Relationship between applicability of current-based synapses and uniformity of firing patterns

The purpose of this paper is to identify situations in neural network modeling where current-based synapses are applicable. The applicability of current-based synapse model for studying post-transient behavior of neural networks is discussed in terms of average synaptic current strength induced by per spike during one firing cycle of a neuron (or briefly per spike synaptic current strength). It was found that current-based synapse models are applicable in both situations where both the interspike intervals of the neurons and the distribution of firing times of the neurons are uniform, and where the firing of all neurons is synchronized. If neither the interspike intervals nor the distribution of firing times of the neurons is uniform or the reversal potential is between the rest and threshold potentials, current-based synapse models may be oversimplified.     

Presynaptic learning and memory with a persistent firing neuron and a habituating synapse: a model of short term persistent habituation

Our paper explores the interaction of persistent firing axonal and presynaptic processes in the generation of short term memory for habituation. We first propose a model of a sensory neuron whose axon is able to switch between passive conduction and persistent firing states, thereby triggering short term retention to the stimulus. Then we propose a model of a habituating synapse and explore all nine of the behavioral characteristics of short term habituation in a two neuron circuit. We couple the persistent firing neuron to the habituation synapse and investigate the behavior of short term retention of habituating response. Simulations show that, depending on the amount of synaptic resources, persistent firing either results in continued habituation or maintains the response, both leading to longer recovery times. The effectiveness of the model as an element in a bio-inspired memory system is discussed.     

A Robust In Vivo-Like Persistent Firing Supported by a Hybrid of Intracellular and Synaptic Mechanisms

Persistent firing is believed to support short-term information retention in the brain. Established hypotheses make use of the recurrent synaptic connectivity to support persistent firing. However, this mechanism is known to suffer from a lack of robustness. On the other hand, persistent firing can be supported by an intrinsic cellular mechanism in multiple brain areas. However, the consequences of having both the intrinsic and the synaptic mechanisms (a hybrid model) on persistent firing remain largely unknown. The goal of this study is to investigate whether a hybrid neural network model with these two mechanisms has advantages over a conventional recurrent network based model. Our computer simulations were based on in vitro recordings obtained from hippocampal CA3 pyramidal cells under cholinergic receptor activation. Calcium activated non-specific cationic (CAN) current supported persistent firing in the Hodgkin-Huxley style cellular models. Our results suggest that the hybrid model supports persistent firing within a physiological frequency range over a wide range of different parameters, eliminating parameter sensitivity issues generally recognized in network based persistent firing. In addition, persistent firing in the hybrid model is substantially more robust against distracting inputs, can coexist with theta frequency oscillations, and supports pattern completion.     

Effects of active versus passive dendritic membranes on the transfer properties of a simulated neuron

In a simulated neuron with a dendritic tree, the relative effects of active and passive dendritic membranes on transfer properties were studied. The simulations were performed by means of a digital computer. The computations calculated the changes in transmembrane voltages of many compartments over time as a function of other biophysical variables. These variables were synaptic input intensity, critical firing threshold, rate of leakage of current across the membrane, and rate of longitudinal current spread between compartments. For both passive and active dendrites, the transfer properties of the soma studied for different rates of longitudinal current spread. With low rates of current spread, graded changes in firing threshold produced correspondingly graded changes in output discharge. With high rates of current spread, the neuron became a bistable operator where spiking was enhanced if the threshold was below a certain level and suppressed if the threshold was above that level. Since alterations in firing threshold were shown to have the same effect on firing rate as alterations in synaptic input intensity, the neuron can be said to change from graded to contrast-enhancing in its response to stimuli of different intensities. The presence or absence of dendritic spiking was found to have a significant effect on the integrative properties of the simulated neuron. In particular, contrast enhancement was considerably more pronounced in neurons with passive than with active dendrites in that somatic spike rates reached a higher maximum when dendrites were passive. With active dendrites, a less intense input was needed to initiate somatic spiking than with passive dendrites because a distal dendritic spike could easily propagate by means of longitudinal current spread to the soma. Once somatic spiking was initiated, though, spike rates tended to be lower with active than with passive dendrites because the soma recovered more slowly from its post-spike refractory period if it was also influenced by refractory periods in the dendrites. The experiment of comparing neurons with active and passive dendrites was repeated at a different, higher value of synaptic input. The same differences in transfer properties between the active and passive cases emerged as before. Spiking patterns in neurons with active dendrites were also affected by the time distribution of synaptic inputs. In a previous study, inputs had been random over both space and time, varying about a predetermined mean, whereas in the present study, inputs were random over space but uniform over time. When inputs were made uniform over time, spiking became more difficult to initiate and the transition from graded to bistable response became less sharp.     

Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons

The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrate-and-fire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory's predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.     

Spike tranfer in statistical neuron assemblies. II. Neuron--nonlinear spike source]

The mathematical model of the neuron function is known to rely on space summing of excitement. The spikes contribute to the inner state of the neuron the farther from cell soma the synapses are located. The difference between excitatory and inhibitory effect results in spike firing if only neural firing threshold is achieved. The values of spike flux have been estimated on the basis of the model of CA3 sector of the Hippocampus and were found to be 15 divided by 35 imp/s.     

Dendritic Nonlinearities Reduce Network Size Requirements and Mediate ON and OFF States of Persistent Activity in a PFC Microcircuit Model

Technological advances have unraveled the existence of small clusters of co-active neurons in the neocortex. The functional implications of these microcircuits are in large part unexplored. Using a heavily constrained biophysical model of a L5 PFC microcircuit, we recently showed that these structures act as tunable modules of persistent activity, the cellular correlate of working memory. Here, we investigate the mechanisms that underlie persistent activity emergence (ON) and termination (OFF) and search for the minimum network size required for expressing these states within physiological regimes. We show that (a) NMDA-mediated dendritic spikes gate the induction of persistent firing in the microcircuit. (b) The minimum network size required for persistent activity induction is inversely proportional to the synaptic drive of each excitatory neuron. (c) Relaxation of connectivity and synaptic delay constraints eliminates the gating effect of NMDA spikes, albeit at a cost of much larger networks. (d) Persistent activity termination by increased inhibition depends on the strength of the synaptic input and is negatively modulated by dADP. (e) Slow synaptic mechanisms and network activity contain predictive information regarding the ability of a given stimulus to turn ON and/or OFF persistent firing in the microcircuit model. Overall, this study zooms out from dendrites to cell assemblies and suggests a tight interaction between dendritic non-linearities and network properties (size/connectivity) that may facilitate the short-memory function of the PFC.     

On the role of astrocytes in synchronization of two coupled neurons: a mathematical perspective

Based on recent findings, astrocytes, a subtype of glial cells, dynamically regulate the synaptic transmission of neuronal networks. In this research, a biologically inspired neuronal network model is constructed by connecting two Morris-Lecar neuron models. In this minimal network model, neuron–astrocyte interactions are considered in a functional-based procedure. Utilizing the developed model and according to the theoretical analysis carried out in the article, it is confirmed that, the astrocyte increases the threshold value of synchronization and provides appropriate feedback control in regulating the neural activities. Therefore, the healthy astrocyte has the potential to desynchronize the synchrony between two coupled neurons. Next, we investigate malfunction of the astrocyte in the regulatory feedback loop. Mathematically, we verify that pathologic astrocyte is no longer able to increase the synchronization threshold and therefore, it cannot compensate excessive increase in the excitation level. The main reason behind this is the fact that healthy astrocyte can optimally increase the input current of the individual neurons, while the so-called pathological astrocyte is unable to modify correctly the amount of this current. Consequently, disruptions of the signaling function of astrocyte initiate the hypersynchronous firing of neurons. In other words, reduction in neuron–astrocyte cross-talk will lead to synchronized firing of neurons. Therefore, our results propose that the astrocyte could have a key role in stabilizing neural activity.     

