A dendrite-autonomous mechanism for direction selectivity in retinal starburst amacrine cells

Abstract

Detection of image motion direction begins in the retina, with starburst amacrine cells (SACs) playing a major role. SACs generate larger dendritic Ca(2+) signals when motion is from their somata towards their dendritic tips than for motion in the opposite direction. To study the mechanisms underlying the computation of direction selectivity (DS) in SAC dendrites, electrical responses to expanding and contracting circular wave visual stimuli were measured via somatic whole-cell recordings and quantified using Fourier analysis. Fundamental and, especially, harmonic frequency components were larger for expanding stimuli. This DS persists in the presence of GABA and glycine receptor antagonists, suggesting that inhibitory network interactions are not essential. The presence of harmonics indicates nonlinearity, which, as the relationship between harmonic amplitudes and holding potential indicates, is likely due to the activation of voltage-gated channels. [Ca(2+)] changes in SAC dendrites evoked by voltage steps and monitored by two-photon microscopy suggest that the distal dendrite is tonically depolarized relative to the soma, due in part to resting currents mediated by tonic glutamatergic synaptic input, and that high-voltage-activated Ca(2+) channels are active at rest. Supported by compartmental modeling, we conclude that dendritic DS in SACs can be computed by the dendrites themselves, relying on voltage-gated channels and a dendritic voltage gradient, which provides the spatial asymmetry necessary for direction discrimination.

Figure 1. Voltage and Ca²⁺ Responses of Starburst Cells to Moving Gratings and Circular Waves

(A) Two-photon micrographs of a living, flat-mounted retina stained with Sulforhodamine 101 (different focal planes: GCL, ganglion cell layer; IPL, inner plexiform layer; NFL, nerve fiber layer). ON (displaced) starburst amacrine somata can be identified by shape and size (center of lower left panel). (B) Cell from (A) filled with the Ca²⁺ indicator dye Oregon-Green 488 BAPTA-1 (green) via the patch electrode (shadow from below; maximum-projected image stack; magenta: sulforhodamine). (C) Voltage responses (V _m) evoked by a bar grating (4 Hz; 72% contrast; period 192 μm) moving left or right (yellow arrows) presented to the full field or “behind” masks (gray) recorded from a different SAC. Left: stimuli and their positions relative to the cell. Right: somatic voltage (gray area indicates motion duration). (D) Voltage responses to circular wave stimulation (2 Hz; 72% contrast; period: 192 μm, see Materials and Methods for details) expanding (CF, orange) or contracting (CP, blue). (E) Simultaneous recording of somatic voltage (orange, blue) and dendritic [Ca²⁺] (black) to circular-wave stimulation. Below: response to CF motion at higher magnification. Gray rectangles indicate duration of stimulus presentation. Radial distribution of normalized stimulus intensity for the three frames are shown as curves on frames (white) and as overlay (plot). (C and D) show averages of three trials, (E) shows single trials; V _Rest (mV): (C) −43, (D) −61, and (E) −49.

Figure 2. Quantification by Fourier Decomposition

(A) Voltage responses evoked by circular wave stimuli; gray: individual trials, orange and blue: averages for CF and CP motion, respectively; black: reconstructed waveforms; frame: trace segment used for analysis (V _Rest = −60 mV). Gray area indicates motion duration. (B) Amplitudes (top) and relative phases (φ ₂ − 2 · φ ₁, bottom) versus frequency (f ) for the averaged responses in (A). Symbols (V ₀ at f = 0; V ₁ at f ₁; V ₂, V ₃... at 2·f ₁, 3·f ₁,...) are measured points; connecting lines are only a guide for the eye. Note that the phases for the CF motion decrease linearly except when wrapping around (at −π, π). Reconstructions of the waveforms using V _0–3 and their phases shown as black traces in (A). (C) Histogram of the relative (rel.) phase shift (φ ₂ − 2 · φ ₁) between fundamental and second harmonic (orange for CF, n = 65; blue for CP motion, n = 41 cells; only cells with V₂ ≥ 0.3 mV included; stimulus: 2.5–3 Hz; 46%–73% contrast; period: 192 μm). Inset: fundamental and second harmonic generate a steeply rising flank when the relative phase is close to −π/2. (D) Distribution of V ₀ (n = 83, same cells as in [C]) for CF (orange) and CP motion (blue). (E) Distribution of asymmetry indices, AI ₁, AI ₂, and AI ₃ (n = 83 cells; all AIs are significantly different from zero with p_AI1,AI2,AI3 ≤ 0.0001).

