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.

Download Full-text

A deep convolutional visual encoding model of neuronal responses in the LGN

Brain Informatics ◽

10.1186/s40708-021-00132-6 ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Eslam Mounier ◽

Bassem Abdullah ◽

Hani Mahdi ◽

Seif Eldawlatly

Keyword(s):

Firing Rate ◽

Visual Information ◽

Visual Stimulation ◽

Neuronal Population ◽

Neuronal Firing ◽

Electrode Arrays ◽

Deep Convolutional Neural Networks ◽

Firing Rates ◽

Spatiotemporal Representation

AbstractThe Lateral Geniculate Nucleus (LGN) represents one of the major processing sites along the visual pathway. Despite its crucial role in processing visual information and its utility as one target for recently developed visual prostheses, it is much less studied compared to the retina and the visual cortex. In this paper, we introduce a deep learning encoder to predict LGN neuronal firing in response to different visual stimulation patterns. The encoder comprises a deep Convolutional Neural Network (CNN) that incorporates visual stimulus spatiotemporal representation in addition to LGN neuronal firing history to predict the response of LGN neurons. Extracellular activity was recorded in vivo using multi-electrode arrays from single units in the LGN in 12 anesthetized rats with a total neuronal population of 150 units. Neural activity was recorded in response to single-pixel, checkerboard and geometrical shapes visual stimulation patterns. Extracted firing rates and the corresponding stimulation patterns were used to train the model. The performance of the model was assessed using different testing data sets and different firing rate windows. An overall mean correlation coefficient between the actual and the predicted firing rates of 0.57 and 0.7 was achieved for the 10 ms and the 50 ms firing rate windows, respectively. Results demonstrate that the model is robust to variability in the spatiotemporal properties of the recorded neurons outperforming other examined models including the state-of-the-art Generalized Linear Model (GLM). The results indicate the potential of deep convolutional neural networks as viable models of LGN firing.

Download Full-text

Sparse bursts optimize information transmission in a multiplexed neural code

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1720995115 ◽

2018 ◽

Vol 115 (27) ◽

pp. E6329-E6338 ◽

Cited By ~ 25

Author(s):

Richard Naud ◽

Henning Sprekeler

Keyword(s):

Firing Rate ◽

Cortical Neurons ◽

Neural Code ◽

Spike Timing ◽

Neural Ensemble ◽

Multiple Input ◽

Cortical Hierarchy ◽

Connectivity Patterns ◽

Rate Coding

Many cortical neurons combine the information ascending and descending the cortical hierarchy. In the classical view, this information is combined nonlinearly to give rise to a single firing-rate output, which collapses all input streams into one. We analyze the extent to which neurons can simultaneously represent multiple input streams by using a code that distinguishes spike timing patterns at the level of a neural ensemble. Using computational simulations constrained by experimental data, we show that cortical neurons are well suited to generate such multiplexing. Interestingly, this neural code maximizes information for short and sparse bursts, a regime consistent with in vivo recordings. Neurons can also demultiplex this information, using specific connectivity patterns. The anatomy of the adult mammalian cortex suggests that these connectivity patterns are used by the nervous system to maintain sparse bursting and optimal multiplexing. Contrary to firing-rate coding, our findings indicate that the physiology and anatomy of the cortex may be interpreted as optimizing the transmission of multiple independent signals to different targets.

Download Full-text

Possible Effects of Depolarizing GABAA Conductance on the Neuronal Input–Output Relationship: A Modeling Study

Journal of Neurophysiology ◽

10.1152/jn.00988.2004 ◽

2005 ◽

Vol 93 (6) ◽

pp. 3504-3523 ◽

Cited By ~ 9

Author(s):

Kenji Morita ◽

Kunichika Tsumoto ◽

Kazuyuki Aihara

Keyword(s):

Firing Rate ◽

Cortical Neurons ◽

Reversal Potential ◽

Pyramidal Cells ◽

Resting Potential ◽

Input Output ◽

Wide Range ◽

The Relationship

Recent in vitro experiments revealed that the GABAA reversal potential is about 10 mV higher than the resting potential in mature mammalian neocortical pyramidal cells; thus GABAergic inputs could have facilitatory, rather than inhibitory, effects on action potential generation under certain conditions. However, how the relationship between excitatory input conductances and the output firing rate is modulated by such depolarizing GABAergic inputs under in vivo circumstances has not yet been understood. We examine herewith the input–output relationship in a simple conductance-based model of cortical neurons with the depolarized GABAA reversal potential, and show that a tonic depolarizing GABAergic conductance up to a certain amount does not change the relationship between a tonic glutamatergic driving conductance and the output firing rate, whereas a higher GABAergic conductance prevents spike generation. When the tonic glutamatergic and GABAergic conductances are replaced by in vivo–like highly fluctuating inputs, on the other hand, the effect of depolarizing GABAergic inputs on the input–output relationship critically depends on the degree of coincidence between glutamatergic input events and GABAergic ones. Although a wide range of depolarizing GABAergic inputs hardly changes the firing rate of a neuron driven by noncoincident glutamatergic inputs, a certain range of these inputs considerably decreases the firing rate if a large number of driving glutamatergic inputs are coincident with them. These results raise the possibility that the depolarized GABAA reversal potential is not a paradoxical mystery, but is instead a sophisticated device for discriminative firing rate modulation.

