Petr Marsalek

Coincidence detection in the Hodgkin-Huxley equations.

Some of the cochlear nuclei in the auditory pathway are specialized for the sound localization. They compute the interaural time difference. The difference in sound timing is transduced by the dedicated neuronal circuit into a labeled line difference. The detector neurons along the delay line fire only when synaptic inputs reflecting signals from both cars arrive within a short time window. It was therefore called coincidence detection. We show, (1) what are the limits of coincidence detection in the leaky integrator model, which is a linear system, (2) how should the ideal coincidence detector based on the Hodkin-Huxley equations from real neurons look like, (3) what are the properties and physical limits in the real coincidence detection system. The conclusion is that the neuron with the Hodgkin Huxley dynamics has a fixed precision for the coincidence detection. The limits of the sound localization precision are set by the frequency of the sound and, therefore, by the vector strength of spike trains generated in the neuronal circuit in response to the sound.

Proposed mechanisms for coincidence detection in the auditory brainstem

Sound localization in mammals uses two distinct neural circuits, one for low- and one for high-frequency bands. Recent experiments call for revision of the theory explaining how the direction of incoming sound is calculated. We propose such a revised theory. Our theory is based on probabilistic spiking and probabilistic delay of spikes from both sides. We have applied the mechanism originally proposed as an operation on spike trains resulting in multiplication of firing rates. We have adapted this mechanism for the case of synchronous spike trains. The mechanism has to detect spikes from both sides within a short time window. Therefore, in both circuits neurons act as coincidence detectors. In the excitatory low-frequency circuit we call the mechanism the excitatory coincidence detection, to distinguish it from the mechanism of the inhibitory coincidence detection in the high-frequency circuit. The times to first spike and gains of the two mechanisms are calculated. We show how the output gains of the mechanisms predict the dip within the human frequency sensitivity range. This dip has been described in human psychophysical experiments.

Biological context of Hebb learning in artificial neural networks, a review

In 1949 Donald Olding Hebb formulated a hypothesis describing how neurons excite each other and how the efficiency of this excitation subsequently changes with time. In this paper we present a review of this idea. We evaluate its influences on the development of artificial neural networks and the way we describe biological neural networks. We explain how Hebb?s hypothesis fits into the research both of that time and of present. We highlight how it has gone on to inspire many researchers working on artificial neural networks. The underlying biological principles that corroborate this hypothesis, that were discovered much later, are also discussed in addition to recent results in the field and further possible directions of synaptic learning research.

Neural code for sound localization at low frequencies

Abstract Several nuclei in the auditory pathway perform sound localization. At lower sound frequencies, they compute the interaural time difference. This difference is transduced by the dedicated neuronal circuit into a labeled line difference. The neurons of the circuit fire only when synaptic inputs from both ears arrive within a short time window. We have shown previously the minimum timing difference detectable in the linear model and in the Hodgkin–Huxley-type equations. To better describe the spike code for the sound localization we define a generalized vector strength for point processes. Based on calculations in single cell models, we show how the neural code is transformed depending on the main sound frequency. We conclude that the performance limits of the low-frequency system are set by the frequency of the sound and therefore by both the vector strength and the probability of spike emission in the single unit. This shows the necessity for the existence of two different mechanisms for sound localization (1) one based on the interaural time delay, operating at low sound frequencies, and (2) another based on the interaural intensity difference, operating at high frequencies. The two systems then converge in higher-order neural relay stations.

Stochastic interpolation model of the medial superior olive neural circuit.

This article presents a stochastic model of binaural hearing in the medial superior olive (MSO) circuit. This model is a variant of the slope encoding models. First, a general framework is developed describing the elementary neural operations realized on spike trains in individual parts of the circuit and how the neurons converging onto the MSO are connected. Random delay, coincidence detection of spikes, divergence and convergence of spike trains are operations implemented by the following modules: spike generator, jitter generator, and coincidence detector. Subsequent processing of spike trains computes the sound azimuth in the circuit. The circuit parameters that influence efficiency of slope encoding are studied. In order to measure the overall circuit performance the concept of an ideal observer is used instead of a detailed model of higher relays in the auditory pathway. This makes it possible to bridge the gap between psychophysical observations in humans and recordings taken of small rodents. Most of the results are obtained through numerical simulations of the model.

Neuronal jitter: can we measure the spike timing dispersion differently?

