The dynamical response properties of neocortical neurons to temporally modulated noisy inputs in vitro.

Cortical neurons are often classified by current-frequency relationship. Such a static description is inadequate to interpret neuronal responses to time-varying stimuli. Theoretical studies suggested that single-cell dynamical response properties are necessary to interpret ensemble responses to fast input transients. Further, it was shown that input-noise linearizes and boosts the response bandwidth, and that the interplay between the barrage of noisy synaptic currents and the spike-initiation mechanisms determine the dynamical properties of the firing rate. To test these model predictions, we estimated the linear response properties of layer 5 pyramidal cells by injecting a superposition of a small-amplitude sinusoidal wave and a background noise. We characterized the evoked firing probability across many stimulation trials and a range of oscillation frequencies (1-1000 Hz), quantifying response amplitude and phase-shift while changing noise statistics. We found that neurons track unexpectedly fast transients, as their response amplitude has no attenuation up to 200 Hz. This cut-off frequency is higher than the limits set by passive membrane properties (approximately 50 Hz) and average firing rate (approximately 20 Hz) and is not affected by the rate of change of the input. Finally, above 200 Hz, the response amplitude decays as a power-law with an exponent that is independent of voltage fluctuations induced by the background noise.

[1]  Yuguo Yu,et al.  Properties of action-potential initiation in neocortical pyramidal cells: evidence from whole cell axon recordings. , 2007, Journal of neurophysiology.

[2]  P. C. Murphy,et al.  Cerebral Cortex , 2017, Cerebral Cortex.

[3]  Maria V. Sanchez-Vives,et al.  Cellular and network mechanisms of slow oscillatory activity (<1 Hz) and wave propagations in a cortical network model. , 2003, Journal of neurophysiology.

[4]  William H. Press,et al.  Book-Review - Numerical Recipes in Pascal - the Art of Scientific Computing , 1989 .

[5]  W. Bialek,et al.  Naturalistic stimuli increase the rate and efficiency of information transmission by primary auditory afferents , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[6]  R. Shapley,et al.  Receptive field mechanisms of cat X and Y retinal ganglion cells , 1979, The Journal of general physiology.

[7]  Henry Markram,et al.  Spike frequency adaptation and neocortical rhythms. , 2002, Journal of neurophysiology.

[8]  F. Baldissera,et al.  The dynamic response of cat α-motoneurones investigated by intracellular injection of sinusoidal currents , 2004, Experimental Brain Research.

[9]  David McLaughlin,et al.  States of High Conductance in a Large-Scale Model of the Visual Cortex , 2002, Journal of Computational Neuroscience.

[10]  P Kuyper,et al.  Triggered correlation. , 1968, IEEE transactions on bio-medical engineering.

[11]  Andrew S. French,et al.  Frequency response functions and information capacities of paired spider mechanoreceptor neurons , 2001, Biological Cybernetics.

[12]  D. McCormick,et al.  Comparative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex. , 1985, Journal of neurophysiology.

[13]  Tim Gollisch,et al.  Spike-train variability of auditory neurons in vivo: dynamic responses follow predictions from constant stimuli. , 2005, Journal of neurophysiology.

[14]  A. Destexhe,et al.  The high-conductance state of neocortical neurons in vivo , 2003, Nature Reviews Neuroscience.

[15]  Alan R Palmer,et al.  Phase-locked responses to pure tones in the inferior colliculus. , 2006, Journal of neurophysiology.

[16]  Alain Destexhe,et al.  High-conductance state , 2007, Scholarpedia.

[17]  W. Brogan Modern Control Theory , 1971 .

[18]  Walter Senn,et al.  Comparison between networks of conductance- and current-driven neurons: stationary spike rates and subthreshold depolarization , 2004, Neurocomputing.

[19]  W. Senn,et al.  Neocortical pyramidal cells respond as integrate-and-fire neurons to in vivo-like input currents. , 2003, Journal of neurophysiology.

[20]  M. Gutnick,et al.  Slow inactivation of Na+ current and slow cumulative spike adaptation in mouse and guinea‐pig neocortical neurones in slices. , 1996, The Journal of physiology.

[21]  Irina Erchova,et al.  Subthreshold resonance explains the frequency-dependent integration of periodic as well as random stimuli in the entorhinal cortex. , 2004, Journal of neurophysiology.

[22]  Adrienne L Fairhall,et al.  Two-Dimensional Time Coding in the Auditory Brainstem , 2005, The Journal of Neuroscience.

[23]  G. Buzsáki,et al.  Interneuron Diversity series: Circuit complexity and axon wiring economy of cortical interneurons , 2004, Trends in Neurosciences.

[24]  G. Ermentrout,et al.  Phase-response curves give the responses of neurons to transient inputs. , 2005, Journal of neurophysiology.