Efficiency of neural transmission as a function of synaptic noise, threshold, and source characteristics

There has been a growing interest in the estimation of information carried by a single neuron and multiple single units or population of neurons to specific stimuli. In this paper we analyze, inspired by article of Levy and Baxter (2002), the efficiency of a neuronal communication by considering dendrosomatic summation as a Shannon-type channel (1948) and by considering such uncertain synaptic transmission as part of the dendrosomatic computation. Specifically, we study Mutual Information between input and output signals for different types of neuronal network architectures by applying efficient entropy estimators. We analyze the influence of the following quantities affecting transmission abilities of neurons: synaptic failure, activation threshold, firing rate and type of the input source. We observed a number of surprising non-intuitive effects. It turns out that, especially for lower activation thresholds, significant synaptic noise can lead even to twofold increase of the transmission efficiency. Moreover, the efficiency turns out to be a non-monotonic function of the activation threshold. We find a universal value of threshold for which a local maximum of Mutual Information is achieved for most of the neuronal architectures, regardless of the type of the source (correlated and non-correlated). Additionally, to reach the global maximum the optimal firing rates must increase with the threshold. This effect is particularly visible for lower firing rates. For higher firing rates the influence of synaptic noise on the transmission efficiency is more advantageous. Noise is an inherent component of communication in biological systems, hence, based on our analysis, we conjecture that the neuronal architecture was adjusted to make more effective use of this attribute.     

Predictive features of persistent activity emergence in regular spiking and intrinsic bursting model neurons

Proper functioning of working memory involves the expression of stimulus-selective persistent activity in pyramidal neurons of the prefrontal cortex (PFC), which refers to neural activity that persists for seconds beyond the end of the stimulus. The mechanisms which PFC pyramidal neurons use to discriminate between preferred vs. neutral inputs at the cellular level are largely unknown. Moreover, the presence of pyramidal cell subtypes with different firing patterns, such as regular spiking and intrinsic bursting, raises the question as to what their distinct role might be in persistent firing in the PFC. Here, we use a compartmental modeling approach to search for discriminatory features in the properties of incoming stimuli to a PFC pyramidal neuron and/or its response that signal which of these stimuli will result in persistent activity emergence. Furthermore, we use our modeling approach to study cell-type specific differences in persistent activity properties, via implementing a regular spiking (RS) and an intrinsic bursting (IB) model neuron. We identify synaptic location within the basal dendrites as a feature of stimulus selectivity. Specifically, persistent activity-inducing stimuli consist of activated synapses that are located more distally from the soma compared to non-inducing stimuli, in both model cells. In addition, the action potential (AP) latency and the first few inter-spike-intervals of the neuronal response can be used to reliably detect inducing vs. non-inducing inputs, suggesting a potential mechanism by which downstream neurons can rapidly decode the upcoming emergence of persistent activity. While the two model neurons did not differ in the coding features of persistent activity emergence, the properties of persistent activity, such as the firing pattern and the duration of temporally-restricted persistent activity were distinct. Collectively, our results pinpoint to specific features of the neuronal response to a given stimulus that code for its ability to induce persistent activity and predict differential roles of RS and IB neurons in persistent activity expression.     

Modeling aspects of learning by altering biophysical properties of a simulated neuron

A simulated neuron was constructed in which effects on spike discharge of altering certain fundamental biophysical parameters could be studied. The simulation was performed by use of a digital computer. The simulation was tested by comparing performance of the simulated neuron with that of actual neurons. Rates and patterns of spike discharge were achieved for the simulated neuron that were comparable to those recorded from units in the motor cortex of awake cats. Altering biophysical parameters such as firing threshold, levels of synaptic input or rates of transverse and longitudinal current spread produced appropriate alterations of discharge rate. On the above basis it was possible to investigate interrelated effects on spike discharge of changing levels of synaptic input and rates of current spread within the simulated neuron. With low rates of longitudinal current spread, graded levels of synaptic input produced correspondingly graded levels of ouput discharge. With high rates of longitudinal current spread, the transfer properties of the neuron were markedly altered. The neuron became a bistable operator where synaptic inputs above a certain level were enhanced and all those below were suppressed. A linear relationship was found to exist between firing threshold and the level of synaptic input required to reach the transition from quiescence to near-tetanic rates of discharge.Alterations in behavior are increasingly thought to be subserved by changes in the efficacy of synaptic transmission or in the post-synaptic intergrative propeties of neurons. The results of our investigations describe the interplay between those two processes.     

