Generating oscillatory bursts from a network of regular spiking neurons without inhibition

Avian nucleus isthmi pars parvocellularis (Ipc) neurons are reciprocally connected with the layer 10 (L10) neurons in the optic tectum and respond with oscillatory bursts to visual stimulation. Our in vitro experiments show that both neuron types respond with regular spiking to somatic current injection and that the feedforward and feedback synaptic connections are excitatory, but of different strength and time course. To elucidate mechanisms of oscillatory bursting in this network of regularly spiking neurons, we investigated an experimentally constrained model of coupled leaky integrate-and-fire neurons with spike-rate adaptation. The model reproduces the observed Ipc oscillatory bursting in response to simulated visual stimulation. A scan through the model parameter volume reveals that Ipc oscillatory burst generation can be caused by strong and brief feedforward synaptic conductance changes. The mechanism is sensitive to the parameter values of spike-rate adaptation. In conclusion, we show that a network of regular-spiking neurons with feedforward excitation and spike-rate adaptation can generate oscillatory bursting in response to a constant input.     

Nonlinear electronic circuit with neuron like bursting and spiking dynamics

It is difficult to design electronic nonlinear devices capable of reproducing complex oscillations because of the lack of general constructive rules, and because of stability problems related to the dynamical robustness of the circuits. This is particularly true for current analog electronic circuits that implement mathematical models of bursting and spiking neurons. Here we describe a novel, four-dimensional and dynamically robust nonlinear analog electronic circuit that is intrinsic excitable, and that displays frequency adaptation bursting and spiking oscillations. Despite differences from the classical Hodgkin–Huxley (HH) neuron model, its bifurcation sequences and dynamical properties are preserved, validating the circuit as a neuron model. The circuit's performance is based on a nonlinear interaction of fast–slow circuit blocks that can be clearly dissected, elucidating burst's starting, sustaining and stopping mechanisms, which may also operate in real neurons. Our analog circuit unit is easily linked and may be useful in building networks that perform in real-time.     

Simulating vestibular compensation using recurrent back-propagation

Vestibular compensation is simulated as learning in a dynamic neural network model of the horizontal vestibulo-ocular reflex (VOR). The bilateral, three-layered VOR model consists of nonlinear units representing horizontal canal afferents, vestibular nuclei (VN) neurons and eye muscle motoneurons. Dynamic processing takes place via commissural connections that link the VN bilaterally. The intact network is trained, using recurrent back-propagation, to produce the VOR with velocity storage integration. Compensation is simulated by removing vestibular afferent input from one side and retraining the network. The time course of simulated compensation matches that observed experimentally. The behavior of model VN neurons in the compensated network also matches real data, but only if connections at the motoneurons, as well as at the VN, are allowed to be plastic. The dynamic properties of real VN neurons in compensated and normal animals are found to differ when tested with sinusoidal but not with step stimuli. The model reproduces these conflicting data, and suggests that the disagreement may be due to VN neuron nonlinearity.     

Computer Simulation of After-Inhibition in Crayfish Slowly Adapting Stretch Receptor Neuron

A theoretical model is described which is able to mimic the responses of slowly adapting stretch receptor neurons of crayfish to applied currents. Its principal feature is postspike inhibition, in which each nerve impulses produces a small inhibitory current that decays with a simple exponential time-course that is long compared with normal interspike intervals. The model was simulated with both an analogue and a digital computer. Parameters for particular model neurons were determined both by an analysis of experimental data obtained from adaptation to constant injected currents, and by matching computer output to the data. Parameter values estimated by the two techniques agreed within ±10%. Model parameters determined from adaptation data successfully predicted the magnitude and time-course of posttetanic hyperpolarization (PTH) in the stretch receptor neuron. In addition, model neurons were able to reproduce posttetanic depression (PTD) as seen in stretch receptor cells.     

