Accurate Detection of Interaural Time Differences by a Population of Slowly Integrating Neurons

For localization of a sound source, animals and humans process the microsecond interaural time differences of arriving sound waves. How nervous systems, consisting of elements with time constants of about and more than 1 ms, can reach such high precision is still an open question. In this Letter we present a hypothesis and show theoretical and computational evidence that a rather large population of slowly integrating neurons with inhibitory and excitatory inputs ($EI$ neurons) can detect minute temporal disparities in input signals which are significantly less than any time constant in the system.

Figure 1

(a) Time traces of membrane potential for different ITDs ($\Delta t$). Three examples are shown. Solid lines: ${\alpha }_i=0.20$, ${\alpha }_e=0.17$; dotted line: ${\alpha }_i=0.21$, ${\alpha }_e=0.15$; dashed line: ${\alpha }_i=0.22$, ${\alpha }_e=0.13$. For all examples ${\tau }_n=1\mathrm{ms}$, ${\tau }_i/{\tau }_n=7.5$, and ${\tau }_e/{\tau }_n=2.5$. The times when membrane potential reaches threshold (horizontal dash-dotted line) are indicated as a vertical bar on the top spike diagram. Note that the spike diagram presents only the first spike and does not reflect subsequent spikes. (b) The maximum of membrane potential for the same examples versus ITD. The line type corresponds to the one in (a). The meaning of the gray rectangles is given in the text.

Figure 2

The schematic representation of the formation of the population ITD function (bottom graph) by modulation of trough width (top sketch) and position (middle sketch) of individual neuron ITD functions.

Figure 3

The schematic representation of the general model structure (a) and the model of individual neurons (b). Each $EI$ cell (green circle) is activated by inhibitory [$S(g_i,{\tau }_i)$] and excitatory [$S(g_e,{\tau }_e)$] synaptic currents which are controlled by presynaptic spikes generated by input elements (white rectangles). ITD is represented as a delay between two presynaptic spikes (shown on inset). Two additional delay lines are incorporated into the model to organize a distribution of delay lines or jitter: $\Delta {\tau }_{e,s}$, $\Delta {\tau }_{i,s}$ for excitation and inhibition, respectively. (c): ITD—population-rate transfer function for model with synaptic conductances (solid line) and delay lines (dashed line) gradients. The dotted line (red online) and dash-dotted (blue online) lines correspond to the model with neuron intrinsic noise current and jitter in pathways, correspondingly. Graphs are presented in different scales to show that the ITD function of population overlaps the human ecologically relevant range $[-700,700]\mu \mathrm{s}$ with a precision of $\pm 2\mu \mathrm{s}/\mathrm{\text{neuron}}$. The markers on the right panel show the scanning trials in $10\mu \mathrm{s}$ step.