[25]  S G Lisberger,et al.  Cellular processing of temporal information in medial vestibular nucleus neurons , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[26]  Xiao-Jing Wang Neural Oscillations , 2002 .

[27]  Lynn Nadel,et al.  Encyclopedia of Cognitive Science , 2003 .

[28]  Wulfram Gerstner,et al.  Synaptic Shot Noise and Conductance Fluctuations Affect the Membrane Voltage with Equal Significance , 2005, Neural Computation.

[29]  O. Prospero-Garcia,et al.  Reliability of Spike Timing in Neocortical Neurons , 1995 .

[30]  Kerry J. Kim,et al.  Temporal Contrast Adaptation in the Input and Output Signals of Salamander Retinal Ganglion Cells , 2001, The Journal of Neuroscience.

[31]  Zdzislaw Bubnicki,et al.  Modern Control Theory , 2005 .

[32]  Liam Paninski,et al.  The Spike-Triggered Average of the Integrate-and-Fire Cell Driven by Gaussian White Noise , 2006, Neural Computation.

[33]  B. Knight The Relationship between the Firing Rate of a Single Neuron and the Level of Activity in a Population of Neurons , 1972, The Journal of general physiology.

[34]  J. Victor Nonlinear systems analysis: comparison of white noise and sum of sinusoids in a biological system. , 1979, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Jürgen Kröller,et al.  Band-limited white noise stimulation and reverse correlation analysis in the prediction of impulse responses of encoder models , 1992, Biological Cybernetics.

[36]  Nicolas Brunel,et al.  Dynamics of the Instantaneous Firing Rate in Response to Changes in Input Statistics , 2005, Journal of Computational Neuroscience.

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

[38]  Cheng Ly,et al.  Population density methods for stochastic neurons with realistic synaptic kinetics: Firing rate dynamics and fast computational methods , 2006, Network.

[39]  R K Powers,et al.  Contributions of the input signal and prior activation history to the discharge behaviour of rat motoneurones , 2005, The Journal of physiology.

[40]  Wulfram Gerstner,et al.  Predicting spike timing of neocortical pyramidal neurons by simple threshold models , 2006, Journal of Computational Neuroscience.

[41]  Michele Giugliano,et al.  The Impact of Input Fluctuations on the Frequency–Current Relationships of Layer 5 Pyramidal Neurons in the Rat Medial Prefrontal Cortex , 2007, The Journal of Neuroscience.

[42]  T. Sejnowski,et al.  Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons , 2001, Neuroscience.

[43]  R Iansek,et al.  An analysis of the cable properties of spinal motoneurones using a brief intracellular current pulse , 1973, The Journal of physiology.

[44]  M. Steriade Impact of network activities on neuronal properties in corticothalamic systems. , 2001, Journal of neurophysiology.

[45]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

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

[47]  H Markram,et al.  Dynamics of population rate codes in ensembles of neocortical neurons. , 2004, Journal of neurophysiology.

[48]  Frances S. Chance,et al.  Effects of synaptic noise and filtering on the frequency response of spiking neurons. , 2001, Physical review letters.

[49]  G. Buzsáki,et al.  Gamma Oscillation by Synaptic Inhibition in a Hippocampal Interneuronal Network Model , 1996, The Journal of Neuroscience.

[50]  A. Destexhe,et al.  Impact of spontaneous synaptic activity on the resting properties of cat neocortical pyramidal neurons In vivo. , 1998, Journal of neurophysiology.

[51]  W. Senn,et al.  Multiple time scales of temporal response in pyramidal and fast spiking cortical neurons. , 2006, Journal of neurophysiology.

[52]  William Bialek,et al.  Reading a Neural Code , 1991, NIPS.

[53]  S. Sherman,et al.  Fourier analysis of sinusoidally driven thalamocortical relay neurons and a minimal integrate-and-fire-or-burst model. , 2000, Journal of neurophysiology.

[54]  M. Šilhavý The Dynamic Response , 1997 .

[55]  Nicolas Brunel,et al.  Firing-rate resonance in a generalized integrate-and-fire neuron with subthreshold resonance. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[56]  Paul Horowitz,et al.  The Art of Electronics , 1980 .

[57]  Christof Koch,et al.  Temporal Precision of Spike Trains in Extrastriate Cortex of the Behaving Macaque Monkey , 1999, Neural Computation.

[58]  M. Steriade,et al.  Neocortical very fast oscillations (ripples, 80-200 Hz) during seizures: intracellular correlates. , 2003, Journal of neurophysiology.

[59]  Maria V. Sanchez-Vives,et al.  Influence of low and high frequency inputs on spike timing in visual cortical neurons. , 1997, Cerebral cortex.

[60]  G. Buzsáki,et al.  Neuronal Oscillations in Cortical Networks , 2004, Science.