Attentional modulation of firing rate and synchrony in a model cortical network

The response of a neuron in the visual cortex to stimuli of different contrast placed in its receptive field is commonly characterized using the contrast response curve. When attention is directed into the receptive field of a V4 neuron, its contrast response curve is shifted to lower contrast values (Reynolds et al., 2000). The neuron will thus be able to respond to weaker stimuli than it responded to without attention. Attention also increases the coherence between neurons responding to the same stimulus (Fries et al., 2001). We studied how the firing rate and synchrony of a densely interconnected cortical network varied with contrast and how they were modulated by attention. The changes in contrast and attention were modeled as changes in driving current to the network neurons. We found that an increased driving current to the excitatory neurons increased the overall firing rate of the network, whereas variation of the driving current to inhibitory neurons modulated the synchrony of the network. We explain the synchrony modulation in terms of a locking phenomenon during which the ratio of excitatory to inhibitory firing rates is approximately constant for a range of driving current values. We explored the hypothesis that contrast is represented primarily as a drive to the excitatory neurons, whereas attention corresponds to a reduction in driving current to the inhibitory neurons. Using this hypothesis, the model reproduces the following experimental observations: (1) the firing rate of the excitatory neurons increases with contrast; (2) for high contrast stimuli, the firing rate saturates and the network synchronizes; (3) attention shifts the contrast response curve to lower contrast values; (4) attention leads to stronger synchronization that starts at a lower value of the contrast compared with the attend-away condition. In addition, it predicts that attention increases the delay between the inhibitory and excitatory synchronous volleys produced by the network, allowing the stimulus to recruit more downstream neurons. Action Editor: David Golomb     

How noisy adaptation of neurons shapes interspike interval histograms and correlations

Channel noise is the dominant intrinsic noise source of neurons causing variability in the timing of action potentials and interspike intervals (ISI). Slow adaptation currents are observed in many cells and strongly shape response properties of neurons. These currents are mediated by finite populations of ionic channels and may thus carry a substantial noise component. Here we study the effect of such adaptation noise on the ISI statistics of an integrate-and-fire model neuron by means of analytical techniques and extensive numerical simulations. We contrast this stochastic adaptation with the commonly studied case of a fast fluctuating current noise and a deterministic adaptation current (corresponding to an infinite population of adaptation channels). We derive analytical approximations for the ISI density and ISI serial correlation coefficient for both cases. For fast fluctuations and deterministic adaptation, the ISI density is well approximated by an inverse Gaussian (IG) and the ISI correlations are negative. In marked contrast, for stochastic adaptation, the density is more peaked and has a heavier tail than an IG density and the serial correlations are positive. A numerical study of the mixed case where both fast fluctuations and adaptation channel noise are present reveals a smooth transition between the analytically tractable limiting cases. Our conclusions are furthermore supported by numerical simulations of a biophysically more realistic Hodgkin-Huxley type model. Our results could be used to infer the dominant source of noise in neurons from their ISI statistics.     

A model of visual perception

In this paper we propose a model of visual perception in which a positive feedback mechanism can reproduce the pattern stimulus on a neurons screen. The pattern stimulus reproduction is based on informations coming from the spatial derivatives of visual pattern. This information together with the response of the feature extractors provides to the reproduction of the visual pattern as neuron screen electric activity. We simulate several input patterns and prove that the model reproduces the percept.     

Firing patterns in the adaptive exponential integrate-and-fire model

For simulations of large spiking neuron networks, an accurate, simple and versatile single-neuron modeling framework is required. Here we explore the versatility of a simple two-equation model: the adaptive exponential integrate-and-fire neuron. We show that this model generates multiple firing patterns depending on the choice of parameter values, and present a phase diagram describing the transition from one firing type to another. We give an analytical criterion to distinguish between continuous adaption, initial bursting, regular bursting and two types of tonic spiking. Also, we report that the deterministic model is capable of producing irregular spiking when stimulated with constant current, indicating low-dimensional chaos. Lastly, the simple model is fitted to real experiments of cortical neurons under step current stimulation. The results provide support for the suitability of simple models such as the adaptive exponential integrate-and-fire neuron for large network simulations.     