We propose a novel measure of statistical dispersion of a positive continuous random variable: the entropy-based dispersion (ED). We discuss the properties of ED and contrast them with the widely employed standard deviation (SD) measure. We show that the properties of SD and ED are different: while SD is a second moment characteristics measuring the dispersion relative to the mean value, ED measures an effective spread of the probability distribution and is more closely related to the notion of randomness of spiking activity. We apply both SD and ED to analyze the temporal precision of neuronal spiking activity of the perfect integrate-and-fire model, which is a plausible neural model under the assumption of high input synaptic activity. We show that SD and ED may give strikingly different results for some widely used models of presynaptic activity.

Investigating spike backpropagation induced Ca2+ influx in models of hippocampal and cortical pyramidal neurons.

We modeled the influx of calcium ions into dendrites following active backpropagation of spike trains in a dendritic tree, using compartmental models of anatomically reconstructed pyramidal cells in a GENESIS program. Basic facts of ion channel densities in pyramidal cells were taken into account. The time scale of the backpropagating spike train development was longer than in previous models. We also studied the relationship between intracellular calcium dynamics and membrane voltage. Comparisons were made between two pyramidal cell prototypes and in simplified model. Our results show that: (1) sodium and potassium channels are enough to explain regenerative backpropagating spike trains; (2) intracellular calcium concentration changes are consistent in the range of milliseconds to seconds; (3) the simulations support several experimental observations in both hippocampal and neocortical cells. No additional parameter search optimization was necessary. Compartmental models can be used for investigating the biology of neurons, and then simplified for constructing neural networks.

On the precision of neural computation with interaural level differences in the lateral superior olive

Interaural level difference (ILD) is one of the basic binaural clues in the spatial localization of a sound source. Due to the acoustic shadow cast by the head, a sound source out of the medial plane results in an increased sound level at the nearer ear and a decreased level at the distant ear. In the mammalian auditory brainstem, the ILD is processed by a neuronal circuit of binaural neurons in the lateral superior olive (LSO). These neurons receive major excitatory projections from the ipsilateral side and major inhibitory projections from the contralateral side. As the sound level is encoded predominantly by the neuronal discharge rate, the principal function of LSO neurons is to estimate and encode the difference between the discharge rates of the excitatory and inhibitory inputs. Two general mechanisms of this operation are biologically plausible: (1) subtraction of firing rates integrated over longer time intervals, and (2) detection of coincidence of individual spikes within shorter time intervals. However, the exact mechanism of ILD evaluation is not known. Furthermore, given the stochastic nature of neuronal activity, it is not clear how the circuit achieves the remarkable precision of ILD assessment observed experimentally. We employ a probabilistic model and complementary computer simulations to investigate whether the two general mechanisms are capable of the desired performance. Introducing the concept of an ideal observer, we determine the theoretical ILD accuracy expressed by means of the just-noticeable difference (JND) in dependence on the statistics of the interacting spike trains, the overall firing rate, detection time, the number of converging fibers, and on the neural mechanism itself. We demonstrate that the JNDs rely on the precision of spike timing; however, with an appropriate parameter setting, the lowest theoretical values are similar or better than the experimental values. Furthermore, a mechanism based on excitatory and inhibitory coincidence detection may give better results than the subtraction of firing rates. This article is part of a Special Issue entitled Neural Coding 2012.

Pattern storage in a sparsely coded neural network with cyclic activation

We investigate an artificial neural network model with a modified Hebb rule. It is an auto-associative neural network similar to the Hopfield model and to the Willshaw model. It has properties of both of these models. Another property is that the patterns are sparsely coded and are stored in cycles of synchronous neural activities. The cycles of activity for some ranges of parameter increase the capacity of the model. We discuss basic properties of the model and some of the implementation issues, namely optimizing of the algorithms. We describe the modification of the Hebb learning rule, the learning algorithm, the generation of patterns, decomposition of patterns into cycles and pattern recall.

The Effect of Neural Noise on Spike Time Precision in a Detailed CA3 Neuron Model

Experimental and computational studies emphasize the role of the millisecond precision of neuronal spike times as an important coding mechanism for transmitting and representing information in the central nervous system. We investigate the spike time precision of a multicompartmental pyramidal neuron model of the CA3 region of the hippocampus under the influence of various sources of neuronal noise. We describe differences in the contribution to noise originating from voltage-gated ion channels, synaptic vesicle release, and vesicle quantal size. We analyze the effect of interspike intervals and the voltage course preceding the firing of spikes on the spike-timing jitter. The main finding of this study is the ranking of different noise sources according to their contribution to spike time precision. The most influential is synaptic vesicle release noise, causing the spike jitter to vary from 1 ms to 7 ms of a mean value 2.5 ms. Of second importance was the noise incurred by vesicle quantal size variation causing the spike time jitter to vary from 0.03 ms to 0.6 ms. Least influential was the voltage-gated channel noise generating spike jitter from 0.02 ms to 0.15 ms.