A dendritic model of coincidence detection in the avian brainstem☆
Introduction
Neural coincidence detection is essential in sound localization, which (for frequencies below a few kHz) requires the computation of interaural time differences (ITDs). This task is performed by binaural cells in the avian nucleus laminaris (NL), and its mammalian homologue, the medial superior olive (MSO).
A “coincidence detector” neuron should fire when inputs from two independent neural sources coincide (or almost coincide), but not when two inputs from the same source (almost) coincide. A neuron that sums its inputs linearly would not be able to distinguish between these scenarios. Segregating the inputs on separate dendrites should avoid this problem: post-synaptic depolarization from a synaptic event is reduced if the dendrite is already partially depolarized. This idea was used by Agmon-Snir et al. [1] to model bipolar dendrites as interaural coincidence detectors in NL. This is a more biophysical model of the same system.
The model emulates a single neuron with an axon, soma, and a variable number of dendrites, each with a variable number of equipotential compartments. All geometric, electrical, and channel parameters are adjustable, as are the number of synapses/dendrite (∼30), the synaptic locations, and the distribution of synaptic locations. Channel types include potassium (high- and low-voltage activated [Kv1.1, 1.2], and delayed rectifier), sodium, and passive. The values used for all the tunable parameters are in agreement with those in the literature [2], [3], [4], [5], [6]. The stimulus is a pure tone of adjustable frequency, with variable binaural phase difference (or contralateral monaural stimulus with variable ipsilateral spontaneous activity). More complex stimuli can be easily introduced.
The synapses fire with conductance proportional to an alpha-function, with adjustable time constant, peak conductance, and reversal potential. The synapses fire as individual Poisson processes, with probability rate given by the half-wave rectified sinusoidal input, with adjustable amplitude and base spontaneous firing rate. The fast Kv 3.1 channels of the pre-synaptic neurons are incorporated in a short synaptic time constant.
The implementation is constructed within the NEURON [7] environment and has a graphical user interface for controlling the parameters and running the model. NEURON allows for a real-time display of data and analysis including the potential at various locations, the two stimuli, the synaptic firings, spike counters, period histograms of synaptic firings and the action potentials, and their vector strengths.
Section snippets
Potential curves and period stimulus histograms
Fig. 1 shows typical time plots for a pair of cells each receiving the same stimulus probability distributions (with frequency 500 Hz), with the top cell receiving its inputs binaurally in-phase, and the bottom out-of-phase. The black curve tracks the intracellular potential at soma/axon boundary and the nearby light grapy curve at the axon tip. Below these curves are a pair of curves of the presynaptic probability distribution. The bottom eight curves of each graph show synaptic currents (note
Results
Only a small volume of parameter space for this model is biologically relevant, but due to a relative paucity of experimental data, it is not obvious where the relevant subspace lies. Some parameters are known to have values that fall in a particular range, and different parameters, with respective ranges, may be correlated or not. Some parameters may be particularly relevant for certain species but not for others (e.g. the barn owl can detect ITDs up to 8 kHz, whereas the chicken can detect
Conclusions
The model has parameter ranges that give behavior corresponding to the behavior of real NL neurons. The dendrites aid in the ability of the cell to perform coincidence detection, especially from sublinear addition and dendritic current sinks. The high-voltage activation potassium channels are important for coincidence detection at high frequencies. Coincidence detection is robust against the number of incoming synapses. The model predicts that vector strength is very robust (at fast firing
Jonathan Z. Simon received a Ph.D. in physics (theoretical general relativity) in 1990 from the University of California, Santa Barbara. After postdoctoral positions at the University of Wisconsin, Mulwaukee, and the University of Maryland, he entered the field of computational (and experimental) neuroscience in 1996.
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Jonathan Z. Simon received a Ph.D. in physics (theoretical general relativity) in 1990 from the University of California, Santa Barbara. After postdoctoral positions at the University of Wisconsin, Mulwaukee, and the University of Maryland, he entered the field of computational (and experimental) neuroscience in 1996.
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This work was supported partly by the Office of Naval Research MURI grant N00014-97-1-0501 and National Science Foundation grant 9720334.