Precision of neural timing: effects of convergence and time-windowing

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.

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.

Distinguishing the Causes of Firing with the Membrane Potential Slope

In this letter, we aim to measure the relative contribution of coincidence detection and temporal integration to the firing of spikes of a simple neuron model. To this end, we develop a method to infer the degree of synchrony in an ensemble of neurons whose firing drives a single postsynaptic cell. This is accomplished by studying the effects of synchronous inputs on the membrane potential slope of the neuron and estimating the degree of response-relevant input synchrony, which determines the neuron's operational mode. The measure is calculated using the normalized slope of the membrane potential prior to the spikes fired by a neuron, and we demonstrate that it is able to distinguish between the two operational modes. By applying this measure to the membrane potential time course of a leaky integrate-and-fire neuron with the partial somatic reset mechanism, which has been shown to be the most likely candidate to reflect the mechanism used in the brain for reproducing the highly irregular firing at high rates, we show that the partial reset model operates as a temporal integrator of incoming excitatory postsynaptic potentials and that coincidence detection is not necessary for producing such high irregular firing.

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.

Bat echolocation processing using first-spike latency coding

To perform echolocation, so-called FM-bats emit short pulses i.e., with a duration of a few milliseconds, and analyse the echoes coming from their environment. One individual echo, due to its short duration, will cause neurons in the early auditory system to generate between 1 and 3 spikes only. Hence, we argue that it is advantageous for FM-bats to use spike-time rather that firing rate information. We present a simple spike-time model of the monaural and binaural pathways up to the midbrain, to show that spike-time information can indeed be processed by the known neural architecture. In particular, we show that a First Spike Latency (FSL) code, as provided by the auditory nerves, can represent both the monaural and binaural intensity cues induced by the head-related transfer function in the peripheral system. We also show that ascending centres enhance the cues conveyed by such an FSL code. Finally, we present experimental results, comparing the FSL code based model proposed here with a more classic firing rate code, and we show that first-spike latency is a more biologically plausible alternative.

The volley theory and the spherical cell puzzle

Temporal coding in the auditory nerve is strikingly transformed in the cochlear nucleus. In contrast to fibers in the auditory nerve, some neurons in the cochlear nucleus can show "picket fence" phase-locking to low-frequency pure tones: they fire a precisely timed action potential at every cycle of the stimulus. Such synchronization enhancement and entrainment is particularly prominent in neurons with the spherical and globular morphology, described by Osen [Osen KK (1969) Cytoarchitecture of the cochlear nuclei in the cat. J Comp Neurol 136:453-483]. These neurons receive large axosomatic terminals from the auditory nerve--the end bulbs and modified end bulbs of Held--and project to binaural comparator nuclei in the superior olivary complex. The most popular model to account for picket fence phase-locking is monaural coincidence detection. This mechanism is plausible for globular neurons, which receive a large number of inputs. We draw attention to the existence of enhanced phase-locking and entrainment in spherical neurons, which receive too few end-bulb inputs from the auditory nerve to make a coincidence detection of end-bulb firings a plausible mechanism of synchronization enhancement.

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.