Morphological and electrophysiological properties of L10 and Ipc neurons. (a) Intracellular biocytin fills of three tectal L10 neurons. The U-shaped axon (arrow head) characterizes the center neuron as a shepherd’s crook neuron, which projects to the nucleus isthmi. A U-shaped axon is also visible for the left neuron. Scale bar = 20 μm. (b) Response of a representative L10 neuron to a 0.1 nA current step. (c) Average firing rate (black diamonds) and instantaneous firing rate (the inverse of the first interspike intervals, red triangles) vs. current for the population of recorded L10 neurons. The black line represents a linear fit (F(I)= 217.86 × I − 4.61; r² = 0.9821) of the firing rate, F, as a function of the injected current, I, to the measured average firing rate data points. (d) Intracellular biocytin fill in an Ipc neuron (scale bar = 50 μm). (e) Response of a representative Ipc neuron to a 0.5 nA current step. (f) Average firing rate (black diamonds) and instantaneous firing rate (the inverse of the first interspike intervals, red triangles) vs. current for the population of recorded Ipc neurons. The black line represents a linear fit (F(I) = 63.427× I − 5.73; r² = 0.9988) of the firing rate as a function of the injected current to the measured average firing rate data points.

Cellular and synaptic properties of L10 and Ipc model neurons. (a) The response of the L10 model neuron to an injected current pulse of 0.2 nA amplitude. (b) The response of the Ipc model neuron to an injected current pulse of 0.7 nA amplitude. (c) The fitted F-I curve of the L10 model neuron, F(I) = 268.4 × I − 7.5; r² = 0.9883. The experimental data (average firing rates from Fig. 2(c)) of the recorded real L10 neurons in response to current injections are shown for comparison (gray squares). (d) The fitted F-I curve of the Ipc model neuron, F(I) = 73.0 × I − 6.5; r² = 0.9992. The experimental data (average firing rates from Fig. 2(f)) of the recorded real Ipc neurons in response to current injections are shown for comparison (gray squares). (e) The fitted ISI curve, ISI(t) = A(1 − exp(−t/B)), of the L10 model neuron for a current injection of 0.2 nA (see Table 2). The experimental data from 9 recorded real L10 neurons in response to the same current injection are shown for comparison (gray circles). (f) The fitted ISI curve, ISI(t) = A(1 − exp(−t/B)), of the Ipc model neuron for a current injection of 1.0 nA (see Table 3). The experimental data from 18 recorded real Ipc neurons in response to the same current injection are shown for comparison (gray circles). (g) The synaptic response of the L10 model neuron to a single pre-synaptic action potential. The synaptic parameters were g_Ipc→L10 = 2.08 nS, τ_1,Ipc→L10 = 10 ms, τ_2,Ipc→L10 = 1 ms and the cellular parameters were the same as described in the text and Table 1. (h) The synaptic response of an Ipc neuron to a single pre-synaptic action potential. The synaptic parameters were g_L10→Ipc = 5.2 nS, τ_1,L10→Ipc = 5.6 ms, τ_2,L10→Ipc = 0.3 ms, and the cellular parameters were the same as described in the text and Table 1. The synaptic input caused the Ipc neuron to spike two times in a short period of time. The number of spikes depends on the chosen value of the maximum synaptic conductance.