Download Full-text

Physiological properties of individual cerebral axons studied in vivo for as long as one year

Journal of Neurophysiology ◽

10.1152/jn.1985.54.5.1346 ◽

1985 ◽

Vol 54 (5) ◽

pp. 1346-1362 ◽

Cited By ~ 82

Author(s):

H. A. Swadlow

Keyword(s):

Conduction Velocity ◽

Cortical Neurons ◽

Refractory Period ◽

Antidromic Activation ◽

Conduction Velocities ◽

Supernormal Period ◽

Velocity Changes ◽

The Stability ◽

Over Time

The long-term stability of conduction velocity and recovery processes were studied in a fast-conducting (corticotectal) and in a more slowly conducting (visual callosal) axonal system. Chronic microelectrode recording methods were used in conjunction with antidromic activation via electrical stimulation at one or more axonal site. These methods enabled 54 axons to be studied for greater than 20 days and seven of these cells to be studied for 101-448 days. The conduction velocities of corticotectal axons were characteristic of myelinated axons and were very stable over time. The conduction velocities of most callosal axons were characteristic of nonmyelinated axons, and 68% of callosal axons had conduction velocities that were stable over long periods of time. Of the remaining callosal axons, approximately one third showed an increase in conduction velocity (8-14%), whereas two thirds showed a progressive and systematic decrease in conduction velocity (6-81%). These changes in conduction velocity were distributed along the callosal axon, rather than limited to a single segment of axon. Although the refractory period of callosal and corticotectal axons showed considerable variability over time, the minimal interval between two conducted impulses was stable. The stability of this property was remarkable because the minimal interspike intervals of different axons with similar conduction velocities often differed greatly. Callosal axons show a supernormal period of increased conduction velocity following the relative refractory period and a subsequent subnormal period of decreased conduction velocity following a burst of prior impulses. In different callosal axons the magnitude of the velocity changes (percent change) differs greatly, even among axons of the same conduction velocity. For a given axon, however, these properties are very stable over time. These results on axonal properties may be useful in studies requiring the examination of extracellular responses of individual neurons over long periods of time. Antidromic latency provides a useful means of identifying a cell, particularly when conduction times are long. The stability of the minimal interspike interval and the supernormal period within individual axons make them suitable as ancillary criteria in identifying individual neurons. These three measures are independent of spike amplitude and waveform, and together they provide a "signature" by which individual cortical neurons can be identified over periods that represent a significant portion of the lifespan of adult mammals.

Download Full-text

Changes in the Response Rate and Response Variability of Area V4 Neurons During the Preparation of Saccadic Eye Movements

Journal of Neurophysiology ◽

10.1152/jn.00689.2009 ◽

2010 ◽

Vol 103 (3) ◽

pp. 1171-1178 ◽

Cited By ~ 28

Author(s):

Nicholas A. Steinmetz ◽

Tirin Moore

Keyword(s):

Eye Movements ◽

Reaction Time ◽

Firing Rate ◽

Response Rate ◽

Saccadic Eye Movements ◽

Response Variability ◽

Area V4 ◽

The Mean ◽

V4 Neurons ◽

Saccade Preparation

The visually driven responses of macaque area V4 neurons are modulated during the preparation of saccadic eye movements, but the relationship between presaccadic modulation in area V4 and saccade preparation is poorly understood. Recent neurophysiological studies suggest that the variability across trials of spiking responses provides a more reliable signature of motor preparation than mean firing rate across trials. We compared the dynamics of the response rate and the variability in the rate across trials for area V4 neurons during the preparation of visually guided saccades. As in previous reports, we found that the mean firing rate of V4 neurons was enhanced when saccades were prepared to stimuli within a neuron's receptive field (RF) in comparison with saccades to a non-RF location. Further, we found robust decreases in response variability prior to saccades and found that these decreases predicted saccadic reaction times for saccades both to RF and non-RF stimuli. Importantly, response variability predicted reaction time whether or not there were any accompanying changes in mean firing rate. In addition to predicting saccade direction, the mean firing rate could also predict reaction time, but only for saccades directed to the RF stimuli. These results demonstrate that response variability of area V4 neurons, like mean response rate, provides a signature of saccade preparation. However, the two signatures reflect complementary aspects of that preparation.

