Shared input to a population of neurons induces noise correlations, which can decrease the information carried by a population activity. Inhibitory feedback in recurrent neural networks can reduce the noise correlations and thus increase the information carried by the population activity. However, the activity of inhibitory neurons is costly. This inhibitory feedback decreases the gain of the population. Thus, depolarization of its neurons requires stronger excitatory synaptic input, which is associated with higher ATP consumption. Given that the goal of neural populations is to transmit as much information as possible at minimal metabolic costs, it is unclear whether the increased information transmission reliability provided by inhibitory feedback compensates for the additional costs. We analyze this problem in a network of leaky integrate-and-fire neurons receiving correlated input. By maximizing mutual information with metabolic cost constraints, we show that there is an optimal strength of recurrent connections in the network, which maximizes the value of mutual information-per-cost. For higher values of input correlation, the mutual information-per-cost is higher for recurrent networks with inhibitory feedback compared to feedforward networks without any inhibitory neurons. Our results, therefore, show that the optimal synaptic strength of a recurrent network can be inferred from metabolically efficient coding arguments and that decorrelation of the input by inhibitory feedback compensates for the associated increased metabolic costs.

• MeSH
• akční potenciály fyziologie   MeSH
• modely neurologické MeSH
• nervová síť * fyziologie   MeSH
• nervový přenos * fyziologie   MeSH
• nervový útlum fyziologie   MeSH
• neuronové sítě MeSH
• počítačová simulace MeSH
• reprodukovatelnost výsledků MeSH
• Publikační typ
• časopisecké články MeSH

We present a comparison of the intrinsic saturation of firing frequency in four simple neural models: leaky integrate-and-fire model, leaky integrate-and-fire model with reversal potentials, two-point leaky integrate-and-fire model, and a two-point leaky integrate-and-fire model with reversal potentials. "Two-point" means that the equivalent circuit has two nodes (dendritic and somatic) instead of one (somatic only). The results suggest that the reversal potential increases the slope of the "firing rate vs input" curve due to a smaller effective membrane time constant, but does not necessarily induce saturation of the firing rate. The two-point model without the reversal potential does not limit the voltage or the firing rate. In contrast to the previous models, the two-point model with the reversal potential limits the asymptotic voltage and the firing rate, which is the main result of this paper. The case of excitatory inputs is considered first and followed by the case of both excitatory and inhibitory inputs.

• MeSH
• akční potenciály fyziologie   MeSH
• fyzikální jevy MeSH
• membránové potenciály fyziologie   MeSH
• modely neurologické * MeSH
• neurony * fyziologie   MeSH
• Publikační typ
• časopisecké články MeSH

In this paper we investigate the rate coding capabilities of neurons whose input signal are alterations of the base state of balanced inhibitory and excitatory synaptic currents. We consider different regimes of excitation-inhibition relationship and an established conductance-based leaky integrator model with adaptive threshold and parameter sets recreating biologically relevant spiking regimes. We find that given mean post-synaptic firing rate, counter-intuitively, increased ratio of inhibition to excitation generally leads to higher signal to noise ratio (SNR). On the other hand, the inhibitory input significantly reduces the dynamic coding range of the neuron. We quantify the joint effect of SNR and dynamic coding range by computing the metabolic efficiency-the maximal amount of information per one ATP molecule expended (in bits/ATP). Moreover, by calculating the metabolic efficiency we are able to predict the shapes of the post-synaptic firing rate histograms that may be tested on experimental data. Likewise, optimal stimulus input distributions are predicted, however, we show that the optimum can essentially be reached with a broad range of input distributions. Finally, we examine which parameters of the used neuronal model are the most important for the metabolically efficient information transfer.

• MeSH
• adenosintrifosfát metabolismus   MeSH
• akční potenciály fyziologie   MeSH
• excitační postsynaptické potenciály fyziologie   MeSH
• membránové potenciály fyziologie   MeSH
• modely neurologické * MeSH
• nervové vedení fyziologie   MeSH
• nervový přenos fyziologie   MeSH
• nervový útlum fyziologie   MeSH
• neurony fyziologie   MeSH
• počítačová simulace MeSH
• poměr signál - šum MeSH
• výpočetní biologie MeSH
• zvířata MeSH
• Check Tag
• zvířata MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH

Statistical properties of spike trains as well as other neurophysiological data suggest a number of mathematical models of neurons. These models range from entirely descriptive ones to those deduced from the properties of the real neurons. One of them, the diffusion leaky integrate-and-fire neuronal model, which is based on the Ornstein-Uhlenbeck (OU) stochastic process that is restricted by an absorbing barrier, can describe a wide range of neuronal activity in terms of its parameters. These parameters are readily associated with known physiological mechanisms. The other model is descriptive, Gamma renewal process, and its parameters only reflect the observed experimental data or assumed theoretical properties. Both of these commonly used models are related here. We show under which conditions the Gamma model is an output from the diffusion OU model. In some cases, we can see that the Gamma distribution is unrealistic to be achieved for the employed parameters of the OU process.

• MeSH
• difuze * MeSH
• kybernetika MeSH
• modely neurologické * MeSH
• neurony * MeSH
• stochastické procesy MeSH
• Publikační typ
• časopisecké články MeSH

Leaky integrate-and-fire neuronal models with reversal potentials have a number of different diffusion approximations, each depending on the form of the amplitudes of the postsynaptic potentials. Probability distributions of the first-passage times of the membrane potential in the original model and its diffusion approximations are numerically compared in order to find which of the approximations is the most suitable one. The properties of the random amplitudes of postsynaptic potentials are discussed. It is shown on a simple example that the quality of the approximation depends directly on them.

