Figure 1.
Short-Term Synaptic Depression Can Contribute to Direction Selectivity in an Elementary Reichardt Detector
(A) Information from two channels (blue and red: right and left, respectively) converges on a post-synaptic cell. The blue channel exhibits short-term synaptic depression (D), which nonlinearly filters the stimulus, advancing the timing of the channel's peak response relative to the timing of the peak of the stimulus (blue dashed lines). The red channel exhibits no depression (ND), which linearly scales the stimulus, leaving the timing of the channel's peak response to coincide with the timing of the stimulus (red dashed lines). Differences in temporal processing interact with a spatial separation of the two channels' receptive fields to produce direction selectivity. A moving stimulus pulse first activating the red channel leads to the summation of coincident peaks in the post-synaptic cell. A stimulus pulse moving in the opposite direction leads to the summation of disparate peaks and hence a weaker response in the post-synaptic cell.
(B) A schematic outline depicting the ascending electrosensory system in Apteronotus and Eigenmannia and other Gymnotiform genera. In short, electrosensory information from receptors in the skin (RF 1 and RF 2) project topographically onto the electrosensory lateral line lobe (ELL). Neurons in the ELL in turn project topographically onto neurons in the torus semicircularis (Torus) in the midbrain via the lateral lemniscus (LL). Midbrain afferents include both depressing and nondepressing synapses that converge on to individual neurons: this convergence of information meets the requirements for the proposed elementary Reichardt motion detector. We used three categories of stimuli: global stimuli (social signals that stimulate the entire sensory surface simultaneously), a localized moving bar (shown), and a larger moving sinewave grating.
Figure 2.
Response of Model to a Moving Sine Grating Following 500 msec Initialization with 50% Grey
(A) The one-state model with the fast process alone, s = 1.
(B) The two-state model with both the fast and slow processes, s = 0.99. Blue and red (middle trace of each subpanel) shows membrane potential, V∞(t). Cyan and magenta shows firing rate, F(t) (beneath V∞(t), and timing of action potentials determined from F(t) by a Poisson process (above). Blue and cyan (top subpanel in both A and B): preferred direction (σ = 1); red and magenta (bottom subpanel): non-preferred direction (σ = −1). Small numbers are the expected action potentials in each cycle. Black dotted line indicates threshold for action potentials. In the one-state model, the direction index (defined in Model) is constant across all cycles at 0.48. In the two-state model, the direction index increases from 0.49 to 1—the two-state model becomes more direction selective with time. Other parameters of model are Rb = 5 Hz, Rc = 172 Hz × log(67 × 0.2), xn = −45°, xd = 45°, tD = 150 msec, tS = 3,000 msec, d = 0.4, gd = 15, gn = 0.7,V0 = 0.7, V0 = 70 mV, VE = 0 mV, Vt = −64 mV, Vr = −65 mV, tm = 30 msec, tR = 10 msec. Other parameters of the stimulus are t0 = −500 msec, ts = 0 msec, tf = 3,000 msec, f = 2 Hz, p0 = ∞, p1 = −∞.
Figure 3.
Response, V∞(t), of the Two State Model to a Pulse Stimulus
(A,C) Initialized with a temporally and spatially uniform 50% grey stimulus.
(B,D) Initialized with global synchronous gamma-band oscillations. Solid lines represent responses to movement in the preferred direction, dashed lines to the non-preferred direction. The responses in each plot are aligned to the peak of the PSP from the depressing synapse. This facilitates the comparison between the preferred and non-preferred directions of movement, but as a result, the onsets of the moving stimuli are not aligned. In the preferred direction, the object passes first through the nondepressing part of the receptive field and then enters the depressing part. Parameters of the model for this and all remaining figures are the same as listed in Figure 2 except for the synaptic factors, which vary. For A and B (magenta): gn = 0.2, gd = 8. For C and D (green): gn = 0.6, gd = 4. The stimulus parameters used throughout for the pulse stimulus are fg = 20 Hz, Ag = 0.7, or Ag = 0 (respectively, with or without initializing global synchronous oscillations), t0 = −1,000 msec, ts = 0 msec, tf = 5,500 msec, φ = 135°; σ, p0, and p1 differed depending on direction of movement: σ = 1, p0 = −16p, p1 = −19p, (preferred direction); σ = −1, p0 = −15p, p1 = −19p (non-preferred direction).