A computer model of generation of the motor cortex neuron processes seen in the course of execution of instrumental movement

A computer model of neuronal processes in the motor cortex column is presented. The model is consisted of two pyramidal cell layers with two groups of inhibitory interneurons, selectively controlling pyramidal cell soma and dendrite, in each. Active Na, Ca and K conductances are included in the model of a single neuron. Horizontal excitatory connections between pyramidal cells in the upper layer are largely of NMDA-receptor type, that in the lower layer--of non-NMDA-type. All inhibitory synapses are of GABA(A)-type. The model reproduces the main phenomenon observed in the motor cortex during the execution of conditioned movements. Consequent to an early excitation the upper layer pyramidal cells generate a late NMDA-dependent reflexive response to afferent conditional stimulation, which as in a real case is diminished by GABA(A)-type synaptic inhibition and afferent stimulus strength increase. The characteristic inverse relation between the late response manifestation and the stimulus strength observed in the real cortex can be reproduced in the model only if NMDA-glutamate receptors were preferentially localized in the terminals of pyramidal cell backward collaterals, not in the terminals of the afferent fibers on pyramidal neurons. The intended component of motor cortex neuronal activity is generated in NMDA-independent manner by the pyramidal cells of lower layer. The slow time coarse of intended component as compared with short duration of AMPA epsp's is due to a consecutive relay-race--like activation of pyramidal neurons with different dendrit-to-soma ratio.     

The effects of cholinergic neuromodulation on neuronal phase-response curves of modeled cortical neurons

The response of an oscillator to perturbations is described by its phase-response curve (PRC), which is related to the type of bifurcation leading from rest to tonic spiking. In a recent experimental study, we have shown that the type of PRC in cortical pyramidal neurons can be switched by cholinergic neuromodulation from type II (biphasic) to type I (monophasic). We explored how intrinsic mechanisms affected by acetylcholine influence the PRC using three different types of neuronal models: a theta neuron, single-compartment neurons and a multi-compartment neuron. In all of these models a decrease in the amount of a spike-frequency adaptation current was a necessary and sufficient condition for the shape of the PRC to change from biphasic (type II) to purely positive (type I).     

A Model Study of Cellular Short-Term Memory Produced by Slowly Inactivating Potassium Conductances

We analyzed the cellular short-term memory effects induced by a slowly inactivating potassium (Ks) conductance using a biophysical model of a neuron. We first described latency-to-first-spike and temporal changes in firing frequency as a function of parameters of the model, injected current and prior history of the neuron (deinactivation level) under current clamp. This provided a complete set of properties describing the Ks conductance in a neuron. We then showed that the action of the Ks conductance is not generally appropriate for controlling latency-to-first-spike under random synaptic stimulation. However, reliable latencies were found when neuronal population computation was used. Ks inactivation was found to control the rate of convergence to steady-state discharge behavior and to allow frequency to increase at variable rates in sets of synaptically connected neurons. These results suggest that inactivation of the Ks conductance can have a reliable influence on the behavior of neuronal populations under real physiological conditions.     

A burst-feedback model of fast-phase burst generation during nystagmus

 Vestibular and optokinetic nystagmus are characterized by alternating slow-phase eye rotations that stabilize the retinal image, and fast-phase eye rotations that reset eye position. Nystagmus is coordinated in the brainstem by burst neurons that fire an intense, temporally circumscribed burst that terminates the slow phase and drives the fast phase. This paper demonstrates that such a burst can be generated during nystagmus using a simple neural network model containing only known brainstem neurons and their interconnections. These include the feedback connections of the burst neuron (burst feedback). The burst neuron excites itself directly, and disinhibits itself by inhibiting the pause neuron (positive feedback). It also inhibits itself by inhibiting the vestibular neuron (negative feedback). The burst neuron begins to fire after its inhibitory bias is overcome by excitation from the vestibular neuron, and burst neuron positive feedback then produces an intense burst with an abrupt onset. The burst causes the vestibular and pause neurons to pause. The benefit of the pause neuron loop is that it contributes to burst neuron positive feedback when it is needed at burst onset, but that contribution is eliminated when the pause neuron pauses and opens the loop. The burst can then terminate, with an offset duration proportional to burst amplitude, under the control of burst neuron self-excitation and inhibitory bias. Model neuron behavior is comparable to that of real brainstem neurons. Synchronized bursts can be produced over the population of burst neurons in a distributed version of the network. Variability in connection weights in the distributed network results in variability in prelude activity among burst neurons that is similar to the spread in lead observed for real burst neurons during nystagmus. Received: 11 April 1996 / Accepted in revised form: 6 August 1996     