[61]  Nicolas Brunel,et al.  Contributions of intrinsic membrane dynamics to fast network oscillations with irregular neuronal discharges. , 2005, Journal of neurophysiology.

[62]  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.

[63]  Wulfram Gerstner,et al.  Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking , 2000, Neural Computation.

[64]  J. Movshon,et al.  Spatial summation in the receptive fields of simple cells in the cat's striate cortex. , 1978, The Journal of physiology.

[65]  E J Chichilnisky,et al.  A simple white noise analysis of neuronal light responses , 2001, Network.

[66]  Thomas J. Palmeri,et al.  ENCYCLOPEDIA OF COGNITIVE SCIENCE , 2001 .

[67]  Wulfram Gerstner,et al.  Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. , 2005, Journal of neurophysiology.

[68]  G. Stuart,et al.  Site of Action Potential Initiation in Layer 5 Pyramidal Neurons , 2006, The Journal of Neuroscience.

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

[70]  J. Csicsvari,et al.  Oscillatory Coupling of Hippocampal Pyramidal Cells and Interneurons in the Behaving Rat , 1999, The Journal of Neuroscience.

[71]  A. S. French,et al.  Practical nonlinear system analysis by Wiener kernel estimation in the frequency domain , 1976, Biological Cybernetics.

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

[73]  Fredric M. Wolf,et al.  Action Potential Onset Dynamics and the Response Speed of Neuronal Populations , 2004, Journal of Computational Neuroscience.

[74]  J. Movshon,et al.  Spike train encoding by regular-spiking cells of the visual cortex. , 1996, Journal of neurophysiology.

[75]  Idan Segev,et al.  Subthreshold oscillations and resonant frequency in guinea‐pig cortical neurons: physiology and modelling. , 1995, The Journal of physiology.

[76]  Sean J. Slee,et al.  Diversity of Gain Modulation by Noise in Neocortical Neurons: Regulation by the Slow Afterhyperpolarization Conductance , 2006, The Journal of Neuroscience.

[77]  G. Buzsáki,et al.  High-frequency network oscillation in the hippocampus. , 1992, Science.

[78]  N. Brunel,et al.  From subthreshold to firing-rate resonance. , 2003, Journal of neurophysiology.

[79]  D. McCormick,et al.  Modulation of intracortical synaptic potentials by presynaptic somatic membrane potential , 2006, Nature.

[80]  Michael Rudolph,et al.  Inferring network activity from synaptic noise , 2004, Journal of Physiology-Paris.

[81]  R. Miura,et al.  Subthreshold membrane resonance in neocortical neurons. , 1996, Journal of neurophysiology.

[82]  Liam Paninski,et al.  Noise-driven adaptation: in vitro and mathematical analysis , 2003, Neurocomputing.

[83]  Rajesh P. N. Rao,et al.  Frequency dependence of spike timing reliability in cortical pyramidal cells and interneurons. , 2001, Journal of neurophysiology.

[84]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[85]  Bruce W. Knight,et al.  Dynamics of Encoding in a Population of Neurons , 1972, The Journal of general physiology.

[86]  Sm Hus Use of avidin-biotin-peroxidase complex (ABC) in immunoperoxidase techniques: a comparison between ABC and unlabeled antibody (PAP) procedures , 1981 .

[87]  R. Shapley,et al.  A method of nonlinear analysis in the frequency domain. , 1980, Biophysical journal.

[88]  Kazuyuki Aihara,et al.  Coding of Temporally Varying Signals in Networks of Spiking Neurons with Global Delayed Feedback , 2005, Neural Computation.

[89]  J. C. Anderson,et al.  Estimates of the net excitatory currents evoked by visual stimulation of identified neurons in cat visual cortex. , 1998, Cerebral cortex.

[90]  M Giugliano,et al.  Single-neuron discharge properties and network activity in dissociated cultures of neocortex. , 2004, Journal of neurophysiology.

[91]  Hugh P. C. Robinson Conductance injection , 1994, Trends in Neurosciences.

[92]  A. Pugh The art of electronics. 2nd edn: By Paul Horowitz and Winfield Hill. Pp. 1125. Cambridge University Presss. 1989. £29.95, US$49.50 , 1990 .

[93]  D. Hansel,et al.  How Spike Generation Mechanisms Determine the Neuronal Response to Fluctuating Inputs , 2003, The Journal of Neuroscience.

[94]  H M Sakai,et al.  White-noise analysis in neurophysiology. , 1992, Physiological reviews.

[95]  R. Shapley,et al.  The nonlinear pathway of Y ganglion cells in the cat retina , 1979, The Journal of general physiology.

[96]  E. Godaux,et al.  Resonance of spike discharge modulation in neurons of the guinea pig medial vestibular nucleus. , 2001, Journal of neurophysiology.

[97]  D. McCormick,et al.  Neurophysiology: Hodgkin and Huxley model — still standing? , 2007, Nature.