Firing Rate Distribution Research Articles

Firing rate distributions and efficiency of information transmission of inferior temporal cortex neurons to natural visual stimuli.

The distribution of responses of sensory neurons to ecological stimulation has been proposed to be designed to maximize information transmission, which according to a simple model would imply an exponential distribution of spike counts in a given time window. We have used recordings from inferior temporal cortex neurons responding to quasi-natural visual stimulation (presented using a video of everyday lab scenes and a large number of static images of faces and natural scenes) to assess the validity of this exponential model and to develop an alternative simple model of spike count distributions. We find that the exponential model has to be rejected in 84% of cases (at the p < 0.01 level). A new model, which accounts for the firing rate distribution found in terms of slow and fast variability in the inputs that produce neuronal activation, is rejected statistically in only 16% of cases. Finally, we show that the neurons are moderately efficient at transmitting information but not optimally efficient.

Place cell discharge is extremely variable during individual passes of the rat through the firing field.

The idea that the rat hippocampus stores a map of space is based on the existence of "place cells" that show "location-specific" firing. The discharge of place cells is confined with remarkable precision to a cell-specific part of the environment called the cell's "firing field." We demonstrate here that firing is not nearly as reliable in the time domain as in the positional domain. Discharge during passes through the firing field was compared with a model with Poisson variance of the location-specific firing determined by the time-averaged positional firing rate distribution. Place cells characteristically fire too little or too much compared with expectations from the random model. This fundamental property of place cells is referred to as "excess firing variance" and has three main implications: (i) Place cell discharge is not only driven by the summation of many small, asynchronous excitatory synaptic inputs. (ii) Place cell discharge may encode a signal in addition to the current head location. (iii) The excess firing variance helps explain why the errors in computing the rat's position from the simultaneous activity of many place cells are large.

Probabilities associated with counting average motor unit firing rates in active human muscle.

Motor unit firing rates in human muscle can be determined from recordings made with small-diameter microelectrodes inserted directly into the muscle during voluntary contraction. Frequently, these counts are pooled to give an average motor unit firing rate under a given set of conditions. Since the fibers of one motor unit are dispersed among the cells of several others, it is conceivable that discharge rates can be measured in more than one cell from the same unit. If this occurred frequently, the distribution of firing rates could be influenced by those from units counted more than once. Based on literature values, we made the following assumptions: vastus lateralis contains approximately 300 motor units, with an average innervation ratio of 1500. Muscle cell diameter is about 50 to 100 microns and cells are randomly distributed over a motor unit territory of 10 microns diameter. The recording range of a microelectrode is about 600 microns. Given the distribution of cells normally found in whole human muscle, the probability of recording from two or more cells of the same motor unit at 50% MVC follows a Poisson distribution with a mean of 0.44. This model suggests that although there is a low probability of some duplication in this technique, the extent to which it influences the distribution of average motor unit firing rates is minimal over the entire range of forces produced by vastus lateralis.

Dynamics of a recurrent network of spiking neurons before and following learning

Extensive simulations of large recurrent networks of integrate-and-fire excitatory and inhibitory neurons in realistic cortical conditions (before and after Hebbian unsupervised learning of uncorrelated stimuli) exhibit a rich phenomenology of stochastic neural spike dynamics and, in particular, coexistence between two types of stable states: spontaneous activity upon stimulation by an unlearned stimulus, and ‘working memory’ states strongly correlated with learned stimuli. Firing rates have very wide distributions, due to the variability in the connectivity from neuron to neuron. ISI histograms are exponential, except for small intervals. Thus the spike emission processes are well approximated by a Poisson process. The variability of the spike emission process is effectively controlled by the magnitude of the post-spike reset potential relative to the mean depolarization of the cell. Cross-correlations (CC) exhibit a central peak near zero delay, flanked by damped oscillations. The magnitude of the central peak in the CCs depends both on the probability that a spike emitted by a neuron affects another randomly chosen neuron and on firing rates. It increases when average rates decrease. Individual CCs depend very weakly on the synaptic interactions between the pairs of neurons. The dependence of individual CCs on the rates of the pair of neurons is in agreement with experimental data. The distribution of firing rates among neurons is in very good agreement with a simple theory, indicating that correlations between spike emission processes in the network are effectively small.

Spatio-temporal representation of multichannel EMG firing patterns and its clinical applications

Analyzing motor unit (MU) activity is essential for studying the neurological dysfunction of upper motor neuron disorders (UMND). This study employs multichannel surface electromyographic (EMG) signals, as recorded from the upper arm during elbow flexion and extension, to analyze the temporal changes and spatial distribution of the dominant firing rate. To estimate the dominant firing rate, the autoregressive (AR) spectrum analysis method is utilized to detect the peaks and poles of the AR model, of the surface EMG spectrum below 40 Hz. The temporal changes in firing rates are also observed by using the spectrogram representation of low-frequency EMG spectra. The EMG spectrogram facilitates examination of the time-varying characteristics of firing rates and recruitment of MUs from surface EMG signal. The low-frequency spectra of multichannel EMG are then represented in a polar form to visualize the spatial distribution of firing patterns across muscles. Via spatio-temporal representation techniques, this study provides a viable approach of observing both the spatial and temporal patterns of MU activities in normal subjects and patients with UMND, including cerebrovascular disease and Parkinson's disease.

Dynamics of a recurrent network of spiking neurons before and following learning

Extensive simulations of large recurrent networks of integrate-and-fire excitatory and inhibitory neurons in realistic cortical conditions (before and after Hebbian unsupervised learning of uncorrelated stimuli) exhibit a rich phenomenology of stochastic neural spike dynamics and, in particular, coexistence between two types of stable states: spontaneous activity upon stimulation by an unlearned stimulus, and ‘working memory’ states strongly correlated with learned stimuli. Firing rates have very wide distributions, due to the variability in the connectivity from neuron to neuron. ISI histograms are exponential, except for small intervals. Thus the spike emission processes are well approximated by a Poisson process. The variability of the spike emission process is effectively controlled by the magnitude of the post-spike reset potential relative to the mean depolarization of the cell. Cross-correlations (CC) exhibit a central peak near zero delay, flanked by damped oscillations. The magnitude of the central peak in the CCs depends both on the probability that a spike emitted by a neuron affects another randomly chosen neuron and on firing rates. It increases when average rates decrease. Individual CCs depend very weakly on the synaptic interactions between the pairs of neurons. The dependence of individual CCs on the rates of the pair of neurons is in agreement with experimental data. The distribution of firing rates among neurons is in very good agreement with a simple theory, indicating that correlations between spike emission processes in the network are effectively small.

Information in the neuronal representation of individual stimuli in the primate temporal visual cortex.

To analyze the information provided about individual visual stimuli in the responses of single neurons in the primate temporal lobe visual cortex, neuronal responses to a set of 65 visual stimuli were recorded in macaques performing a visual fixation task and analyzed using information theoretical measures. The population of neurons analyzed responded primarily to faces. The stimuli included 23 faces and 42 nonface images of real-world scenes, so that the function of this brain region could be analyzed when it was processing relatively natural scenes. It was found that for the majority of the neurons significant amounts of information were reflected about which of several of the 23 faces had been seen. Thus the representation was not local, for in a local representation almost all the information available can be obtained when the single stimulus to which the neuron responds best is shown. It is shown that the information available about any one stimulus depended on how different (for example, how many standard deviations) the response to that stimulus was from the average response to all stimuli. This was the case for responses below the average response as well as above. It is shown that the fraction of information carried by the low firing rates of a cell was large--much larger than that carried by the high firing rates. Part of the reason for this is that the probability distribution of different firing rates is biased toward low values (though with fewer very low values than would be predicted by an exponential distribution). Another factor is that the variability of the response is large at intermediate and high firing rates. Another finding is that at short sampling intervals (such as 20 ms) the neurons code information efficiently, by effectively acting as binary variables and behaving less noisily than would be expected of a Poisson process.

Binding Hierarchies: A Basis for Dynamic Perceptual Grouping

Since it has been suggested that the brain binds its fragmentary representations of perceptual events via phase-locking of stimulated neural oscillators, it is important to determine how extended synchronization can occur in a clustered organization of cells possessing a distribution of firing rates. To answer that question, we establish the basic conditions for the existence of a binding mechanism based on synchronized oscillations. In addition, we present a simple hierarchical architecture of feedback units that not only induces robust phase-locking within and segregation between perceptual groups, but also serves as a generic binding machine.

What determines the capacity of autoassociative memories in the brain?

Threshold-linear (graded response) units approximate the real firing behaviour of pyramidal neurons in a simplified form, suited to the analytical study of large autoassociative networks. Here we extend previous results on threshold-linear networks to a much larger class of models, by considering different connectivities (including full feedback, highly diluted and multilayer feedforward architectures), different forms of Hebbian learning rules, and different distributions of firing rates (including realistic, continuous distributions of rates). This allows an evaluation of the main factors which may affect, in real cortical networks, the capacity for storage and retrieval of discrete firing patterns.In each case a single equation is derived, which determines both αc, the maximum number of retrievable patterns per synapse, and Im, the maximum amount of retrievable information per synapse. It is shown that: 1. Non-speeific effects, such as those usually ascribed to inhibition, or to neuramodulatary afferen...

Firing patterns of single units in the prefrontal cortex and neural network models

The occurrences of high-frequency bursts of neural activity and the probability distribution of firing rates of neurons were investigated in the behaving monkey. The activity of 8 to 11 single units was recorded in parallel through six metal microelectrodes from the frontal cortical areas. High-frequency (>150 Hz) bursts of three or more spikes in succession were extremely rare, occurring at an average rate of 0.068 per second per neuron. The probability of observing a burst in one neuron was not affected by the fact that another adjacent neuron emitted a burst. Thus, if a high-frequency burst represents the ‘on’ state of a neuron, we failed to demonstrate persistent states in which a group of neurons is turned ‘on’ together. The firing rates of the neurons were usually low. The probability of a neuron firing a few (2–5) spikes within a narrow (10–100 ms) time window was very low (<0.003). The probability density of firing rates did not show any sign of inhomogeneity, thus failing to show that the neurons...

