Separating Spike Count Correlation from Firing Rate Correlation

Populations of cortical neurons exhibit shared fluctuations in spiking activity over time. When measured for a pair of neurons over multiple repetitions of an identical stimulus, this phenomenon emerges as correlated trial-to-trial response variability via spike count correlation (SCC). However, spike counts can be viewed as noisy versions of firing rates, which can vary from trial to trial. From this perspective, the SCC for a pair of neurons becomes a noisy version of the corresponding firing rate correlation (FRC). Furthermore, the magnitude of the SCC is generally smaller than that of the FRC and is likely to be less sensitive to experimental manipulation. We provide statistical methods for disambiguating time-averaged drive from within-trial noise, thereby separating FRC from SCC. We study these methods to document their reliability, and we apply them to neurons recorded in vivo from area V4 in an alert animal. We show how the various effects we describe are reflected in the data: within-trial effects are largely negligible, while attenuation due to trial-to-trial variation dominates and frequently produces comparisons in SCC that, because of noise, do not accurately reflect those based on the underlying FRC.

[1]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[2]  Asohan Amarasingham,et al.  Statistical Identification of Synchronous Spiking , 2013 .

[3]  Robert E Kass,et al.  Trial-to-trial variability and its effect on time-varying dependency between two neurons. , 2005, Journal of neurophysiology.

[4]  Jonathan D. Victor,et al.  Spike timing : mechanisms and function , 2013 .

[5]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

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

[7]  Alexander S. Ecker,et al.  State Dependence of Noise Correlations in Macaque Primary Visual Cortex , 2014, Neuron.

[8]  Yong Gu,et al.  Perceptual Learning Reduces Interneuronal Correlations in Macaque Visual Cortex , 2011, Neuron.

[9]  Wei Ji Ma,et al.  Bayesian inference with probabilistic population codes , 2006, Nature Neuroscience.

[10]  K. Harris,et al.  Cortical state and attention , 2011, Nature Reviews Neuroscience.

[11]  Tai Sing Lee,et al.  Local field potentials indicate network state and account for neuronal response variability , 2010, Journal of Computational Neuroscience.

[12]  M. A. Smith,et al.  Spatial and Temporal Scales of Neuronal Correlation in Primary Visual Cortex , 2008, The Journal of Neuroscience.

[13]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[14]  J. Maunsell,et al.  Attention improves performance primarily by reducing interneuronal correlations , 2009, Nature Neuroscience.

[15]  Y. Benjamini,et al.  THE CONTROL OF THE FALSE DISCOVERY RATE IN MULTIPLE TESTING UNDER DEPENDENCY , 2001 .

[16]  Jude F. Mitchell,et al.  Spatial Attention Decorrelates Intrinsic Activity Fluctuations in Macaque Area V4 , 2009, Neuron.

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

[18]  M. Cohen,et al.  Measuring and interpreting neuronal correlations , 2011, Nature Neuroscience.

[19]  Marc A Sommer,et al.  Spatial and Temporal Scales of Neuronal Correlation in Visual Area V4 , 2013, The Journal of Neuroscience.

[20]  Eero P. Simoncelli,et al.  Partitioning neuronal variability , 2014, Nature Neuroscience.

[21]  Timothy Q. Gentner,et al.  Associative Learning Enhances Population Coding by Inverting Interneuronal Correlation Patterns , 2013, Neuron.

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

[23]  M Steriade,et al.  Disfacilitation and active inhibition in the neocortex during the natural sleep-wake cycle: an intracellular study. , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Robert E. Kass,et al.  Spike Count Correlation Increases with Length of Time Interval in the Presence of Trial-to-Trial Variation , 2006, Neural Computation.

[25]  A. Pouget,et al.  Variance as a Signature of Neural Computations during Decision Making , 2011, Neuron.

[26]  J. Anthony Movshon,et al.  Comparison of Recordings from Microelectrode Arrays and Single Electrodes in the Visual Cortex , 2007, The Journal of Neuroscience.

[27]  Robert E Kass,et al.  Bayesian correction for attenuation of correlation in multi-trial spike count data. , 2009, Journal of neurophysiology.

[28]  C. Wilson,et al.  Spontaneous firing patterns and axonal projections of single corticostriatal neurons in the rat medial agranular cortex. , 1994, Journal of neurophysiology.

[29]  D. Butts,et al.  Tuning Curves, Neuronal Variability, and Sensory Coding , 2006, PLoS biology.

[30]  Sonja Grün,et al.  Can Spike Coordination Be Differentiated from Rate Covariation? , 2008, Neural Computation.

[31]  M. Steriade,et al.  Natural waking and sleep states: a view from inside neocortical neurons. , 2001, Journal of neurophysiology.

[32]  Maria L. Rizzo,et al.  Brownian distance covariance , 2009, 1010.0297.

[33]  Asohan Amarasingham,et al.  Ambiguity and nonidentifiability in the statistical analysis of neural codes , 2015, Proceedings of the National Academy of Sciences.

[34]  Robert E. Kass,et al.  A Framework for Evaluating Pairwise and Multiway Synchrony Among Stimulus-Driven Neurons , 2012, Neural Computation.

[35]  J. A. Movshon,et al.  The dependence of response amplitude and variance of cat visual cortical neurones on stimulus contrast , 1981, Experimental Brain Research.

[36]  Emery N. Brown,et al.  Analysis of Neural Data , 2014 .

[37]  G. J. Tomko,et al.  Neuronal variability: non-stationary responses to identical visual stimuli. , 1974, Brain research.

[38]  Angelo J. Canty,et al.  Bootstrap diagnostics and remedies , 2006 .