The mechanics of state-dependent neural

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

[2]  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.

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

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

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

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

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

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

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

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

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

[12]  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.

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

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

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

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

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

[18]  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.

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

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

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

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

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

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

[25]  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.

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

[27]  A. Faisal,et al.  Noise in the nervous system , 2008, Nature Reviews Neuroscience.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[50]  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..

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

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

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

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

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

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

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

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

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

[60]  Albert Compte,et al.  Sensory integration dynamics in a hierarchical network explains choice probabilities in cortical area MT , 2015, Nature Communications.

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

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

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

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

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

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

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

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

[69]  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.

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

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

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

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

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

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

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

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

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

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

[80]  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.

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

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

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

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

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

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

[87]  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.

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

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

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

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

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

[93]  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.

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

[95]  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.

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

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

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

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

[100]  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.

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

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

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

[104]  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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[122]  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.

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

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

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

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

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

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

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

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

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

[132]  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..

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

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

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

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

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

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

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

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

[141]  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.

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

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

[144]  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.

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

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