REVIEW ARTICLE: Neuronal coding and spiking randomness

Fast information transfer in neuronal systems rests on series of action potentials, the spike trains, conducted along axons. Methods that compare spike trains are crucial for characterizing different neuronal coding schemes. In this paper we review recent results on the notion of spiking randomness, and discuss its properties with respect to the rate and temporal coding schemes. This method is compared with other widely used characteristics of spiking activity, namely the variability of interspike intervals, and it is shown that randomness and variability provide two distinct views. We demonstrate that estimation of spiking randomness from simulated and experimental data is capable of capturing characteristics that would otherwise be difficult to obtain with conventional methods.

[1]  Henry C. Tuckwell,et al.  Introduction to theoretical neurobiology , 1988 .

[2]  J. Victor Binless strategies for estimation of information from neural data. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  H K Hartline,et al.  Variability of interspike intervals in optic nerve fibers of Limulus: effect of light and dark adaptation. , 1968, Proceedings of the National Academy of Sciences of the United States of America.

[4]  M. Tribus,et al.  Probability theory: the logic of science , 2003 .

[5]  Petr Lánský,et al.  Variability and randomness in stationary neuronal activity , 2007, Biosyst..

[6]  William R. Softky,et al.  Simple codes versus efficient codes , 1995, Current Opinion in Neurobiology.

[7]  Professor Moshe Abeles,et al.  Local Cortical Circuits , 1982, Studies of Brain Function.

[8]  L. Devroye Non-Uniform Random Variate Generation , 1986 .

[9]  A. J. Lawrance,et al.  An exponential moving-average sequence and point process (EMA1) , 1977, Journal of Applied Probability.

[10]  J. García-Ojalvo,et al.  Effects of noise in excitable systems , 2004 .

[11]  Kelvin E. Jones,et al.  Neuronal variability: noise or part of the signal? , 2005, Nature Reviews Neuroscience.

[12]  D. T. Kaplan,et al.  Nonlinear dynamics and time series : building a bridge between the natural and statistical sciences , 2006 .

[13]  A. Tsybakov,et al.  Root-N consistent estimators of entropy for densities with unbounded support , 1994, Proceedings of 1994 Workshop on Information Theory and Statistics.

[14]  T. Albright,et al.  Gauging sensory representations in the brain , 1999, Trends in Neurosciences.

[15]  E. D. Adrian,et al.  The Basis of Sensation , 1928, The Indian Medical Gazette.

[16]  John W. Fisher,et al.  ICA Using Spacings Estimates of Entropy , 2003, J. Mach. Learn. Res..

[17]  Petr Lánský,et al.  Two-Compartment Stochastic Model of a Neuron with Periodic Input , 1999, IWANN.

[18]  G. P. Moore,et al.  Statistical analysis and functional interpretation of neuronal spike data. , 1966, Annual review of physiology.

[19]  P. Lánský,et al.  Randomness and variability of the neuronal activity described by the Ornstein–Uhlenbeck model , 2007, Network.

[20]  W. Newsome,et al.  The Variable Discharge of Cortical Neurons: Implications for Connectivity, Computation, and Information Coding , 1998, The Journal of Neuroscience.

[21]  P. Lánský,et al.  Properties of the extra-positional signal in hippocampal place cell discharge derived from the overdispersion in location-specific firing , 2002, Neuroscience.

[22]  G. Poggio,et al.  TIME SERIES ANALYSIS OF IMPULSE SEQUENCES OF THALAMIC SOMATIC SENSORY NEURONS. , 1964, Journal of neurophysiology.

[23]  R Ratnam,et al.  Nonrenewal Statistics of Electrosensory Afferent Spike Trains: Implications for the Detection of Weak Sensory Signals , 2000, The Journal of Neuroscience.

[24]  M. Alexander,et al.  Principles of Neural Science , 1981 .

[25]  William R. Softky,et al.  The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[26]  D. R. Smith,et al.  A STATISTICAL ANALYSIS OF THE CONTINUAL ACTIVITY OF SINGLE CORTICAL NEURONES IN THE CAT UNANAESTHETIZED ISOLATED FOREBRAIN. , 1965, Biophysical journal.

[27]  Don H. Johnson,et al.  When does interval coding occur? , 2003, Neurocomputing.

[28]  Lutz Schimansky-Geier,et al.  Maximizing spike train coherence or incoherence in the leaky integrate-and-fire model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Wulfram Gerstner,et al.  SPIKING NEURON MODELS Single Neurons , Populations , Plasticity , 2002 .

[30]  J. Goldberg,et al.  RESPONSE OF NEURONS OF THE SUPERIOR OLIVARY COMPLEX OF THE CAT TO ACOUSTIC STIMULI OF LONG DURATION. , 1964, Journal of neurophysiology.

[31]  R. Quiroga,et al.  Kulback-Leibler and renormalized entropies: applications to electroencephalograms of epilepsy patients. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  M. Tsukada,et al.  Effect of correlated adjacent interspike interval sequences of the excitatory motor axon on the opening movement of the crayfish claw opener muscles , 1978, Biological Cybernetics.

[33]  J. Leroy Folks,et al.  The Inverse Gaussian Distribution: Theory: Methodology, and Applications , 1988 .

[34]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[35]  S Yamada,et al.  Information theoretic analysis of action potential trains , 2004, Biological Cybernetics.