Figure 3. Contrast Dependence

(A) Voltage responses evoked by circular wave stimuli (3 Hz; period: 192 μm, contrasts from 10% to 72%); traces are averages of three trials; CF motion in orange, CP in blue (V _Rest = −63 mV). Gray area indicates motion duration. (B) Amplitudes of DC (V ₀), fundamental (V ₁), and harmonics V ₂ and V ₃ as a function of stimulus contrast (average of eight cells). Prestimulus data (no-motion; open gray symbols) included. (C) Relative phases of second harmonic (φ ₂ − 2 · φ ₁) as function of contrast (same cells as in [B]). (D) AIs for V₁ (open squares) and V₂ (filled diamonds) from (B). For statistics, see Table 1

Figure 4. Effects of GABA Receptor Antagonists

(A and B) Voltage responses to circular wave stimuli recorded before (control, black; V _Rest [A] −62 mV, [B] −49 mV) and during bath application of a mixture of GABA_A, GABA_C, and glycine receptor antagonists ([A] blue traces; Gbz+TPMPA+strychnine; V _Rest = −53 mV) and Gbz alone ([B] purple traces; V _Rest = −48 mV). Traces (averages of three trials) overlaid to facilitate comparison; the vertical shifts reflect drug-induced changes in V _Rest ; (A) and (B) show different cells. Gray area indicates motion duration. (C–G) Top row: averaged amplitudes of DC (V ₀), the fundamental (V ₁), and the harmonics (V ₂ and V ₃) for different GABA/glycine receptor antagonists and mixtures thereof (25–50 μM Gbz, 50–75 μM TPMPA, 300 μM PTX, 1 μM strychnine; CF motion: orange circles; CP motion: blue triangles; gray box: during drug application; stimuli: 2–3 Hz, 57%–72% contrast, stimulus period 192 or 256 μm). Middle row: AIs for fundamental (open squares) and second harmonic (filled diamonds). Bottom row: potential differences between CF and CP motion responses for depolarizing peaks and hyperpolarizing valleys. For statistics, see text and Table 1. Ctrl, control.

Figure 5. Voltage Dependence

(A) Whole-cell voltage-clamp current responses evoked by circular wave stimuli (3 Hz; 46% contrast; period: 192 μm; averages of three trials; Cs⁺-based intracellular solution) while the somatic potential (V_COM) was stepped from −75 mV to the potentials indicated. Stimulation sequence was repeated for different step potentials after waiting for 2 s. Gray area indicates motion duration. (B) Traces for CF motion (orange) and CP motion (blue) from (A) (for the voltage step to −58 mV) magnified and aligned (shifted by 167 ms) to illustrate difference in waveforms. (C) Amplitudes of the fundamental (I ₁), and the second and third harmonics (I ₂, and I ₃) as a function of V _COM (analysis as in Figure 2.; averages of nine trials; same cell as in [A] and [B]). Motion (orange/blue-filled symbols) and no-motion (gray open symbols) data, both during voltage steps, are plotted. (D) AIs for V ₁ (open squares) and V ₂ (filled diamonds) as functions of V _COM.

Figure 6. Effects of Cd²⁺

(A) Voltage responses to circular wave stimuli (3 Hz; 57% contrast; period: 192 μm) recorded before (control, V _Rest = −63 mV; black), during (V _Rest = −52 mV; purple) and after (washout, V _Rest = −63 mV; blue) bath application of 10 μM Cd²⁺. Traces (averages of three trials) are overlaid to facilitate comparison. Gray area indicates motion duration. (B–D) Amplitudes of DC (V ₀), fundamental (V ₁), and harmonics (V ₂ and V ₃) plotted over time (in minutes after break-in; CF motion: orange circles; CP motion: blue triangles). Three different cells are shown ([B] shows the data from the cell in [A]; traces in [A] are at 6.5, 15, and 47 min after break-in). (E) AIs for V ₁ (open squares) and V ₂ (filled diamonds). For statistics, see Table 1.

Figure 7. Voltage-Dependent Dendritic Ca²⁺ Signals

(A) Somatic voltage step (from V _COM = −75 mV) evoked changes in somatic current (I _m) and dendritic [Ca²⁺] (single trials). Oregon-Green 488 BAPTA-1 (100 μM) signals (ΔF/F in percentages) recorded by two-photon imaging; Cs⁺-based intracellular solution. (B) Example of spiky [Ca²⁺] transients riding on smooth responses (different cell but same protocol as in [A], single trials; some traces omitted). (C) Ca²⁺ responses (circles) as a function of V _COM for cells lacking spiky activity; each symbol represents a single response; for each cell, amplitudes were normalized to the response-amplitude at −35 mV (see Materials and Methods); continuous line: fitted activation curve (using Equation 5). (D) [Ca²⁺] versus voltage data before (control; black) during (purple) and after (washout; blue) bath application of CNQX (10 μM). (E) Curve fits from C and D overlaid with fits (Equation 5) to data from the literature for P/Q-type (cyan upward triangles, g = −0.023 ± 0.001; V ₅₀ = −10.9 ± 0.5 mV; V _Slope = 4.56 ± 0.35; E _Ca = 46.8 ± 1.2 mV; [45] and R-type (orange downward triangles, g = −0.013 ± 0.003; V ₅₀ = −27.5 ± 2.1 mV; V _Slope = 8.57 ± 1.09; E _Ca = 81.2 ± 13.1 mV; [60] calcium channels, as well as for TTX-resistant Na⁺ channels (blue diamonds, g = −0.013 ± 0.0003; V ₅₀ = −26.9 ± 0.2 mV; V _Slope = 4.00 ± 0.15; E _Na = 66.2 ± 1.1 mV; [78]. (F) Somatic current as function of the step-to potential (filled circles: cell in [A], I(−75 mV) = −64 pA; open circles: cell in [B], I(−75 mV) = −86 pA).