Threshold behavior in the initiation of hippocampal population bursts

Hippocampal population discharges such as sharp waves, epileptiform firing, and GDPs recur at long and variable intervals. The mechanisms for their precise timing are not well understood. Here, we show that population bursts in the disinhibited CA3 region are initiated at a threshold level of population firing after recovery from a previous event. Each population discharge follows an active buildup period when synaptic traffic and cell firing increase to threshold levels. Single-cell firing can advance burst onset by increasing population firing to suprathreshold values. Population synchrony is suppressed when threshold frequencies cannot be reached due to reduced cellular excitability or synaptic efficacy. Reducing synaptic strength reveals partially synchronous population bursts that are curtailed by GABA(B)-mediated conductances. Excitatory glutamatergic transmission and delayed GABA(B)-mediated signals have opposing feedback effects on CA3 cell firing and so determine threshold behavior for population synchrony.     

Pyramidal neuron as two-layer neural network

The pyramidal neuron is the principal cell type in the mammalian forebrain, but its function remains poorly understood. Using a detailed compartmental model of a hippocampal CA1 pyramidal cell, we recorded responses to complex stimuli consisting of dozens of high-frequency activated synapses distributed throughout the apical dendrites. We found the cell's firing rate could be predicted by a simple formula that maps the physical components of the cell onto those of an abstract two-layer "neural network." In the first layer, synaptic inputs drive independent sigmoidal subunits corresponding to the cell's several dozen long, thin terminal dendrites. The subunit outputs are then summed within the main trunk and cell body prior to final thresholding. We conclude that insofar as the neural code is mediated by average firing rate, a two-layer neural network may provide a useful abstraction for the computing function of the individual pyramidal neuron.     

Sensitive dependence of the coefficient of variation of interspike intervals on the lower boundary of membrane potential for the leaky integrate-and-fire neuron model

After the report of Softky and Koch [Softky, W.R., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334-350], leaky integrate-and-fire models have been investigated to explain high coefficient of variation (CV) of interspike intervals (ISIs) at high firing rates observed in the cortex. The purpose of this paper is to study the effect of the position of a lower boundary of membrane potential on the possible value of CV of ISIs based on the diffusional leaky integrate-and-fire models with and without reversal potentials. Our result shows that the irregularity of ISIs for the diffusional leaky integrate-and-fire neuron significantly changes by imposing a lower boundary of membrane potential, which suggests the importance of the position of the lower boundary as well as that of the firing threshold when we study the statistical properties of leaky integrate-and-fire neuron models. It is worth pointing out that the mean-CV plot of ISIs for the diffusional leaky integrate-and-fire neuron with reversal potentials shows a close similarity to the experimental result obtained in Softky and Koch [Softky, W.R., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334-350].     

Information maintenance and statistical dependence reduction in simple neural networks

This study compares the ability of excitatory, feed-forward neural networks to construct good transformations on their inputs. The quality of such a transformation is judged by the minimization of two information measures: the information loss of the transformation and the statistical dependency of the output. The networks that are compared differ from each other in the parametric properties of their neurons and in their connectivity. The particular network parameters studied are output firing threshold, synaptic connectivity, and associative modification of connection weights. The network parameters that most directly affect firing levels are threshold and connectivity. Networks incorporating neurons with dynamic threshold adjustment produce better transformations. When firing threshold is optimized, sparser synaptic connectivity produces a better transformation than denser connectivity. Associative modification of synaptic weights confers only a slight advantage in the construction of optimal transformations. Additionally, our research shows that some environments are better suited than others for recoding. Specifically, input environments high in statistical dependence, i.e. those environments most in need of recoding, are more likely to undergo successful transformations.     

