ITDs curve steepness is influenced by stochastic delays in auditory pathways

Over the last two decade several new strategies for interaural time differences (ITDs) coding and corresponded mechanisms of ITDs detection have emerged to address recent experimental facts inconsistent with classical strategy based on coincidence detectors (e.g. Jeffress model [1]). Indeed ITDs processing is still remaining an open question in relation to neuronal mechanisms underlaying precise temporal resolution. It is required, in terms of coding, that pattern neuronal activity should be significantly changed by microsecond variation in arrival time of two input signals which are far beyond the neurobiological timescales. Therefore, inner stochastic processes which are randomly disturb the time courses of individual neuron activity may play an important role and have prominent contribution to robustness of investigated mechanisms.

In a previous study, the model of neural mechanism that rely on population coding strategy and provide robust ITDs detection based on collective activity of binaural excitatory – inhibitory (EI) cells was described [2]. According to the nature and location of EI cells, the model consisted of two bilateral symmetrical populations of neurons which receive inhibitory projections from ipsilateral pathways and excitatory inputs from contralateral one. The model exploit, two paradigms of ITDs coding. On one hand bilateral population model correspond to “two-channels model”; and on the other, each population produces “average population code” [3]. The stable dependence of population firing rates on ITD value were demonstrated in presence of both neuronal noise and random synaptic conductances through populations. Here we explore the influence of random jitter in primary auditory pathways and the model's ability to detect ITDs. To estimate and quantify the quality of such detection we assume an ideal case when the firing rates linearly change (inversely for each population) from minimum (zero spikes) to maximum (product cells number and maximum spike rate of an individual cell), when ITD is linearly varied within biological relevant range. Here the relevant range for humans [-0.8mS; +0.8mS] was chosen. The quality factor Q was denoted as 100/(100+D(xi,xo)), where D - Euclidean distance between ideal ITDs curve (xi) and obtained from model (xo). To eliminate the influence of all other disturbance factors the homogeneous model without other stochastic processes was considered.

Figure below shows how the ITDs curve for single population is changed by increasing standard deviation of jitter (top-left panel). It is easily seen that jitter's SD variation modulates the steepness of population ITDs curve from sharp step to flat line. It should be stressed that the signal-to-nose ratio for curve marked by arrow is equal 0.2; it means that random delays in simulated auditory pathways were 5 times more then maximal interaural time difference. Top-right panel shows an example of individual ITDs curves for different neurons in the population. The curves were obtained in model with maximal quality factor. It is obviously that jitter significant decreases the robustness of individual neuronal response, while on average, the population rate is stable and rather close to ideal coder properties. Left-bottom panel shows how two independent ITDs curves match to “two-channels” strategy. Finally the right-bottom panel depicts the relation between quality factor Q and jitter standard deviation. Remarkable quality peak detection shows that there is an optimal stochastic disturbance of population which correspond to best ITDs sensitivities.

References
1. Jeffress LA. (1948) J Comp Physiol Psychol, 41:35-39.
2. Vasilkov VA, Tikidji-Hamburyan RA. ( 2008) BMC Neuroscience, 9(Suppl 1):P12.
3. Grothe B et al. (2010) Physiol Rev, 90:983-1012.