The quantitative single-neuron modeling competition

As large-scale, detailed network modeling projects are flourishing in the field of computational neuroscience, it is more and more important to design single neuron models that not only capture qualitative features of real neurons but are quantitatively accurate in silico representations of those. Recent years have seen substantial effort being put in the development of algorithms for the systematic evaluation and optimization of neuron models with respect to electrophysiological data. It is however difficult to compare these methods because of the lack of appropriate benchmark tests. Here, we describe one such effort of providing the community with a standardized set of tests to quantify the performances of single neuron models. Our effort takes the form of a yearly challenge similar to the ones which have been present in the machine learning community for some time. This paper gives an account of the first two challenges which took place in 2007 and 2008 and discusses future directions. The results of the competition suggest that best performance on data obtained from single or double electrode current or conductance injection is achieved by models that combine features of standard leaky integrate-and-fire models with a second variable reflecting adaptation, refractoriness, or a dynamic threshold.     

Towards an artificial brain

Three components of a brain model operating on neuromolecular computing principles are described. The first component comprises neurons whose input-output behavior is controlled by significant internal dynamics. Models of discrete enzymatic neurons, reaction-diffusion neurons operating on the basis of the cyclic nucleotide cascade, and neurons controlled by cytoskeletal dynamics are described. The second component of the model is an evolutionary learning algorithm which is used to mold the behavior of enzyme-driven neurons or small networks of these neurons for specific function, usually pattern recognition or target seeking tasks. The evolutionary learning algorithm may be interpreted either as representing the mechanism of variation and natural selection acting on a phylogenetic time scale, or as a conceivable ontogenetic adaptation mechanism. The third component of the model is a memory manipulation scheme, called the reference neuron scheme. In principle it is capable of orchestrating a repertoire of enzyme-driven neurons for coherent function. The existing implementations, however, utilize simple neurons without internal dynamics. Spatial navigation and simple game playing (using tic-tac-toe) provide the task environments that have been used to study the properties of the reference neuron model. A memory-based evolutionary learning algorithm has been developed that can assign credit to the individual neurons in a network. It has been run on standard benchmark tasks, and appears to be quite effective both for conventional neural nets and for networks of discrete enzymatic neurons. The models have the character of artificial worlds in that they map the hierarchy of processes in the brain (at the molecular, neuronal, and network levels), provide a task environment, and use this relatively self-contained setup to develop and evaluate learning and adaptation algorithms.     

Dynamics of the exponential integrate-and-fire model with slow currents and adaptation

In order to properly capture spike-frequency adaptation with a simplified point-neuron model, we study approximations of Hodgkin-Huxley (HH) models including slow currents by exponential integrate-and-fire (EIF) models that incorporate the same types of currents. We optimize the parameters of the EIF models under the external drive consisting of AMPA-type conductance pulses using the current-voltage curves and the van Rossum metric to best capture the subthreshold membrane potential, firing rate, and jump size of the slow current at the neuron’s spike times. Our numerical simulations demonstrate that, in addition to these quantities, the approximate EIF-type models faithfully reproduce bifurcation properties of the HH neurons with slow currents, which include spike-frequency adaptation, phase-response curves, critical exponents at the transition between a finite and infinite number of spikes with increasing constant external drive, and bifurcation diagrams of interspike intervals in time-periodically forced models. Dynamics of networks of HH neurons with slow currents can also be approximated by corresponding EIF-type networks, with the approximation being at least statistically accurate over a broad range of Poisson rates of the external drive. For the form of external drive resembling realistic, AMPA-like synaptic conductance response to incoming action potentials, the EIF model affords great savings of computation time as compared with the corresponding HH-type model. Our work shows that the EIF model with additional slow currents is well suited for use in large-scale, point-neuron models in which spike-frequency adaptation is important.     

Reproducing bursting interspike interval statistics of the gustatory cortex

Cortical neurons in vivo generate highly irregular spike sequences. Recently, it was experimentally found that the local variation of interspike intervals, LV, is nearly constant for every spike sequence for the same neurons. On the contrary, the coefficient of variation, CV, varies over different spike sequences. Here, we first show that these characteristic features are also applicable in bursting spike sequences that are obtained from the rat gustatory cortex. Next, we show that the conventional leaky integrate-and-fire model does not fully account for reproducing these statistical features in data of real bursting spike sequences. We resolve this difficulty by proposing an alternative neuron model which is a reduction of the bursting neuron model involving the persistent sodium current. Our study implies that (1) the characteristic features of CV and LV are the results of the endogenous bursting and (2) the bursting behavior in the gustatory cortex is caused mainly by the persistent sodium current.     

