Spike encoding mechanisms in the sound localization pathway

Predicting the Influence of Axon Myelination on Sound Localization Precision Using a Spiking Neural Network Model of Auditory Brainstem

Spatial hearing allows animals to rapidly detect and localize auditory events in the surrounding environment. The auditory brainstem plays a central role in processing and extracting binaural spatial cues through microsecond-precise binaural integration, especially for detecting interaural time differences (ITDs) of low-frequency sounds at the medial superior olive (MSO). A series of mechanisms exist in the underlying neural circuits for preserving accurate action potential timing across multiple fibers, synapses and nuclei along this pathway. One of these is the myelination of afferent fibers that ensures reliable and temporally precise action potential propagation in the axon. There are several reports of fine-tuned myelination patterns in the MSO circuit, but how specifically myelination influences the precision of sound localization remains incompletely understood. Here we present a spiking neural network (SNN) model of the Mongolian gerbil auditory brainstem with myelinated axons to investigate whether different axon myelination thicknesses alter the sound localization process. Our model demonstrates that axon myelin thickness along the contralateral pathways can substantially modulate ITD detection. Furthermore, optimal ITD sensitivity is reached when the MSO receives contralateral inhibition via thicker myelinated axons compared to contralateral excitation, a result that is consistent with previously reported experimental observations. Our results suggest specific roles of axon myelination for extracting temporal dynamics in ITD decoding, especially in the pathway of the contralateral inhibition.

Ergodicity and parameter estimates in auditory neural circuits

This paper discusses ergodic properties and circular statistical characteristics in neuronal spike trains. Ergodicity means that the average taken over a long time period and over smaller population should equal the average in less time and larger population. The objectives are to show simple examples of design and validation of a neuronal model, where the ergodicity assumption helps find correspondence between variables and parameters. The methods used are analytical and numerical computations, numerical models of phenomenological spiking neurons and neuronal circuits. Results obtained using these methods are the following. They are: a formula to calculate vector strength of neural spike timing dependent on the spike train parameters, description of parameters of spike train variability and model of output spiking density based on assumption of the computation realized by sound localization neural circuit. Theoretical results are illustrated by references to experimental data. Examples of neurons where spike trains have and do not have the ergodic property are then discussed.

Analytical description of coincidence detection synaptic mechanisms in the auditory pathway

Localization of sound source azimuth within horizontal plane uses interaural time differences (ITDs) between sounds arriving through the left and right ear. In mammals, ITDs are processed primarily in the medial superior olive (MSO) neurons. These are the first binaural neurons in the auditory pathway. The MSO neurons are notable because they possess high time precision in the range of tens of microseconds. Several theories and experimental studies explain how neurons are able to achieve such precision. In most theories, neuronal coincidence detection processes the ITDs and encodes azimuth in ascending neurons of the auditory pathway using modalities that are more tractable than the ITD. These modalities have been described as firing rate codes, place codes (labeled line codes) and similarly. In this theoretical model it is described how the ITD is processed by coincidence detection and converted into spikes by summing the postsynaptic potentials. Particular postsynaptic conductance functions are used in order to obtain an analytical solution in a closed form. Specifically, postsynaptic response functions are derived from the exponential decay of postsynaptic conductances and the MSO neuron is modeled as a simplified version of the Spike Response Model (SRM0) which uses linear summations of the membrane responses to synaptic inputs. For plausible ratios of time constants, an analytical solution used to describe properties of coincidence detection window is obtained. The parameter space is then explored in the vicinity of the analytical solution. The variation of parameters does not change the solution qualitatively.

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.

The stochastic properties of input spike trains control neuronal arithmetic

In the nervous system, the representation of signals is based predominantly on the rate and timing of neuronal discharges. In most everyday tasks, the brain has to carry out a variety of mathematical operations on the discharge patterns. Recent findings show that even single neurons are capable of performing basic arithmetic on the sequences of spikes. However, the interaction of the two spike trains, and thus the resulting arithmetic operation may be influenced by the stochastic properties of the interacting spike trains. If we represent the individual discharges as events of a random point process, then an arithmetical operation is given by the interaction of two point processes. Employing a probabilistic model based on detection of coincidence of random events and complementary computer simulations, we show that the point process statistics control the arithmetical operation being performed and, particularly, that it is possible to switch from subtraction to division solely by changing the distribution of the inter-event intervals of the processes. Consequences of the model for evaluation of binaural information in the auditory brainstem are demonstrated. The results accentuate the importance of the stochastic properties of neuronal discharge patterns for information processing in the brain; further studies related to neuronal arithmetic should therefore consider the statistics of the interacting spike trains.

Stochastic model explains the role of excitation and inhibition in binaural sound localization in mammals

Interaural time differences (ITDs), the differences of arrival time of the sound at the two ears, provide a major cue for low-frequency sound localization in the horizontal plane. The first nucleus involved in the computation of ITDs is the medial superior olive (MSO). We have modeled the neural circuit of the MSO using a stochastic description of spike timing. The inputs to the circuit are stochastic spike trains with a spike timing distribution described by a given probability density function (beta density). The outputs of the circuit reproduce the empirical firing rates found in experiment in response to the varying ITD. The outputs of the computational model are calculated numerically and these numerical simulations are also supported by analytical calculations. We formulate a simple hypothesis concerning how sound localization works in mammals. According to this hypothesis, there is no array of delay lines as in the Jeffress' model, but the inhibitory input is shifted in time as a whole. This is consistent with experimental observations in mammals.

Modulation of dendritic synaptic processing in the lateral superior olive by hyperpolarization-activated currents

We have previously shown that mice lateral superior olive (LSO) neurons exhibit a large hyperpolarization-activated current (I(h) ), and that hyperpolarization-activated cyclic-nucleotide-gated type 1 channels are present in both the soma and dendrites of these cells. Here we show that the dendritic I(h) in LSO neurons modulates the integration of multiple synaptic inputs. We tested the LSO neuron's ability to integrate synaptic inputs by evoking excitatory post-synaptic potentials (EPSPs) in conjunction with brief depolarizing current pulses (to simulate a second excitatory input) at different time delays. We compared LSO neurons with the native I(h) present in both the soma and dendrites (control) with LSO neurons without I(h) (blocked with ZD7288) and with LSO neurons with I(h) only present peri-somatically (ZD7288+ computer-simulated I(h) using a dynamic clamp). LSO neurons without I(h) had a wider time window for firing in response to inputs with short time separations. Simulated somatic I(h) (dynamic clamp) could not reverse this effect. Blocking I(h) also increased the summation of EPSPs elicited at both proximal and distal dendritic regions, and dramatically altered the integration of EPSPs and inhibitory post-synaptic potentials. The addition of simulated peri-somatic I(h) could not abolish a ZD7288-induced increase of responsiveness to widely separated excitatory inputs. Using a compartmental LSO model, we show that dendritic I(h) can reduce EPSP integration by locally decreasing the input resistance. Our results suggest a significant role for dendritic I(h) in LSO neurons, where the activation/deactivation of I(h) can alter the LSO response to synaptic inputs.

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.