Figure 4.
Magnitude of Direction Selectivity to a Moving Pulse Stimulus as a Function of Synaptic Factors
(A) Initialized with 50% grey. (B) Initialized with Global Synchronous Gamma-Band Oscillations. Direction selectivity is quantified, in each condition, as the ratio (in decibels) of the peak values of V∞(t) – V0 in response to the pulse in the preferred to the non-preferred directions (solid and dotted curves in Figure 3). Brighter shades of grey indicate more direction selectivity. Colored circles indicate parameter values used in Figure 3.
(C) Magnitude of enhancement (magenta) or reduction (green) of the directional response caused by the addition of global synchronous gamma-band oscillations. This measurement was quantified by the difference between the values calculated for (A) and (B). The color indicates sign of difference; intensity indicates magnitude.
Figure 5.
PSD Depression as a Function of Synaptic Factors and Exemplary Traces Used To Calculate This Measure
(A) Measure of PSP depression (measured at the soma—a sum of all synaptic inputs) as a function of synaptic factors. Brighter shades of grey indicate more synaptic depression.
(B–D) Exemplary traces of V∞(t) in response to the initializing global synchronous oscillations at three positions in parameter space (indicated in (A) with dots of corresponding colors). This measure of PSP depression is identical to that used in previous studies of midbrain neurons in Eigenmannia [17–19]. Specifically, depression was quantified as the ratio (in decibels) of the peak value of V∞(t) − V0 in the first cycle of the initializing global synchronous stimulation to the average of the peak values for 11 consecutive cycles, starting 3 seconds into the stimulus.
Figure 6.
Reproducing the Properties of a Population of Midbrain Neurons
(A) Experimental data from a population of midbrain neurons in Eigenmannia (replotted from [17]). PSP depression plotted against direction selectivity observed in two conditions for each neuron. Asterisks with solid line: response of each neuron to the moving object. Circles with dashed line: response of the same neurons to the moving object but with concomitantly presented global synchronous gamma-band oscillations. Curves are the best fit second degree polynomials.
(B) Hypothetical distributions of synaptic properties in model populations of neurons. The background gradient is a region of Figure 4C where the addition of global synchronous oscillations enhances direction selectivity. Lines represent one-dimensional restrictions of the parameter space—these lines are four hypothetical distributions of parameter values across a population of neurons, lines labeled C through F.
(C–F) Model data plotted in the same manner as the experimental data shown in (A). The data shown in each of the plots in (C–F) correspond to the labeled lines in (B). In (C–F), the lower curve shows direction selectivity to the moving object and the upper curve shows direction selectivity to the moving object with concomitant oscillations. For this plot, the parameters determining the relative contributions of the depressing and the nondepressing synapses have been expressed as a count of more numerous, but individually weaker, synapses. We arbitrarily model the numbers of depressing and nondepressing synapses, as well as their contributions to the post-synaptic potentials as roughly equal. To achieve these approximate equalities, we multiplied the number of the depressing synapses by a weight of 0.2 and the nondepressing synapses by a weight of 0.01. The hypothetical distribution are: (C) constant total number of synapses (80) with variable ratio of numbers of depressing to nondepressing; (D) constant number of depressing synapses (80) with variable number of nondepressing synapses; (E) constant ratio of numbers of depressing to nondepressing synapses (5/3) with variable total numbers of synapses; (F) constant number of nondepressing synapses (12) with variable number of depressing synapses. (E) and (F) are most similar to the experimental data shown in (A).