Predicting the synaptic information efficacy in cortical layer 5 pyramidal neurons using a minimal integrate-and-fire model

Synaptic information efficacy (SIE) is a statistical measure to quantify the efficacy of a synapse. It measures how much information is gained, on the average, about the output spike train of a postsynaptic neuron if the input spike train is known. It is a particularly appropriate measure for assessing the input–output relationship of neurons receiving dynamic stimuli. Here, we compare the SIE of simulated synaptic inputs measured experimentally in layer 5 cortical pyramidal neurons in vitro with the SIE computed from a minimal model constructed to fit the recorded data. We show that even with a simple model that is far from perfect in predicting the precise timing of the output spikes of the real neuron, the SIE can still be accurately predicted. This arises from the ability of the model to predict output spikes influenced by the input more accurately than those driven by the background current. This indicates that in this context, some spikes may be more important than others. Lastly we demonstrate another aspect where using mutual information could be beneficial in evaluating the quality of a model, by measuring the mutual information between the model’s output and the neuron’s output. The SIE, thus, could be a useful tool for assessing the quality of models of single neurons in preserving input–output relationship, a property that becomes crucial when we start connecting these reduced models to construct complex realistic neuronal networks.     

Firing properties of the soma and axon of the abdominal stretch receptor neurons in the crayfish (Astacus leptodactylus)

Action potentials (APs) and impulse responses in the soma and axon of the rapidly and slowly adapting (SA) abdominal stretch receptor neurons of the crayfish (Astacus leptodactylus) were recorded with single microelectrode current-clamp technique. Impulse frequency response to constant current injection was almost constant in the SA neuron while the response decayed completely in the rapidly adapting (RA) neuron. Mean impulse frequency responses to current stimulations were similar in the receptor neuron pairs. In the RA neuron additional current steps evoked additional impulses while a sudden drop in the current amplitude caused adaptation. Impulse duration was dependent on the rate of rise when current ramps were used. Adaptation was facilitated when calculated receptor current was used. Exposing the neuron to 3 mmol/l TEA or scorpion venom resulted in partly elongated impulse responses. SA neuron could continuously convert the current input into impulse frequency irrespective of previous stimulation conditions. Exposing the SA neuron to 3 mmol/l TEA or 1 mmol/l Lidocaine reduced impulse duration to large current stimulations. The SA neuron fired spontaneously if it was exposed to 5-10 mmol/l Lidocaine or 10(-2) mg/ml Leiurus quinquestriatus venom. The action potential (AP) amplitudes in the RA soma, RA axon, SA soma, and SA axon were significantly different between components of all pairs. Duration of the AP in the axon of the RA neuron was significantly shorter than those in the RA soma, SA soma, and SA axon. Diameter of the RA axon was larger than that of the SA axon. Non-adapting impulse responses were promptly observed only in the SA axons. The results indicate that the RA neuron is a sort of rate receptor transducing the rapid length changes in the receptor muscle while the SA neuron is capable of transducing the maintained length changes in the receptor muscle. The differences in firing properties mainly originate from the differences in the active and passive properties of the receptor neurons.     

The effect of neural adaptation on population coding accuracy

Most neurons in the primary visual cortex initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. The functional consequences of adaptation are unclear. Typically a reduction of firing rate would reduce single neuron accuracy as less spikes are available for decoding, but it has been suggested that on the population level, adaptation increases coding accuracy. This question requires careful analysis as adaptation not only changes the firing rates of neurons, but also the neural variability and correlations between neurons, which affect coding accuracy as well. We calculate the coding accuracy using a computational model that implements two forms of adaptation: spike frequency adaptation and synaptic adaptation in the form of short-term synaptic plasticity. We find that the net effect of adaptation is subtle and heterogeneous. Depending on adaptation mechanism and test stimulus, adaptation can either increase or decrease coding accuracy. We discuss the neurophysiological and psychophysical implications of the findings and relate it to published experimental data.