Analyzing Functional Connectivity Using a Network Likelihood Model of Ensemble Neural Spiking Activity

Analyzing the dependencies between spike trains is an important step in understanding how neurons work in concert to represent biological signals. Usually this is done for pairs of neurons at a time using correlation-based techniques. Chornoboy, Schramm, and Karr (1988) proposed maximum likelihood methods for the simultaneous analysis of multiple pair-wise interactions among an ensemble of neurons. One of these methods is an iterative, continuous-time estimation algorithm for a network likelihood model formulated in terms of multiplicative conditional intensity functions. We devised a discrete-time version of this algorithm that includes a new, efficient computational strategy, a principled method to compute starting values, and a principled stopping criterion. In an analysis of simulated neural spike trains from ensembles of interacting neurons, the algorithm recovered the correct connectivity matrices and interaction parameters. In the analysis of spike trains from an ensemble of rat hippocampal place cells, the algorithm identified a connectivity matrix and interaction parameters consistent with the pattern of conjoined firing predicted by the overlap of the neurons' spatial receptive fields. These results suggest that the network likelihood model can be an efficient tool for the analysis of ensemble spiking activity.

[1]  David Eugene Smith,et al.  A source book in mathematics , 1930 .

[2]  B G Lindsey,et al.  Functional connectivity among ventrolateral medullary respiratory neurones and responses during fictive cough in the cat , 2000, The Journal of physiology.

[3]  Carlos D. Brody,et al.  Disambiguating Different Covariation Types , 1999, Neural Computation.

[4]  Andrea Mechelli,et al.  A report of the functional connectivity workshop, Dusseldorf 2002 , 2003, NeuroImage.

[5]  B G Lindsey,et al.  Functional connectivity between brain stem midline neurons with respiratory-modulated firing rates. , 1992, Journal of neurophysiology.

[6]  C. Brody Slow covariations in neuronal resting potentials can lead to artefactually fast cross-correlations in their spike trains. , 1998, Journal of neurophysiology.

[7]  E N Brown,et al.  A Statistical Paradigm for Neural Spike Train Decoding Applied to Position Prediction from Ensemble Firing Patterns of Rat Hippocampal Place Cells , 1998, The Journal of Neuroscience.

[8]  J. B. Ranck,et al.  Spatial firing patterns of hippocampal complex-spike cells in a fixed environment , 1987, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[9]  Y. Pawitan In all likelihood : statistical modelling and inference using likelihood , 2002 .

[10]  H. L. Bryant,et al.  Identification of synaptic interactions , 1976, Biological Cybernetics.

[11]  M. Wilson,et al.  Temporally Structured Replay of Awake Hippocampal Ensemble Activity during Rapid Eye Movement Sleep , 2001, Neuron.

[12]  D. Perkel,et al.  Cooperative firing activity in simultaneously recorded populations of neurons: detection and measurement , 1985, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[13]  D. Brillinger The Identification of Point Process Systems , 1975 .

[14]  Kevin L. Briggman,et al.  Towards neural circuit reconstruction with volume electron microscopy techniques , 2006, Current Opinion in Neurobiology.

[15]  George L. Gerstein,et al.  Improvements to the Sensitivity of Gravitational Clustering for Multiple Neuron Recordings , 2000, Neural Computation.

[16]  G. Schoenbaum,et al.  Changes in Functional Connectivity in Orbitofrontal Cortex and Basolateral Amygdala during Learning and Reversal Training , 2000, The Journal of Neuroscience.

[17]  V. I. Kryukov,et al.  A new statistical method for identifying interconnections between neuronal network elements , 1985, Biological Cybernetics.

[18]  Karl J. Friston,et al.  Functional Connectivity: The Principal-Component Analysis of Large (PET) Data Sets , 1993, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[19]  Matthew A. Wilson,et al.  Dynamic Analyses of Information Encoding in Neural Ensembles , 2004, Neural Computation.

[20]  Donald L. Snyder,et al.  Random Point Processes in Time and Space , 1991 .

[21]  David G. Luenberger,et al.  Linear and Nonlinear Programming: Second Edition , 2003 .

[22]  David R. Brillinger,et al.  Nerve Cell Spike Train Data Analysis: A Progression of Technique , 1992 .

[23]  G. P. Moore,et al.  Statistical signs of synaptic interaction in neurons. , 1970, Biophysical journal.

[24]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[25]  G L Gerstein,et al.  Mutual temporal relationships among neuronal spike trains. Statistical techniques for display and analysis. , 1972, Biophysical journal.

[26]  E. K. Miller,et al.  Functional interactions among neurons in inferior temporal cortex of the awake macaque , 2004, Experimental Brain Research.

[27]  Matthew A Wilson,et al.  A combinatorial method for analyzing sequential firing patterns involving an arbitrary number of neurons based on relative time order. , 2004, Journal of neurophysiology.

[28]  Carlos D. Brody,et al.  Correlations Without Synchrony , 1999, Neural Computation.

[29]  Rhonda Dzakpasu,et al.  Measuring asymmetric temporal interdependencies in simulated and biological networks. , 2006, Chaos.

[30]  H. Boogaard Maximum likelihood estimations in a nonlinear self-exciting point process model , 1986, Biological Cybernetics.