Download Full-text

Computing and Stability in Cortical Networks

Neural Computation ◽

10.1162/089976604323057434 ◽

2004 ◽

Vol 16 (7) ◽

pp. 1385-1412 ◽

Cited By ~ 44

Author(s):

Peter E. Latham ◽

Sheila Nirenberg

Keyword(s):

Cortical Neurons ◽

Unstable State ◽

Stable States ◽

Attractor Networks ◽

Firing Rates ◽

The Face ◽

Multiple Stable States ◽

Background State ◽

Do So

Cortical neurons are predominantly excitatory and highly interconnected. In spite of this, the cortex is remarkably stable: normal brains do not exhibit the kind of runaway excitation one might expect of such a system. How does the cortex maintain stability in the face of this massive excitatory feedback? More importantly, how does it do so during computations, which necessarily involve elevated firing rates? Here we address these questions in the context of attractor networks—networks that exhibit multiple stable states, or memories. We find that such networks can be stabilized at the relatively low firing rates observed in vivo if two conditions are met: (1) the background state, where all neurons are firing at low rates, is inhibition dominated, and (2) the fraction of neurons involved in a memory is above some threshold, so that there is sufficient coupling between the memory neurons and the background. This allows “dynamical stabilization” of the attractors, meaning feedback from the pool of background neurons stabilizes what would otherwise be an unstable state. We suggest that dynamical stabilization may be a strategy used for a broad range of computations, not just those involving attractors.

Download Full-text

Neuronal firing rates diverge during REM and homogenize during non-REM

10.1101/069237 ◽

2016 ◽

Author(s):

Hiroyuki Miyawaki ◽

Brendon Watson ◽

Kamran Diba

Keyword(s):

Firing Rate ◽

Frontal Cortex ◽

Rem Sleep ◽

Cortical Neurons ◽

Nrem Sleep ◽

Regression To The Mean ◽

Firing Rates ◽

The Mean ◽

High Firing ◽

Interneuron Activity

AbstractNeurons fire at highly variable innate rates and recent evidence suggests that low and high firing rate neurons display different plasticity and dynamics. Furthermore, recent publications imply possibly differing rate-dependent effects in hippocampus versus neocortex, but those analyses were carried out separately and with possibly important differences. To more effectively synthesize these questions, we analyzed the firing rate dynamics of populations of neurons in both hippocampal CA1 and frontal cortex under one framework that avoids pitfalls of previous analyses and accounts for regression-to-the-mean. We observed remarkably consistent effects across these regions. While rapid eye movement (REM) sleep was marked by decreased hippocampal firing and increased neocortical firing, in both regions firing rates distributions widened during REM due to differential changes in high-firing versus low-firing cells in parallel with increased interneuron activity. In contrast, upon non-REM (NREM) sleep, firing rate distributions narrowed while interneuron firing decreased. Interestingly, hippocampal interneuron activity closely followed the patterns observed in neocortical principal cells rather than the hippocampal principal cells, suggestive of long-range interactions. Following these undulations in variance, the net effect of sleep was a decrease in firing rates. These decreases were greater in lower-firing hippocampal neurons but higher-firing frontal cortical neurons, suggestive of greater plasticity in these cell groups. Our results across two different regions and with statistical corrections indicate that the hippocampus and neocortex show a mixture of differences and similarities as they cycle between sleep states with a unifying characteristic of homogenization of firing during NREM and diversification during REM.Significance StatementMiyawaki and colleagues analyze firing patterns across low-firing and high-firing neurons in the hippocampus and the frontal cortex throughout sleep in a framework that accounts for regression-to-the-mean. They find that in both regions REM sleep activity is relatively dominated by high-firing neurons and increased inhibition, resulting in a wider distribution of firing rates. On the other hand, NREM sleep produces lower inhibition, and results in a more homogenous distribution of firing rates. Integration of these changes across sleep results in net decrease of firing rates with largest drops in low-firing hippocampal pyramidal neurons and high-firing neocortical principal neurons. These findings provide insights into the effects and functions of different sleep stages on cortical neurons.

Download Full-text

Change-Based Inference in Attractor Nets: Linear Analysis

Neural Computation ◽

10.1162/neco_a_00051 ◽

2010 ◽

Vol 22 (12) ◽

pp. 3036-3061 ◽

Cited By ~ 3

Author(s):

Reza Moazzezi ◽

Peter Dayan

Keyword(s):

Linear Approximation ◽

Cortical Neurons ◽

Linear Analysis ◽

Alternative Interpretation ◽

Standard Interpretation ◽

Firing Rates ◽

Chance Performance ◽

Perfect Performance ◽

Population Codes ◽

Over Time

One standard interpretation of networks of cortical neurons is that they form dynamical attractors. Computations such as stimulus estimation are performed by mapping inputs to points on the networks' attractive manifolds. These points represent population codes for the stimulus values. However, this standard interpretation is hard to reconcile with the observation that the firing rates of such neurons constantly change following presentation of stimuli. We have recently suggested an alternative interpretation according to which computations are realized by systematic changes in the states of such networks over time. This way of performing computations is fast, accurate, readily learnable, and robust to various forms of noise. Here we analyze the computation of stimulus discrimination in this change-based setting, relating it directly to the computation of stimulus estimation in the conventional attractor-based view. We use a common linear approximation to compare the two methods and show that perfect performance at estimation implies chance performance at discrimination.