[36]  Petr Lánský,et al.  Similarity of interspike interval distributions and information gain in a stationary neuronal firing , 2006, Biological Cybernetics.

[37]  Robert E Kass,et al.  Statistical issues in the analysis of neuronal data. , 2005, Journal of neurophysiology.

[38]  A. Kraskov,et al.  Estimating mutual information. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Anthony N. Burkitt,et al.  A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input , 2006, Biological Cybernetics.

[40]  William Bialek,et al.  Entropy and information in neural spike trains: progress on the sampling problem. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  John P. Miller,et al.  Temporal encoding in nervous systems: A rigorous definition , 1995, Journal of Computational Neuroscience.

[42]  Shanbao Tong,et al.  Advances in quantitative electroencephalogram analysis methods. , 2004, Annual review of biomedical engineering.

[43]  Liam Paninski,et al.  Estimation of Entropy and Mutual Information , 2003, Neural Computation.

[44]  Jonathan D. Victor,et al.  Metric-space analysis of spike trains: theory, algorithms and application , 1998, q-bio/0309031.

[45]  Don H. Johnson,et al.  Information-theoretic analysis of neural coding , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[46]  Don H. Johnson,et al.  Information-Theoretic Analysis of Neural Coding , 2004, Journal of Computational Neuroscience.

[47]  Michael N. Shadlen,et al.  Noise, neural codes and cortical organization , 1994, Current Opinion in Neurobiology.

[48]  M. E. Castellanos,et al.  MONTE CARLO COMPARISON OF FOUR NORMALITY TESTS USING DIFFERENT ENTROPY ESTIMATES , 2001 .

[49]  J. Rospars,et al.  Patterns of spontaneous activity in single rat olfactory receptor neurons are different in normally breathing and tracheotomized animals. , 2005, Journal of neurobiology.

[50]  Michael W. Levine,et al.  The distribution of the intervals between neural impulses in the maintained discharges of retinal ganglion cells , 1991, Biological Cybernetics.

[51]  Oldrich A Vasicek,et al.  A Test for Normality Based on Sample Entropy , 1976 .

[52]  L. Györfi,et al.  Nonparametric entropy estimation. An overview , 1997 .

[53]  L. Maler,et al.  Negative Interspike Interval Correlations Increase the Neuronal Capacity for Encoding Time-Dependent Stimuli , 2001, The Journal of Neuroscience.

[54]  F. Downton Bivariate Exponential Distributions in Reliability Theory , 1970 .

[55]  M. Abeles,et al.  Firing Rates and Weil-Timed Events in the Cerebral Cortex , 1994 .

[56]  G. Mandl,et al.  Coding for stimulus velocity by temporal patterning of spike discharges in visual cells of cat superior colliculus , 1993, Vision Research.

[57]  Nader Ebrahimi,et al.  Testing exponentiality based on Kullback-Leibler information , 1992 .

[58]  B. Burns,et al.  Contrast discrimination by neurones in the cat's visual cerebral cortex , 1964, The Journal of physiology.

[59]  K. Kopitzki,et al.  Quantitative analysis by renormalized entropy of invasive electroencephalograph recordings in focal epilepsy , 1998, physics/9808008.

[60]  R. Adams I. The Synthesis of D- and L-Threo- and D- and L-Erythro-α-Amino-β-hydroxy-n-caproic Acids. II. Experiments on the Preparation of α-Aminoalkanesulfonamides. III. The Influence of Nerve Impulse Sequence on the Contractions of Different Crustacean Muscles , 1950 .

[61]  Eytan Domany,et al.  Models of Neural Networks I , 1991 .

[62]  William Bialek,et al.  Spikes: Exploring the Neural Code , 1996 .

[63]  William Bialek,et al.  Entropy and Information in Neural Spike Trains , 1996, cond-mat/9603127.

[64]  Dorothy E. F. McKeegan,et al.  Spontaneous and odour evoked activity in single avian olfactory bulb neurones , 2002, Brain Research.

[65]  Jack P. Landolt,et al.  Neuromathematical Concepts of Point Process Theory , 1978, IEEE Transactions on Biomedical Engineering.

[66]  K. Pribram,et al.  An analysis of neural spike-train distributions: determinants of the response of visual cortex neurons to changes in orientation and spatial frequency , 2004, Experimental Brain Research.

[67]  Petr Lánský,et al.  Two-compartment stochastic model of a neuron , 1999 .

[68]  Yutaka Sakai,et al.  Temporally correlated inputs to leaky integrate-and-fire models can reproduce spiking statistics of cortical neurons , 1999, Neural Networks.

[69]  Benjamin Lindner,et al.  Interspike interval statistics of neurons driven by colored noise. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[70]  Petr Lánský,et al.  Spontaneous activity of first- and second-order neurons in the frog olfactory system , 1994, Brain Research.

[71]  David R. Cox,et al.  The statistical analysis of series of events , 1966 .

[72]  P. Lánský,et al.  Classification of stationary neuronal activity according to its information rate , 2006, Network.

[73]  R. Stein Some models of neuronal variability. , 1967, Biophysical journal.

[74]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[75]  Gary S Bhumbra,et al.  Assessment of Spike Activity in the Supraoptic Nucleus , 2004, Journal of neuroendocrinology.

[76]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .