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Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity
 Neural Computation
, 2003
"... In model networks of Ecells and Icells (excitatory and inhibitory neurons) , synchronous rhythmic spiking often comes about from the interplay between the two cell groups: the Ecells synchronize the Icells and vice versa. Under ideal conditions  homogeneity in relevant network parameters, ..."
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Cited by 42 (8 self)
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In model networks of Ecells and Icells (excitatory and inhibitory neurons) , synchronous rhythmic spiking often comes about from the interplay between the two cell groups: the Ecells synchronize the Icells and vice versa. Under ideal conditions  homogeneity in relevant network parameters, and alltoall connectivity for instance  this mechanism can yield perfect synchronization.
Characterization of Subthreshold Voltage Fluctuations in Neuronal Membranes
, 2003
"... Synaptic noise due to intense network activity can have a significant impact on the electrophysiological properties of individual neurons. This is the case for the cerebral cortex, where ongoing activity leads to strong barrages of synaptic inputs, which act as the main source of synaptic noise affe ..."
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Cited by 28 (13 self)
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Synaptic noise due to intense network activity can have a significant impact on the electrophysiological properties of individual neurons. This is the case for the cerebral cortex, where ongoing activity leads to strong barrages of synaptic inputs, which act as the main source of synaptic noise affecting on neuronal dynamics. Here, we characterize the subthreshold behavior of neuronal models in which synaptic noise is represented by either additive or multiplicative noise, described by OrnsteinUhlenbeck processes. We derive and solve the FokkerPlanck equation for this system, which describes the time evolution of the probability density function for the membrane potential. We obtain an analytic expression for the membrane potential distribution at steady state and compare this expression with the subthreshold activity obtained in HodgkinHuxleytype models with stochastic synaptic inputs. The differences between multiplicative and additive noise models suggest that multiplicative noise is adequate to describe the highconductance states similar to in vivo conditions. Because the steadystate membrane potential distribution is easily obtained experimentally, this approach provides a possible method to estimate the mean and variance of synaptic conductances in real neurons.
Spike Train Probability Models for StimulusDriven Leaky IntegrateandFire Neurons
, 2007
"... Mathematical models of neurons are widely used to improve understanding of neuronal spiking behavior. These models can produce artificial spike trains that resemble actual spiketrain data in important ways, but they are not very easy to apply to the analysis of spiketrain data. Instead, statistica ..."
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Cited by 6 (3 self)
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Mathematical models of neurons are widely used to improve understanding of neuronal spiking behavior. These models can produce artificial spike trains that resemble actual spiketrain data in important ways, but they are not very easy to apply to the analysis of spiketrain data. Instead, statistical methods based on point process models of spike trains provide a wide range of dataanalytical techniques. Two simplified point process models have been introduced in the literature: the timerescaled renewal process (TRRP) and the multiplicative inhomogeneous Markov interval (mIMI) model. In this article we investigate the extent to which the TRRP and mIMI models are able to fit spike trains produced by stimulusdriven leaky integrateandfire (LIF) neurons. With a constant stimulus the LIF spike train is a renewal process, and the mIMI and TRRP models will describe accurately the LIF spike train variability. With a timevarying stimulus, the probability of spiking under all three of these models depends on both the experimental clock time relative to the stimulus and the time since the previous spike, but it does so differently for the LIF, mIMI, and TRRP models. We assessed the distance between the LIF model and each of the two empirical models in the presence of a timevarying 1 stimulus. We found that while lack of fit of a Poisson model to LIF spiketrain data can be evident even in small samples, the mIMI and TRRP models tend to fit well, and much larger samples are required before there is statistical evidence of lack of fit of either the mIMI or TRRP models. We also found that when the mean of the stimulus varies across time the mIMI model provides a better fit to the LIF data than the TRRP, while when the variance of the stimulus varies across time the TRRP provides the better fit. 1
Interspike Interval Variability for Balanced Networks With Reversal Potentials for Large Numbers of Inputs
, 2000
"... The hypothesis that the variability in the discharge of cortical neurons results from balanced excitation and inhibition is analyzed. A method is presented for analyzing the integrate and re neural model with reversal potentials which enables the interspike interval distribution to be calculated in ..."
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The hypothesis that the variability in the discharge of cortical neurons results from balanced excitation and inhibition is analyzed. A method is presented for analyzing the integrate and re neural model with reversal potentials which enables the interspike interval distribution to be calculated in the Gaussian approximation. Results are presented for the perfect integrator model, for which a stable value of the membrane potential in the absence of the spiking mechanism exists. The results show close agreement with numerical simulations for large numbers of small amplitude inputs. The coecient of variation is consistently less than 1.0, as observed in cortical neurons. Key words: Integrate and re neurons, Reversal potentials, Perfect integrator, Interspike interval variability, Firstpassage time. 1 Introduction The origin of the variability in the discharge of cortical neurons is not well understood. An analysis of the coecient of variation in the spikes generated by an integrate an...
An InformationTheoretic Analysis of the Coding of a Periodic Synaptic Input by IntegrateandFire Neurons
, 2002
"... An expression for the mutual information between the phase of a periodic stimulus and the timing of the output spikes generated by the stimulus is given in the low output spikingrate regime. The mutual information is calculated for the leaky integrateandfire neuron in the Gaussian approximation. ..."
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An expression for the mutual information between the phase of a periodic stimulus and the timing of the output spikes generated by the stimulus is given in the low output spikingrate regime. The mutual information is calculated for the leaky integrateandfire neuron in the Gaussian approximation. The mutual information is found to be e#ectively described as a function of the synchronization of the output spikes and their average spikingrate. The results in the subthreshold input regime shed light upon the role of stochastic resonance in such models.
Inferring network activity from synaptic noise
, 2004
"... During intense network activity in vivo, cortical neurons are in a highconductance state, in which the membrane potential (Vm) is subject to a tremendous fluctuating activity. Clearly, this ‘‘synaptic noise’ ’ contains information about the activity of the network, but there are presently no method ..."
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During intense network activity in vivo, cortical neurons are in a highconductance state, in which the membrane potential (Vm) is subject to a tremendous fluctuating activity. Clearly, this ‘‘synaptic noise’ ’ contains information about the activity of the network, but there are presently no methods available to extract this information. We focus here on this problem from a computational neuroscience perspective, with the aim of drawing methods to analyze experimental data. We start from models of cortical neurons, in which highconductance states stem from the random release of thousands of excitatory and inhibitory synapses. This highly complex system can be simplified by using global synaptic conductances described by effective stochastic processes. The advantage of this approach is that one can derive analytically a number of properties from the statistics of resulting Vm fluctuations. For example, the global excitatory and inhibitory conductances can be extracted from synaptic noise, and can be related to the mean activity of presynaptic neurons. We show here that extracting the variances of excitatory and inhibitory synaptic conductances can provide estimates of the mean temporal correlation—or level of synchrony—among thousands of neurons in the network. Thus, ‘‘probing the network’ ’ through intracellular V m activity is possible and constitutes a promising approach, but it will require a continuous effort combining theory, computational models and intracellular physiology.
LETTER Communicated by Adrienne Fairhall Spike Train Probability Models for StimulusDriven Leaky IntegrateandFire Neurons
"... Mathematical models of neurons are widely used to improve understanding of neuronal spiking behavior. These models can produce artificial spike trains that resemble actual spike train data in important ways, but they are not very easy to apply to the analysis of spike train data. Instead, statistica ..."
Abstract
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Mathematical models of neurons are widely used to improve understanding of neuronal spiking behavior. These models can produce artificial spike trains that resemble actual spike train data in important ways, but they are not very easy to apply to the analysis of spike train data. Instead, statistical methods based on point process models of spike trains provide a wide range of dataanalytical techniques. Two simplified point process models have been introduced in the literature: the timerescaled renewal process (TRRP) and the multiplicative inhomogeneous Markov interval (mIMI) model. In this letter we investigate the extent to which the TRRP and mIMI models are able to fit spike trains produced by stimulusdriven leaky integrateandfire (LIF) neurons. With a constant stimulus, the LIF spike train is a renewal process, and the mIMI and TRRP models will describe accurately the LIF spike train variability. With a timevarying stimulus, the probability of spiking under all three of these models depends on both the experimental clock time relative to the stimulus and the time since the previous spike, but it does so differently for the LIF, mIMI, and TRRP models. We assessed the distance between the LIF model and each of the two empirical models in the presence of a timevarying stimulus. We found that while lack of fit of a Poisson model to LIF spike train data can be evident even in small samples, the mIMI and TRRP models tend to fit well, and much larger samples are required before there is statistical evidence of lack of fit of the mIMI or TRRP models. We also found that when the mean of the stimulus varies across time, the mIMI model provides a better fit to the LIF data than the TRRP, and when the variance of the stimulus varies across time, the TRRP provides the better fit. 1