Figure 9. Two-Compartment Model of a Dendritic Branch of a Starburst Cell

(A) Schematic of SAC electrotonics, illustrating the proposed gradient between dendritic and somatic voltages (V _D and V _S; red represents relative depolarization; see also Equation 1); circuit components: longitudinal resistors between soma and proximal compartment (R _SP) and between proximal and distal compartment (R _PD), distal leak resistance (R _leak), a voltage-gated Ca²⁺ and the somatic K⁺ conductance (with respective reversal potentials E _rev,leak, E _Ca²⁺, and E _K⁺), and the patch-clamp amplifier. (B) The model consists of two identical dendritic compartments, P (proximal) and D (distal), that each contain in parallel a capacitor (C), a leak resistance (R _leak) and a Hodgkin-Huxley–type voltage-gated conductance with identical properties in both compartments (g _P or g _D). The compartments are connected by a resistor (R _PD). The inputs from bipolar cells are represented by sinusoidal currents (I _P,osc and I _D,osc) that are injected into the compartments. The resting potentials are set by additionally injecting DC currents (I _P,zero and I _D,zero). Image motion is simulated by setting the relative phase of the sinusoidal currents injected into the two compartments to either +90 or −90 degrees. For equations, see Materials and Methods. We analyzed the direction discrimination of the model using R _PD = 1 GΩ, C = 183 pF, g _open·n _ch = 5 nS, R _leak = 160 MΩ, and a VGC with E _rev = 50 mV, k _m = 1,000/s, k _h = 7.25/s, V _m50 = −15 mV, V _h50 = −15 mV, V _mSlope = 4.5 mV, and V _hSlope = −4 mV. Although the channel parameters do not apply to a specific type of VGC, they are in the range that is plausible for the types of Ca²⁺ channels found in SACs. To mimic a dendritic voltage gradient, the resting potential of the two compartments were set to −19 and −16.5 mV, by setting I _P,zero = 195 pA and I _D,zero = 183 pA (outward currents). This configuration is stable, i.e., in the absence of sinusoidal input currents the voltage remains steady and behaves largely linearly, as shown by numerical simulation. (C) Sinusoidal input currents (with a frequency of 2.86 Hz and an amplitude of 1.25 pA) injected into the two compartments. During the first stimulation period, the current injected into compartment D is delayed relative to compartment P (simulating “CF” motion, from P to D). During the second stimulation period, the timing is reversed (simulating “CP” motion, from D to P). (D) Voltages in both compartments in response to the injection of oscillating currents from (C). Amplitudes are given as root mean square at the fundamental frequency. In both compartments, the response is larger when the current in the compartment that has the more depolarized resting potential (−16.5 mV), in this case compartment D, is delayed. It is this compartment that shows a strong (1.09 mV vs. 0.13 mV, i.e., ≈8.5-fold larger) preference for one “motion direction” (blue trace). The other compartment has a much weaker preference (1.26 vs. 0.98 mV, i.e., ≈1.3-fold) but for the same direction (orange trace). For details, see Table 2. (E) If the injected DC current was set such that both compartments rest at the same potential, e.g., at −16.5 mV, the two compartments prefer different directions.

Figure 8. Stimulus-Coverage Dependence

(A–D) Voltage responses to circular wave stimuli (3 Hz; 72% contrast; period: 192 μm) that cover different areas of the SAC dendritic field (see Materials and Methods; averages of three trials; CF motion in orange, CP in blue). Left column: stimulus masks, white areas indicate where the moving stimulus is presented (V _Rest = −62 mV). (E) Amplitudes of DC (V ₀), fundamental (V ₁), and harmonics (V ₂ and V ₃) plotted versus mask configuration (averages of eight cells). Leftmost data (gray box): “standard” stimulus from (A). (F) AIs for V ₁ (open squares) and V ₂ (filled diamonds) from (E). For statistics, see Table 1.