The mechanics of state-dependent neural correlations

Simultaneous recordings from large neural populations are becoming increasingly common. An important feature of population activity is the trial-to-trial correlated fluctuation of spike train outputs from recorded neuron pairs. Similar to the firing rate of single neurons, correlated activity can be modulated by a number of factors, from changes in arousal and attentional state to learning and task engagement. However, the physiological mechanisms that underlie these changes are not fully understood. We review recent theoretical results that identify three separate mechanisms that modulate spike train correlations: changes in input correlations, internal fluctuations and the transfer function of single neurons. We first examine these mechanisms in feedforward pathways and then show how the same approach can explain the modulation of correlations in recurrent networks. Such mechanistic constraints on the modulation of population activity will be important in statistical analyses of high-dimensional neural data.

[1]  M. Tsodyks,et al.  Working models of working memory , 2014, Current Opinion in Neurobiology.

[2]  C. Petersen,et al.  Cholinergic signals in mouse barrel cortex during active whisker sensing. , 2014, Cell reports.

[3]  Kenneth D Miller,et al.  Processing in layer 4 of the neocortical circuit: new insights from visual and somatosensory cortex , 2001, Current Opinion in Neurobiology.

[4]  George H. Denfield,et al.  Pupil Fluctuations Track Fast Switching of Cortical States during Quiet Wakefulness , 2014, Neuron.

[5]  H. Sompolinsky,et al.  Theory of orientation tuning in visual cortex. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Benjamin Lindner,et al.  Spike-count distribution in a neuronal population under weak common stimulation. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Fred Wolf,et al.  Correlations and synchrony in threshold neuron models. , 2008, Physical review letters.

[8]  Henry Markram,et al.  Coding of temporal information by activity-dependent synapses. , 2002, Journal of neurophysiology.

[9]  Dmitry R Lyamzin,et al.  Nonlinear Transfer of Signal and Noise Correlations in Cortical Networks , 2015, The Journal of Neuroscience.

[10]  Maurice J. Chacron,et al.  Activation of Parallel Fiber Feedback by Spatially Diffuse Stimuli Reduces Signal and Noise Correlations via Independent Mechanisms in a Cerebellum-Like Structure , 2015, PLoS Comput. Biol..

[11]  D. Vere-Jones.  SIMPLE STOCHASTIC MODELS FOR THE RELEASE OF QUANTA OF TRANSMITTER FROM A NERVE TERMINAL , 1966 .

[12]  D. W. Wheeler,et al.  Brightness Induction: Rate Enhancement and Neuronal Synchronization as Complementary Codes , 2006, Neuron.

[13]  Jessica A. Cardin,et al.  Cellular Mechanisms Underlying Stimulus-Dependent Gain Modulation in Primary Visual Cortex Neurons In Vivo , 2008, Neuron.

[14]  Haim Sompolinsky,et al.  Chaotic Balanced State in a Model of Cortical Circuits , 1998, Neural Computation.

[15]  Srdjan Ostojic,et al.  Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons , 2014, Nature Neuroscience.

[16]  John Hertz,et al.  Cross-Correlations in High-Conductance States of a Model Cortical Network , 2010, Neural Computation.

[17]  D. Ferster,et al.  Neural mechanisms of orientation selectivity in the visual cortex. , 2000, Annual review of neuroscience.

[18]  B. Doiron,et al.  Short-term synaptic depression and stochastic vesicle dynamics reduce and shape neuronal correlations. , 2013, Journal of neurophysiology.

[19]  Alexander S. Ecker,et al.  The Effect of Noise Correlations in Populations of Diversely Tuned Neurons , 2011, The Journal of Neuroscience.

[20]  Xiao-Jing Wang,et al.  The importance of mixed selectivity in complex cognitive tasks , 2013, Nature.

[21]  Nicolas Fourcaud-Trocmé,et al.  Correlation-induced Synchronization of Oscillations in Olfactory Bulb Neurons , 2022 .

[22]  Kenneth D Harris,et al.  Stochastic transitions into silence cause noise correlations in cortical circuits , 2015, Proceedings of the National Academy of Sciences.

[23]  K. Svoboda,et al.  Genetic Dissection of Neural Circuits , 2008, Neuron.