Modulation of a feeding neural circuit by microinjection of K+ channel expression genes into a single identified neuron in Aplysia kurodai

In Aplysia buccal ganglion expression genes for voltage-dependent K(+) channels (AKv1.1a) were injected into one of four electrically coupled multi-action (MA) neurons that directly inhibit jaw-closing (JC) motor neurons and may cooperatively generate their firing pattern during the feeding response. Following the DNA injection, the firing threshold increased and the spike frequency at the same current decreased in the current-induced excitation of the MA neuron; indicating a decrease in excitability of the MA neuron. This procedure also reduced the firing activity of MA neurons during the feeding-like rhythmic responses induced by the electrical nerve stimulation. Moreover, the firing pattern in JC motor neurons was remarkably changed, suggesting the effective contribution of a single MA neuron or electrically coupled MA neurons to the generation of the firing pattern in the JC motor neurons. This method appears useful for exploring the functional roles of specific neurons in complex neural circuits.     

A homeostatic model of neuronal firing governed by feedback signals from the extracellular matrix

Molecules of the extracellular matrix (ECM) can modulate the efficacy of synaptic transmission and neuronal excitability. These mechanisms are crucial for the homeostatic regulation of neuronal firing over extended timescales. In this study, we introduce a simple mathematical model of neuronal spiking balanced by the influence of the ECM. We consider a neuron receiving random synaptic input in the form of Poisson spike trains and the ECM, which is modeled by a phenomenological variable involved in two feedback mechanisms. One feedback mechanism scales the values of the input synaptic conductance to compensate for changes in firing rate. The second feedback accounts for slow fluctuations of the excitation threshold and depends on the ECM concentration. We show that the ECM-mediated feedback acts as a robust mechanism to provide a homeostatic adjustment of the average firing rate. Interestingly, the activation of feedback mechanisms may lead to a bistability in which two different stable levels of average firing rates can coexist in a spiking network. We discuss the mechanisms of the bistability and how they may be related to memory function.     

A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties

The integrate-and-fire neuron model describes the state of a neuron in terms of its membrane potential, which is determined by the synaptic inputs and the injected current that the neuron receives. When the membrane potential reaches a threshold, an action potential (spike) is generated. This review considers the model in which the synaptic input varies periodically and is described by an inhomogeneous Poisson process, with both current and conductance synapses. The focus is on the mathematical methods that allow the output spike distribution to be analyzed, including first passage time methods and the Fokker–Planck equation. Recent interest in the response of neurons to periodic input has in part arisen from the study of stochastic resonance, which is the noise-induced enhancement of the signal-to-noise ratio. Networks of integrate-and-fire neurons behave in a wide variety of ways and have been used to model a variety of neural, physiological, and psychological phenomena. The properties of the integrate-and-fire neuron model with synaptic input described as a temporally homogeneous Poisson process are reviewed in an accompanying paper (Burkitt in Biol Cybern, 2006).     

Emergence of resonances in neural systems: the interplay between adaptive threshold and short-term synaptic plasticity

In this work we study the detection of weak stimuli by spiking (integrate-and-fire) neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present activity-dependent processes, such as short-term synaptic depression and facilitation. Employing mean-field techniques as well as numerical simulations, we found that there are two possible noise levels which optimize signal transmission. This new finding is in contrast with the classical theory of stochastic resonance which is able to predict only one optimal level of noise. We found that the complex interplay between adaptive neuron threshold and activity-dependent synaptic mechanisms is responsible for this new phenomenology. Our main results are confirmed by employing a more realistic FitzHugh-Nagumo neuron model, which displays threshold variability, as well as by considering more realistic stochastic synaptic models and realistic signals such as poissonian spike trains.     

Bidirectional modification of presynaptic neuronal excitability accompanying spike timing-dependent synaptic plasticity

Correlated pre- and postsynaptic activity that induces long-term potentiation is known to induce a persistent enhancement of the intrinsic excitability of the presynaptic neuron. Here we report that, associated with the induction of long-term depression in hippocampal cultures and in somatosensory cortical slices, there is also a persistent reduction in the excitability of the presynaptic neuron. This reduction requires postsynaptic Ca(2+) elevation and presynaptic PKA- and PKC-dependent modification of slow-inactivating K(+) channels. The bidirectional changes in neuronal excitability and synaptic efficacy exhibit identical requirements for the temporal order of pre- and postsynaptic activation but reflect two distinct aspects of activity-induced modification of neural circuits.