28:493–522. Motulsky HJ, Christopoulos A. Fitting models to biological data using linear and nonlinear regression. A practical guide to curve fitting. San Diego: GraphPad Software Inc; 2003. Paninski L, Lau B, Reyes A. Noise-driven adaptation: in vitro and mathematical analysis. Neurocomputing 2003;52/54:877–83. Paninski L. Maximum likelihood estimation of cascade point-process neural encoding models. Computation Neural Syst 2004;15:243–62. Pavlov AN, Sosnovtseva OV, Moseckilde E, Anishchenko VS. Chaotic dynamics from interspike intervals. Phys Rev E 2001;63(5):36205. Perkel DH, Gerstein GL, Moore GP. Neuronal spike trains and stochastic point processes. I. The single spike train. Biophys J 1967a;7:391–418. Perkel DH, Gerstein GL, Moore GP. Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. Biophys J 1967b;7:419–40. Pillow JW, Simoncelli EP. Biases in white noise analysis due to non- Poisson spike generation. Neurocomputing 2003;52–54:109–15. Plant RE. Bifurcation and resonance in a model for bursting nerve cells. J Math Biol 1981;11:15–32. Racicot DM, Longtin A. Interspike interval attractors from chaotically driven neuron models. Physica D 1997;104:184–204. Rosenberg JR, Amjad AM, Breeze P, Brillinger DR, Halliday DM. The Fourier approach to the identification of functional coupling between neuronal spike trains. Prog Biophys Mol Biol 1989;53:1–31. Sameshima K, Baccala LA. Using partial directed coherence to describe neuronal ensemble interactions. J Neurosci Meth 1999;94:93–103. Sauer T. Reconstruction of dynamical systems from interspike intervals. Phy Rev Lett 1994;72:3811–4. Segundo JP. Nonlinear dynamics of point process systems and data. Int J Bifurcat Chaos 2003;13(8):2035–116. Stein RB. Some models of neuronal variability. Biophys J 1967;7:37–68. van Vreeswijk CA, Abbott LF, Ermentrout GB. Inhibition, not excitation, synchronizes coupled neurons. J Comput Neurosci 1995;1:303–13.