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

[25]  Ovidiu F. Jurjuţ,et al.  Effects of Locomotion Extend throughout the Mouse Early Visual System , 2014, Current Biology.

[26]  Valentin Dragoi,et al.  Correlated Variability in Laminar Cortical Circuits , 2012, Neuron.

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

[28]  Stefan Rotter,et al.  How Structure Determines Correlations in Neuronal Networks , 2011, PLoS Comput. Biol..

[29]  D. Hubel,et al.  Receptive fields, binocular interaction and functional architecture in the cat's visual cortex , 1962, The Journal of physiology.

[30]  Mark S. Goldman,et al.  Enhancement of Information Transmission Efficiency by Synaptic Failures , 2004, Neural Computation.

[31]  Wulfram Gerstner,et al.  Neuronal Dynamics: From Single Neurons To Networks And Models Of Cognition , 2014 .

[32]  A. Pouget,et al.  Neural correlations, population coding and computation , 2006, Nature Reviews Neuroscience.

[33]  P. J. Sjöström,et al.  Functional specificity of local synaptic connections in neocortical networks , 2011, Nature.

[34]  Brent Doiron,et al.  The Spatial Structure of Stimuli Shapes the Timescale of Correlations in Population Spiking Activity , 2012, PLoS Comput. Biol..

[35]  Henry Markram,et al.  Neural Networks with Dynamic Synapses , 1998, Neural Computation.

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

[37]  Mauricio Barahona,et al.  Emergence of Slow-Switching Assemblies in Structured Neuronal Networks , 2015, PLoS Comput. Biol..

[38]  Mamiko Niwa,et al.  Task Engagement Selectively Modulates Neural Correlations in Primary Auditory Cortex , 2015, The Journal of Neuroscience.

[39]  Eric Shea-Brown,et al.  Time scales of spike-train correlation for neural oscillators with common drive. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  R. Romo,et al.  Correlated Neuronal Discharges that Increase Coding Efficiency during Perceptual Discrimination , 2003, Neuron.

[41]  R. Guillery,et al.  On the actions that one nerve cell can have on another: distinguishing "drivers" from "modulators". , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[42]  Eric Shea-Brown,et al.  Impact of Network Structure and Cellular Response on Spike Time Correlations , 2011, PLoS Comput. Biol..

[43]  Randy M Bruno,et al.  Feedforward Mechanisms of Excitatory and Inhibitory Cortical Receptive Fields , 2002, The Journal of Neuroscience.

[44]  A. Litwin-Kumar,et al.  Slow dynamics and high variability in balanced cortical networks with clustered connections , 2012, Nature Neuroscience.

[45]  Byron M. Yu,et al.  Dimensionality reduction for large-scale neural recordings , 2014, Nature Neuroscience.

[46]  D. Hansel,et al.  How Noise Contributes to Contrast Invariance of Orientation Tuning in Cat Visual Cortex , 2002, The Journal of Neuroscience.

[47]  J. Poulet,et al.  Internal brain state regulates membrane potential synchrony in barrel cortex of behaving mice , 2008, Nature.

[48]  Moritz Helias,et al.  Correlations in spiking neuronal networks with distance dependent connections , 2009, Journal of Computational Neuroscience.

[49]  Guangying K. Wu,et al.  Defining cortical frequency tuning with recurrent excitatory circuitry , 2007, Nature Neuroscience.

[50]  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.

[51]  M. Carandini.  Amplification of Trial-to-Trial Response Variability by Neurons in Visual Cortex , 2004, PLoS biology.

[52]  Cheng Ly,et al.  Cellular and Circuit Mechanisms Maintain Low Spike Co-Variability and Enhance Population Coding in Somatosensory Cortex , 2012, Front. Comput. Neurosci..

[53]  Brent Doiron,et al.  Subtractive and Divisive Inhibition: Effect of Voltage-Dependent Inhibitory Conductances and Noise , 2001, Neural Computation.

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

[55]  Shawn D. Burton,et al.  Impact of neuronal heterogeneity on correlated colored noise-induced synchronization , 2013, Front. Comput. Neurosci..

[56]  Timothy D. Hanks,et al.  Probabilistic Population Codes for Bayesian Decision Making , 2008, Neuron.