• MeSH
• akční potenciály fyziologie   MeSH
• difuze MeSH
• lidé MeSH
• matematika MeSH
• membránové potenciály fyziologie   MeSH
• modely neurologické * MeSH
• neurony fyziologie   MeSH
• normální rozdělení MeSH
• počítačová simulace MeSH
• Poissonovo rozdělení MeSH
• pravděpodobnost MeSH
• stochastické procesy MeSH
• synaptické potenciály MeSH
• Check Tag
• lidé MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH

The Ornstein-Uhlenbeck neuronal model is specified by two types of parameters. One type corresponds to the properties of the neuronal membrane, whereas the second type (local average rate of the membrane depolarization and its variability) corresponds to the input of the neuron. In this article, we estimate the parameters of the second type from an intracellular record during neuronal firing caused by stimulation (audio signal). We compare the obtained estimates with those from the spontaneous part of the record. As predicted from the model construction, the values of the input parameters are larger for the periods when neuron is stimulated than for the spontaneous ones. Finally, the firing regimen of the model is checked. It is confirmed that the neuron is in the suprathreshold regimen during the stimulation.

• MeSH
• akční potenciály fyziologie   MeSH
• akustická stimulace metody   MeSH
• časové faktory MeSH
• elektroencefalografie MeSH
• membránové potenciály fyziologie   MeSH
• modely neurologické MeSH
• morčata MeSH
• nervové dráhy fyziologie   MeSH
• neurony klasifikace   fyziologie   MeSH
• počítačové zpracování signálu MeSH
• reakční čas fyziologie   MeSH
• stochastické procesy MeSH
• zvířata MeSH
• Check Tag
• morčata MeSH
• zvířata MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH

Parameters in diffusion neuronal models are divided into two groups; intrinsic and input parameters. Intrinsic parameters are related to the properties of the neuronal membrane and are assumed to be known throughout the paper. Input parameters characterize processes generated outside the neuron and methods for their estimation are reviewed here. Two examples of the diffusion neuronal model, which are based on the integrate-and-fire concept, are investigated--the Ornstein--Uhlenbeck model as the most common one and the Feller model as an illustration of state-dependent behavior in modeling the neuronal input. Two types of experimental data are assumed-intracellular describing the membrane trajectories and extracellular resulting in knowledge of the interspike intervals. The literature on estimation from the trajectories of the diffusion process is extensive and thus the stress in this review is set on the inference made from the interspike intervals.

• MeSH
• modely neurologické MeSH
• neurony MeSH
• Publikační typ
• práce podpořená grantem MeSH
• přehledy MeSH

An optimum signal in the Ornstein-Uhlenbeck neuronal model is determined on the basis of interspike interval data. Two criteria are proposed for this purpose. The first, the classical one, is based on searching for maxima of the slope of the frequency transfer function. The second one uses maximum of the Fisher information, which is, under certain conditions, the inverse variance of the best possible estimator. The Fisher information is further normalized with respect to the time required to make the observation on which the signal estimation is performed. Three variants of the model are investigated. Beside the basic one, we use the version obtained by inclusion of the refractory period. Finally, we investigate such a version of the model in which signal and the input parameter of the model are in a nonlinear relationship. The results show that despite qualitative similarity between the criteria, there is substantial quantitative difference. As a common feature, we found that in the Ornstein-Uhlenbeck model with increasing noise the optimum signal decreases and the coding range gets broader.

• MeSH
• akční potenciály fyziologie   MeSH
• algoritmy MeSH
• financování organizované MeSH
• lidé MeSH
• membránové potenciály fyziologie   MeSH
• modely neurologické MeSH
• nervové vedení fyziologie   MeSH
• neurony fyziologie   MeSH
• refrakterní doba elektrofyziologická fyziologie   MeSH
• stochastické procesy MeSH
• zvířata MeSH
• Check Tag
• lidé MeSH
• zvířata MeSH

Five parameters of one of the most common neuronal models, the diffusion leaky integrate-and-fire model, also known as the Ornstein-Uhlenbeck neuronal model, were estimated on the basis of intracellular recording. These parameters can be classified into two categories. Three of them (the membrane time constant, the resting potential and the firing threshold) characterize the neuron itself. The remaining two characterize the neuronal input. The intracellular data were collected during spontaneous firing, which in this case is characterized by a Poisson process of interspike intervals. Two methods for the estimation were applied, the regression method and the maximum-likelihood method. Both methods permit to estimate the input parameters and the membrane time constant in a short time window (a single interspike interval). We found that, at least in our example, the regression method gave more consistent results than the maximum-likelihood method. The estimates of the input parameters show the asymptotical normality, which can be further used for statistical testing, under the condition that the data are collected in different experimental situations. The model neuron, as deduced from the determined parameters, works in a subthreshold regimen. This result was confirmed by both applied methods. The subthreshold regimen for this model is characterized by the Poissonian firing. This is in a complete agreement with the observed interspike interval data.

• MeSH
• akční potenciály fyziologie   MeSH
• buněčná membrána fyziologie   MeSH
• financování organizované MeSH
• lidé MeSH
• mozek fyziologie   MeSH
• nervové dráhy fyziologie   MeSH
• nervový přenos fyziologie   MeSH
• neuronové sítě MeSH
• neurony fyziologie   MeSH
• počítačové zpracování signálu MeSH
• Poissonovo rozdělení MeSH
• stochastické procesy MeSH
• synapse fyziologie   MeSH
• zvířata MeSH
• Check Tag
• lidé MeSH
• zvířata MeSH