Download Full-text

Firing rate homeostasis occurs in the absence of neuronal activity-regulated transcription

10.1101/675728 ◽

2019 ◽

Author(s):

Kelsey M. Tyssowski ◽

Katherine C. Letai ◽

Samuel D. Rendall ◽

Anastasia Nizhnik ◽

Jesse M. Gray

Keyword(s):

Firing Rate ◽

Neuronal Activity ◽

Cortical Neurons ◽

Molecular Mechanisms ◽

Neuronal Circuits ◽

Electrode Arrays ◽

Knock Out ◽

Firing Rates ◽

The Face ◽

Homeostatic Mechanisms

ABSTRACTDespite dynamic inputs, neuronal circuits maintain relatively stable firing rates over long periods. This maintenance of firing rate, or firing rate homeostasis, is likely mediated by homeostatic mechanisms such as synaptic scaling and regulation of intrinsic excitability. Because some of these homeostatic mechanisms depend on transcription of activity-regulated genes, including Arc and Homer1a, we hypothesized that activity-regulated transcription would be required for firing rate homeostasis. Surprisingly, however, we found that cultured mouse cortical neurons grown on multi-electrode arrays homeostatically adapt their firing rates to persistent pharmacological stimulation even when activity-regulated transcription is disrupted. Specifically, we observed firing rate homeostasis Arc knock-out neurons, as well as knock-out neurons lacking activity-regulated transcription factors, AP1 and SRF. Firing rate homeostasis also occurred normally during acute pharmacological blockade of transcription. Thus, firing rate homeostasis in response to increased neuronal activity can occur in the absence of neuronal-activity-regulated transcription.SIGNIFICANCE STATEMENTNeuronal circuits maintain relatively stable firing rates even in the face of dynamic circuit inputs. Understanding the molecular mechanisms that enable this firing rate homeostasis could potentially provide insight into neuronal diseases that present with an imbalance of excitation and inhibition. However, the molecular mechanisms underlying firing rate homeostasis are largely unknown.It has long been hypothesized that firing rate homeostasis relies upon neuronal activity-regulated transcription. For example, a 2012 review (PMID 22685679) proposed it, and a 2014 modeling approach established that transcription could theoretically both measure and control firing rate (PMID 24853940). Surprisingly, despite this prediction, we found that cortical neurons undergo firing rate homeostasis in the absence of activity-regulated transcription, indicating that firing rate homeostasis is controlled by non-transcriptional mechanisms.

Download Full-text

Dynamic Gain Changes During Attentional Modulation

Neural Computation ◽

10.1162/neco.2006.18.8.1847 ◽

2006 ◽

Vol 18 (8) ◽

pp. 1847-1867 ◽

Cited By ~ 19

Author(s):

Arun P. Sripati ◽

Kenneth O. Johnson

Keyword(s):

Firing Rate ◽

Cortical Neurons ◽

Model Neuron ◽

Rate Adaptation ◽

Recognition Task ◽

Fano Factor ◽

Attentional Modulation ◽

Firing Rates ◽

Spike Threshold ◽

Firing Rate Adaptation

Attention causes a multiplicative effect on firing rates of cortical neurons without affecting their selectivity (Motter, 1993; McAdams & Maunsell, 1999a) or the relationship between the spike count mean and variance (McAdams & Maunsell, 1999b). We analyzed attentional modulation of the firing rates of 144 neurons in the secondary somatosensory cortex (SII) of two monkeys trained to switch their attention between a tactile pattern recognition task and a visual task. We found that neurons in SII cortex also undergo a predominantly multiplicative modulation in firing rates without affecting the ratio of variance to mean firing rate (i.e., the Fano factor). Furthermore, both additive and multiplicative components of attentional modulation varied dynamically during the stimulus presentation. We then used a standard conductance-based integrate-and-fire model neuron to ascertain which mechanisms might account for a multiplicative increase in firing rate without affecting the Fano factor. Six mechanisms were identified as biophysically plausible ways that attention could modify the firing rate: spike threshold, firing rate adaptation, excitatory input synchrony, synchrony between all inputs, membrane leak resistance, and reset potential. Of these, only a change in spike threshold or in firing rate adaptation affected model firing rates in a manner compatible with the observed neural data. The results indicate that only a limited number of biophysical mechanisms can account for observed attentional modulation.

Download Full-text