[57]  David Hansel,et al.  Asynchronous Rate Chaos in Spiking Neuronal Circuits , 2015, bioRxiv.

[58]  N. Parga,et al.  Short-term Synaptic Depression Causes a Non-monotonic Response to Correlated Stimuli , 2022 .

[59]  Valentin Dragoi,et al.  Adaptive coding of visual information in neural populations , 2008, Nature.

[60]  A. Pouget,et al.  Information-limiting correlations , 2014, Nature Neuroscience.

[61]  Brent Doiron,et al.  Short Term Synaptic Depression Imposes a Frequency Dependent Filter on Synaptic Information Transfer , 2012, PLoS Comput. Biol..

[62]  David Ferster,et al.  Membrane Potential Synchrony in Primary Visual Cortex during Sensory Stimulation , 2010, Neuron.

[63]  Olivier Ledoit,et al.  A well-conditioned estimator for large-dimensional covariance matrices , 2004 .

[64]  Robert Desimone,et al.  Lesions of prefrontal cortex reduce attentional modulation of neuronal responses and synchrony in V4 , 2014, Nature Neuroscience.

[65]  B. Ermentrout.  Neural networks as spatio-temporal pattern-forming systems , 1998 .

[66]  Ad Aertsen,et al.  Role of Input Correlations in Shaping the Variability and Noise Correlations of Evoked Activity in the Neocortex , 2015, The Journal of Neuroscience.

[67]  Yu Hu,et al.  The Sign Rule and Beyond: Boundary Effects, Flexibility, and Noise Correlations in Neural Population Codes , 2013, PLoS Comput. Biol..

[68]  G A Cecchi,et al.  Noise in neurons is message dependent. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[69]  Brent Doiron,et al.  Kv7 channels regulate pairwise spiking covariability in health and disease. , 2014, Journal of neurophysiology.

[70]  Sungho Hong,et al.  Single Neuron Firing Properties Impact Correlation-Based Population Coding , 2012, The Journal of Neuroscience.

[71]  Lief E. Fenno,et al.  The development and application of optogenetics. , 2011, Annual review of neuroscience.

[72]  Konrad P Kording,et al.  How advances in neural recording affect data analysis , 2011, Nature Neuroscience.

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

[74]  Nicholas J. Priebe,et al.  Inhibition, Spike Threshold, and Stimulus Selectivity in Primary Visual Cortex , 2008, Neuron.

[75]  Robert Rosenbaum,et al.  Mechanisms That Modulate the Transfer of Spiking Correlations , 2011, Neural Computation.

[76]  Brent Doiron,et al.  Balanced neural architecture and the idling brain , 2014, Front. Comput. Neurosci..

[77]  D. McCormick,et al.  Waking State: Rapid Variations Modulate Neural and Behavioral Responses , 2015, Neuron.

[78]  Sompolinsky,et al.  Theory of correlations in stochastic neural networks. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[79]  Haim Sompolinsky,et al.  Stimulus-Dependent Correlations in Threshold-Crossing Spiking Neurons , 2009, Neural Computation.

[80]  J T Rubinstein,et al.  Threshold fluctuations in an N sodium channel model of the node of Ranvier. , 1995, Biophysical journal.

[81]  Martin Vinck,et al.  Arousal and Locomotion Make Distinct Contributions to Cortical Activity Patterns and Visual Encoding , 2014, Neuron.

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

[83]  Yuzhi Chen,et al.  Sensory stimulation shifts visual cortex from synchronous to asynchronous states , 2014, Nature.

[84]  Néstor Parga,et al.  ournal of Statistical Mechanics : J Theory and Experiment Towards a self-consistent description of irregular and asynchronous cortical activity , 2013 .

[85]  Brent Doiron,et al.  Neural Correlation Is Stimulus Modulated by Feedforward Inhibitory Circuitry , 2012, The Journal of Neuroscience.

[86]  Alexander Thiele,et al.  Attention-Induced Variance and Noise Correlation Reduction in Macaque V1 Is Mediated by NMDA Receptors , 2013, Neuron.

[87]  Moritz Helias,et al.  Decorrelation of Neural-Network Activity by Inhibitory Feedback , 2012, PLoS Comput. Biol..