Firing patterns of single units in the prefrontal cortex and neural network models

The occurrences of high-frequency bursts of neural activity and the probability distribution of firing rates of neurons were investigated in the behaving monkey. The activity of 8 to 11 single units was recorded in parallel through six metal microelectrodes from the frontal cortical areas. High-frequency (>150 Hz) bursts of three or more spikes in succession were extremely rare, occurring at an average rate of 0.068 per second per neuron. The probability of observing a burst in one neuron was not affected by the fact that another adjacent neuron emitted a burst. Thus, if a high-frequency burst represents the ‘on’ state of a neuron, we failed to demonstrate persistent states in which a group of neurons is turned ‘on’ together. The firing rates of the neurons were usually low. The probability of a neuron firing a few (2–5) spikes within a narrow (10–100 ms) time window was very low (<0.003). The probability density of firing rates did not show any sign of inhomogeneity, thus failing to show that the neurons tended to be either in a state of high firing rate or in a state of low firing rate for any periods of time. The low probability of finding a neuron with an elevated firing rate means either that a given cortical area is idle most of the time, or that, in a given process, only a few neurons elevate their firing rates at any one time. The relevance of these findings to neural network models is discussed.

Validation of EEG topographical mapping with neuropsychological functional activation

Neocortical pyramidal neurons regulate firing around a stable mean firing rate (FR) that can differ by orders of magnitude between neurons, but the factors that determine where individual neurons sit within this broad FR distribution are not understood. To access low- and high-FR neurons for ex vivo analysis, we used Ca2+- and UV-dependent photoconversion of CaMPARI2 in vivo to permanently label neurons according to mean FR. CaMPARI2 photoconversion was correlated with immediate early gene expression and higher FRs ex vivo and tracked the drop and rebound in ensemble mean FR induced by prolonged monocular deprivation. High-activity L4 pyramidal neurons had greater intrinsic excitability and recurrent excitatory synaptic strength, while E/I ratio, local output strength, and local connection probability were not different. Thus, in L4 pyramidal neurons (considered a single transcriptional cell type), a broad mean FR distribution is achieved through graded differences in both intrinsic and synaptic properties.

Dopaminergic neurons: Effect of acute and chronic morphine administration on single cell activity and transmitter metabolism

At various time points following acute and chronic administration of morphine to rats, dopamine transmitter metabolism and neuronal activity were determined. Following acute injection of morphine (20 mg/kg intraperitoneally), dopamine cell firing rates increased slowly and steadily. This slow increase was accompanied by a similar slow increase in the accumulation of the dopamine metabolite, dihydroxyphenylacetic acid (DOPAC). Apparent in vivo tyrosine hydroxylase activity, measured by dopa accumulation following inhibition of dopa decarboxylase, also increased. In chronically treated animals the average firing rate of dopamine cells was measured two hours after the last injection of morphine. The distribution of dopamine cell firing rates was significantly higher than in controls. DOPAC levels and in vivo tyrosine hydroxylase activity were also increased at this time. When morphine (100 mg/kg intraperitoneally) was administered to chronically treated animals 12 hours after the last injection a slow increase of firing rates was observed similar to that seen in naive animals after an acute morphine injection. In chronically morphine treated animals naloxone caused a rapid dose-dependent decrease in firing rates and DOPAC levels. In vivo tyrosine hydroxylase activity was not changed.

Firing rate and size distribution of the hind limb extensor and flexor motoneuronal units.

Axonal spike size of extensor and flexor motoneurones were subjected to statistical analysis. Extensor motoneurones were isolated in decerebrate cats and the flexor motoneurones in spinalized cats. Smallest spikes were due to gamma motoneurones which could be further classified as small, medium and large. Extensor and flexor alpha motoneuronal units were also divided into these three subgroups. Considering the firing pattern and the cell size extensor alpha units were divided into five types: small-tonic, medium-tonic, large-tonic, large-phasic and largest-phasic. Maximum firing rate of extensor alpha units was directly related to the cell size and was distributed between 5-15, 15-20, 25-40 and 35-55 imp/sec for the small-tonic, medium-tonic, large-tonic and large-phasic motoneurones. Stabilized firing rates were distributed between 5-10, 10-15 and 15-20 imp./sec for the small-tonic, medium-tonic and large-tonic motoneurones. Flexor motoneuronal types and their maximum firing rates were as follows: small-tonic (16 imp./sec), medium-tonic (24 imp./sec), small-phasic (37.5 imp/sec), medium-phasic (30 imp./sec), large-phasic (46 imp./sec) and largest-phasic (only one or two impulses). The functional significance of the results was discussed considering the axonal spike size as an index for the cell size.