Generation of oscillatory bursts in a population model with recurrent excitation and uncorrelated noise. (a) Schematic drawing of the reciprocally coupled populations of L10 and Ipc model neurons with local RGC inputs to a small group of L10 neurons. The projections are topographic, but have a certain width as indicated by the spread of arrows. (b) Sample L10 and Ipc population responses (raster plot of spikes) to a stimulus current step delivered to 80 neurons centered on L10 neuron #200. The concurrent voltage response of Ipc neuron #200 is shown in the bottom trace. Single neuron parameters are listed in Table 1. The stimulus, synaptic, and noise parameters are: I₀ = 0.18 nA, g_L10→Ipc = 1.85 nS, g_Ipc→L10 = 4.69×10⁻³ nS, Δ_L10→Ipc = 50, Δ_Ipc→L10 = 50, σ_e = 0.06 nA, σ_Ipc = 1.5 nA, σ_L10 = 0.1 nA. The stimulus current is turned on at t = 50 ms and lasts for 250 ms. (c) to (f) Ipc responses for four cross sections through the 5-dimensional parameter space spanned by the spatial width of the synaptic weight distributions Δ_L10→Ipc and Δ_Ipc→L10, and the white noise standard deviations σ_e, σ_Ipc, and σ_L10. The four cross sections intersect the point (asterisk) 50, 50, 0.06 nA, 1.5 nA, 0.1 nA, respectively, which is also the parameter set chosen for the sample trace in (b). The Ipc responses are represented in pseudo color (see Fig. 5) by the “average burst score”, which is the burst score (see Methods) averaged over 5 trials. (g) Ipc responses for different values of the Ipc spike-rate adaptation increment,Δg_sra,Ipc, and the decay time constant, τ_sra,Ipc. All other parameters are as in (b).

Schematic drawings of in vivo and in vitro recording set-ups. (a) Recordings in vivo showed that nucleus isthmi pars parvocellularis (Ipc) neurons responded to moving dots and flashing dots with oscillatory bursts (Marin et al. 2005). The rectangle inset shows a schematic lateral view of the chick brain with the retina, optic nerve, and optic tectum (OT) in red. The dashed line indicates the approximate location of the transverse slicing. (b) A transverse slice of the chick midbrain both in histological image and corresponding outlines (scale bar = 2 mm). The nucleus isthmo-opticus (ION) and the nucleus semilunaris (SLu) are not considered in this study. The patch-electrode schematic indicates a typical recording location from an Ipc neuron. The dashed rectangle indicates the location of the schematic circuitry described in (c). (c) Schematic drawings of the isthmo-tectal circuitry consisting of the retinal ganglion cells axons (vertical black arrows), the tectal layer 10 (L10) neurons (red), the Ipc neurons (green), and the nucleus isthmi pars magnocellularis (Imc) neurons (blue).

Synaptic properties of the L10 → Ipc and the Ipc → L10 connections. (a) Brief electrical stimulation with a biphasic current pulse (200 μA, 500 μs) in tectal layer 10 evoked an EPSPs plus spikes or just EPSPs in the recorded Ipc neurons. Inset: Synaptic current recorded from an Ipc neuron in voltage clamp in response to electrical stimulation in tectal layer 10 with a train of 5 pulses of 20 ms interval. The membrane potential was held at −70 mV (scale bars = 20 ms, 200 pA). (b) Brief electrical stimulation in the Ipc nucleus evoked long-lasting EPSPs in recorded L10 neurons. Note the different scale bars in (a) and (b).

Generation of oscillatory bursting in a pair of model neurons with recurrent excitation. (a) Schematic drawing of the reciprocally coupled pair of L10 and Ipc model neurons with retinal (RGC) inputs to the L10 model neuron. (b) and (c) Responses of the reciprocally coupled L10 and Ipc model neurons to depolarizing current injection into the L10 model neuron. The injected current had a duration of 350 ms (starting at time = 50 ms) and an amplitude of 0.2 nA. The cellular and synaptic parameter values were chosen as described in the text and Table 1. The maximum synaptic conductances relative to the membrane conductance were g_L10→Ipc/g_Ipc = 10 and g_Ipc→L10/g_L10 = 0.2. The Ipc burst score (see Methods) for this trace equals14/15 ≅ 0.93. (d), (e), (f) Ipc responses for three cross sections through the 3-dimensional parameter space spanned by the maximum synaptic conductances g_L10→Ipc/g_Ipc and g_Ipc→L10/g_L10, and by the feedforward synaptic fall times τ_1,L10→Ipc. The three cross sections intersect the point (asterisk) 10, 0.2, 5.6 ms, respectively, which is also the parameter set chosen for the sample trace in (b) and (c). The Ipc responses are represented in pseudo color by the burst score. When all spikes belong to bursts the score is 1 (red), when all spikes are isolated the score is 0 (blue), when the firing rate exceeds 1000 Hz the Ipc response is classified as diverging (gray).