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

[89]  P. Dayan,et al.  Supporting Online Material Materials and Methods Som Text Figs. S1 to S9 References the Asynchronous State in Cortical Circuits , 2022 .

[90]  Jaime de la Rocha,et al.  Supplementary Information for the article ‘ Correlation between neural spike trains increases with firing rate ’ , 2007 .

[91]  Nicolas Brunel,et al.  Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates , 1999, Neural Computation.

[92]  W. Bair,et al.  Correlated Firing in Macaque Visual Area MT: Time Scales and Relationship to Behavior , 2001, The Journal of Neuroscience.

[93]  Brent Doiron,et al.  Theory of oscillatory firing induced by spatially correlated noise and delayed inhibitory feedback. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[94]  Nathaniel N. Urban,et al.  Balanced Synaptic Input Shapes the Correlation between Neural Spike Trains , 2011, PLoS Comput. Biol..

[95]  L. Pinneo.  On noise in the nervous system. , 1966, Psychological review.

[96]  Alex D. Bird,et al.  Long-term plasticity determines the postsynaptic response to correlated afferents with multivesicular short-term synaptic depression , 2014, BMC Neuroscience.

[97]  W. Regehr,et al.  Short-term synaptic plasticity. , 2002, Annual review of physiology.

[98]  J. White,et al.  Channel noise in neurons , 2000, Trends in Neurosciences.

[99]  A. Destexhe,et al.  Synaptic background activity enhances the responsiveness of neocortical pyramidal neurons. , 2000, Journal of neurophysiology.

[100]  Xiao-Jing Wang,et al.  What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance. , 2003, Journal of neurophysiology.

[101]  Ronen Segev,et al.  A thesaurus for a neural population code , 2015, eLife.

[102]  G. Ermentrout,et al.  Gamma rhythms and beta rhythms have different synchronization properties. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[103]  György Buzsáki,et al.  Neural Syntax: Cell Assemblies, Synapsembles, and Readers , 2010, Neuron.

[104]  M. Carandini,et al.  The Nature of Shared Cortical Variability , 2015, Neuron.

[105]  L Schimansky-Geier,et al.  Transmission of noise coded versus additive signals through a neuronal ensemble. , 2001, Physical review letters.

[106]  Suchin S. Gururangan,et al.  Analysis of Graph Invariants in Functional Neocortical Circuitry Reveals Generalized Features Common to Three Areas of Sensory Cortex , 2014, PLoS Comput. Biol..

[107]  Néstor Parga,et al.  Auto- and crosscorrelograms for the spike response of leaky integrate-and-fire neurons with slow synapses. , 2006, Physical review letters.

[108]  Christos Constantinidis,et al.  Correlated discharges in the primate prefrontal cortex before and after working memory training , 2012, The European journal of neuroscience.

[109]  Eero P. Simoncelli,et al.  Spatio-temporal correlations and visual signalling in a complete neuronal population , 2008, Nature.

[110]  R. Shapley,et al.  New perspectives on the mechanisms for orientation selectivity , 1997, Current Opinion in Neurobiology.

[111]  Nicholas J. Priebe,et al.  Direction Selectivity of Excitation and Inhibition in Simple Cells of the Cat Primary Visual Cortex , 2005, Neuron.

[112]  Y. Dan,et al.  Neuromodulation of Brain States , 2012, Neuron.

[113]  Maurice J Chacron,et al.  Population coding by electrosensory neurons. , 2008, Journal of neurophysiology.

[114]  A. Zador,et al.  Balanced inhibition underlies tuning and sharpens spike timing in auditory cortex , 2003, Nature.

[115]  J. Schiller,et al.  Dynamics of Excitability over Extended Timescales in Cultured Cortical Neurons , 2010, The Journal of Neuroscience.

[116]  Matteo Carandini,et al.  Five key factors determining pairwise correlations in visual cortex , 2015, Journal of neurophysiology.

[117]  S. Prescott,et al.  Gain control of firing rate by shunting inhibition: Roles of synaptic noise and dendritic saturation , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[118]  Alexander S. Ecker,et al.  Decorrelated Neuronal Firing in Cortical Microcircuits , 2010, Science.