[31]  A. Aertsen,et al.  On the significance of correlations among neuronal spike trains , 2004, Biological Cybernetics.

[32]  Alan F. Karr,et al.  Point Processes and Their Statistical Inference , 1991 .

[33]  Emery N. Brown,et al.  Computational Neuroscience: A Comprehensive Approach , 2022 .

[34]  George L. Gerstein,et al.  Cortical auditory neuron interactions during presentation of 3-tone sequences: effective connectivity , 1988, Brain Research.

[35]  M K Habib,et al.  Dynamics of neuronal firing correlation: modulation of "effective connectivity". , 1989, Journal of neurophysiology.

[36]  J. O'Keefe,et al.  The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. , 1971, Brain research.

[37]  E. S. Chornoboy,et al.  Maximum likelihood identification of neural point process systems , 1988, Biological Cybernetics.

[38]  P. A. W. Lewis,et al.  Multivariate point processes , 2018, Point Processes.

[39]  Sonja Grün,et al.  Non-parametric significance estimation of joint-spike events by shuffling and resampling , 2003, Neurocomputing.

[40]  B. McNaughton,et al.  Multistability of cognitive maps in the hippocampus of old rats , 1997, Nature.

[41]  D. Brillinger Maximum likelihood analysis of spike trains of interacting nerve cells , 2004, Biological Cybernetics.

[42]  A. Aertsen,et al.  Dynamics of neuronal interactions in monkey cortex in relation to behavioural events , 1995, Nature.

[43]  G. P. Moore,et al.  Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. , 1967, Biophysical journal.

[44]  I. Jolliffe Principal Component Analysis , 2002 .

[45]  D. Brillinger The maximum likelihood approach to the identification of neuronal firing systems , 2006, Annals of Biomedical Engineering.

[46]  G L Gerstein,et al.  Detecting spatiotemporal firing patterns among simultaneously recorded single neurons. , 1988, Journal of neurophysiology.

[47]  B J Richmond,et al.  Stochastic nature of precisely timed spike patterns in visual system neuronal responses. , 1999, Journal of neurophysiology.

[48]  J J Eggermont,et al.  Neuronal pair and triplet interactions in the auditory midbrain of the leopard frog. , 1991, Journal of neurophysiology.

[49]  Jerald D. Kralik,et al.  Chronic, multisite, multielectrode recordings in macaque monkeys , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[50]  B. McNaughton,et al.  Replay of Neuronal Firing Sequences in Rat Hippocampus During Sleep Following Spatial Experience , 1996, Science.

[51]  B. McNaughton,et al.  The contributions of position, direction, and velocity to single unit activity in the hippocampus of freely-moving rats , 2004, Experimental Brain Research.

[52]  George L. Gerstein,et al.  Plasticity of Synchronous Activity in a Small Neural Net , 1970, Science.

[53]  James A. Kaltenbach,et al.  Dynamic temporal properties of effective connections in rat dorsal cochlear nucleus , 1990, Brain Research.

[54]  H Preißl,et al.  Dynamics of activity and connectivity in physiological neuronal networks , 1991 .

[55]  R. Kass,et al.  Multiple neural spike train data analysis: state-of-the-art and future challenges , 2004, Nature Neuroscience.

[56]  A. Aertsen,et al.  Evaluation of neuronal connectivity: Sensitivity of cross-correlation , 1985, Brain Research.

[57]  D. Perkel,et al.  Simultaneously Recorded Trains of Action Potentials: Analysis and Functional Interpretation , 1969, Science.

[58]  Mitchell J. Mergenthaler Nonparametrics: Statistical Methods Based on Ranks , 1979 .

[59]  B G Lindsey,et al.  Multimodal medullary neurons and correlational linkages of the respiratory network. , 1999, Journal of neurophysiology.

[60]  B. McNaughton,et al.  Reactivation of hippocampal ensemble memories during sleep. , 1994, Science.

[61]  Emery N. Brown,et al.  The Time-Rescaling Theorem and Its Application to Neural Spike Train Data Analysis , 2002, Neural Computation.

[62]  B. McNaughton,et al.  Spatial Firing Properties of Hippocampal CA1 Populations in an Environment Containing Two Visually Identical Regions , 1998, The Journal of Neuroscience.

[63]  D. Brillinger Estimation of the Second-Order Intensities of a Bivariate Stationary Point Process , 1976 .

[64]  A. Aertsen,et al.  Representation of cooperative firing activity among simultaneously recorded neurons. , 1985, Journal of neurophysiology.

[65]  J. Jacod Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales , 1975 .

[66]  B L McNaughton,et al.  Dynamics of the hippocampal ensemble code for space. , 1993, Science.

[67]  D. Q. Nykamp,et al.  A mathematical framework for inferring connectivity in probabilistic neuronal networks. , 2007, Mathematical biosciences.

[68]  P. Wallis,et al.  A Source Book in Mathematics, 1200-1800 , 1971, The Mathematical Gazette.

[69]  Albert K. Lee,et al.  Memory of Sequential Experience in the Hippocampus during Slow Wave Sleep , 2002, Neuron.

[70]  J. O’Keefe,et al.  Phase relationship between hippocampal place units and the EEG theta rhythm , 1993, Hippocampus.