[119]  Robert Rosenbaum,et al.  The Effects of Pooling on Spike Train Correlations , 2011, Front. Neurosci..

[120]  Brent Doiron,et al.  Oscillatory activity in electrosensory neurons increases with the spatial correlation of the stochastic input stimulus. , 2004, Physical review letters.

[121]  Adam Kohn,et al.  Correlations in V1 Are Reduced by Stimulation Outside the Receptive Field , 2014, The Journal of Neuroscience.

[122]  David A Markowitz,et al.  Rate-specific synchrony: Using noisy oscillations to detect equally active neurons , 2008, Proceedings of the National Academy of Sciences.

[123]  Eric Shea-Brown,et al.  Correlation and synchrony transfer in integrate-and-fire neurons: basic properties and consequences for coding. , 2008, Physical review letters.

[124]  L. Abbott,et al.  Neural network dynamics. , 2005, Annual review of neuroscience.

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

[126]  T. Branco,et al.  The probability of neurotransmitter release: variability and feedback control at single synapses , 2009, Nature Reviews Neuroscience.

[127]  D. McCormick,et al.  Neocortical Network Activity In Vivo Is Generated through a Dynamic Balance of Excitation and Inhibition , 2006, The Journal of Neuroscience.

[128]  Pulin Gong,et al.  Propagating Waves Can Explain Irregular Neural Dynamics , 2015, The Journal of Neuroscience.

[129]  W. Newsome,et al.  Context-Dependent Changes in Functional Circuitry in Visual Area MT , 2008, Neuron.

[130]  Dario L. Ringach,et al.  Dynamics of orientation tuning in macaque primary visual cortex , 1997, Nature.

[131]  Multiplying two numbers together in your head is a difficult task if you did not learn multiplication tables as a child. On the face of it, this is somewhat surprising given the remarkable power of the brain to perform , 2010 .

[132]  Nicolas Brunel,et al.  How Connectivity, Background Activity, and Synaptic Properties Shape the Cross-Correlation between Spike Trains , 2009, The Journal of Neuroscience.

[133]  Naoshige Uchida,et al.  Odor Representations in Olfactory Cortex: Distributed Rate Coding and Decorrelated Population Activity , 2012, Neuron.

[134]  Lisa M. Giocomo,et al.  Computational Models of Grid Cells , 2011, Neuron.

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

[136]  Michael Okun,et al.  Instantaneous correlation of excitation and inhibition during ongoing and sensory-evoked activities , 2008, Nature Neuroscience.

[137]  Frances S. Chance,et al.  Gain Modulation from Background Synaptic Input , 2002, Neuron.

[138]  Andrew M. Clark,et al.  Stimulus onset quenches neural variability: a widespread cortical phenomenon , 2010, Nature Neuroscience.

[139]  R. Yuste.  From the neuron doctrine to neural networks , 2015, Nature Reviews Neuroscience.

[140]  Michael Graupner,et al.  Synaptic Input Correlations Leading to Membrane Potential Decorrelation of Spontaneous Activity in Cortex , 2013, The Journal of Neuroscience.

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

[142]  Bard Ermentrout,et al.  Correlation transfer in stochastically driven neural oscillators over long and short time scales. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[144]  Douglas A Ruff,et al.  Attention can increase or decrease spike count correlations between pairs of neurons depending on their role in a task , 2014, Nature Neuroscience.

[145]  Brent Doiron,et al.  Correlated neural variability in persistent state networks , 2012, Proceedings of the National Academy of Sciences.

[146]  A. Aertsen,et al.  Spike synchronization and rate modulation differentially involved in motor cortical function. , 1997, Science.

[147]  L. Maler,et al.  Inhibition evoked from primary afferents in the electrosensory lateral line lobe of the weakly electric fish (Apteronotus leptorhynchus). , 1998, Journal of neurophysiology.

[148]  Moritz Helias,et al.  The Correlation Structure of Local Neuronal Networks Intrinsically Results from Recurrent Dynamics , 2013, PLoS Comput. Biol..

[149]  Alexander S. Ecker,et al.  Improved Estimation and Interpretation of Correlations in Neural Circuits , 2015, PLoS Comput. Biol..