1. Reciprocal Inhibition of Inhibition: A Circuit Motif for Flexible Categorization in Stimulus Selection 
Shreesh P. Mysore, Eric I. Knudsen 
Neuron 
Volume 73, Issue 1, Pages (January 2012)
DOI: /j.neuron
Copyright © 2012 Elsevier Inc. Terms and Conditions

2. Figure 1 Feedforward Lateral Inhibition to the OTid
(A) Key elements of the midbrain network: the superficial layers of the optic tectum (layers 1–9), the intermediate and deep layers of the optic tectum (OTid), and a GABAergic nucleus in the midbrain tegmentum, the Imc. Space-specific excitation due to a stimulus (black arrows) drives neurons in both the OTid and the Imc. The Imc neurons send long-range, lateral inhibitory projections to OTid neurons coding for all other spatial locations (red line). For clarity, the projections of only one Imc neuron are shown. Consequently, unlike in sensory normalization circuits, in this circuit, a stimulus does not contribute to the suppression of its own responses.
(B) Schematic of a feedforward lateral inhibitory circuit (circuit 1) with long-range inhibitory projections from the Imc (red ovals, inhibitory units) to the OTid (black circles, output units). Black arrows indicate excitatory connections. Two out of many spatial channels in the space map are shown. One channel (1) represents the RF stimulus; the other (2) represents the competing stimulus.
Neuron  , DOI: ( /j.neuron )
Copyright © 2012 Elsevier Inc. Terms and Conditions

3. Figure 2
Neuronal Response Properties and Signatures of Explicit, Flexible Categorization in the Owl OTid
(A) Strength-response function of a typical OTid unit. Curve represents the average loom speed-response function for a single looming stimulus centered in the RF, computed from 61 OTid neurons.
(B) Distant competitor produces divisive suppression of spatial tuning curves in the OTid. Left: stimulus protocol. Dashed ovals indicate RF, black dots indicate RF stimulus, and gray dots indicate competitor located outside the RF, 30° away. The sizes of the dots represent the strengths (loom speeds) of the stimuli. Note that in experiments, both stimuli were always full-contrast dark dots on a light background. Right: black curve indicates azimuthal tuning curve with RF stimulus alone, and red curve indicates tuning curve measured in the presence of a competitor, which produces divisive response suppression.
(C) Effect of divisive influences on stimulus strength-response functions. Red arrows indicate increasing strength of inhibition. Dashed vertical lines represent half-maximum response strengths. Left: effect of input division. Right: effect of output division.
(D) Competitor strength-response profiles (CRPs) measured with competing looming visual stimuli. Left: stimulus protocol. Dashed ovals indicate RF, black dots indicate RF stimulus, and gray dots indicate competitor located outside the RF, 30° away. Strength of the RF stimulus is held constant, whereas that of the competitor is systematically varied. The sizes of the dots represent the strengths (loom speeds) of the stimuli. Middle: a CRP showing a gradual, nonlinear increase in response suppression, with increasing strength of the competitor. RF stimulus strength = 7.2°/s. Horizontal dotted line indicates responses to RF stimulus alone. Vertical dashed lines indicate the transition range (7.5°/s). Right: a switch-like CRP showing an abrupt increase in response suppression, with increasing strength of the competitor over a narrow range. RF stimulus strength = 8°/s. Horizontal dotted line indicates responses to RF stimulus alone. Vertical dashed lines indicate the transition range (0.4°/s). Red dot and arrows indicate the switch value (7.2°/s).
(E) Adaptive shift in the switch values of CRPs with changes in RF stimulus strength. Left: stimulus protocol. The two sets of stimuli were presented in an interleaved fashion. Right: the CRP measured with the stronger RF stimulus (blue) is shifted rightward with respect to the CRP measured with the weaker RF stimulus (magenta).
For (B), (D), and (E), error bars indicate SEM. All panels are adapted from Mysore et al. (2010, 2011). See also Figure S1.
Neuron  , DOI: ( /j.neuron )
Copyright © 2012 Elsevier Inc. Terms and Conditions

4. Figure 3
Feedforward Lateral Inhibition, Circuit 1, Can Produce Switch-like CRPs, but Not Adaptive Shifts in CRP Switch Value
(A) Schematic of the circuit. Recording icon indicates the unit for which responses are shown in (B) and (C).
(B) Effect of varying the parameters of the inhibitory-response function on the CRP transition range of output unit 1. Red line and arrow indicate the range of values of a parameter over which CRPs are switch like (transition ranges ≤ 4°/s). The value of the indicated parameter was varied systematically while the other parameters were held constant at the following values: k = 10, S50 = 8, m = 5, c = 15, din = 1, and dout = 0.05.
(C) The switch-like CRP produced at output unit 1 when the values of the parameters of the inhibitory-response function were set at k = 10, S50 = 8, m = 5, c = 15, din = 1, and dout = 0.05.
(D) CRP shift ratio (shift in CRP switch value / change in the strength of the RF stimulus) as a function of the input and output division factors (din and dout). The change in the RF stimulus strength was 6°/s (chosen to match experimental tests, Mysore et al., 2011). The black-shaded values indicate (din, dout) pairs that yielded CRPs for which at least one of them had a maximum change in response smaller than the threshold of 3.9°/s (Experimental Procedures) or for which one of the CRPs was not switch-like (transition range > 4°/s). Largest value of CRP shift ratio = 0.03, obtained at the (din, dout) pair = (1.5, 0), indicated by the boxed letter E. The resulting CRPs are shown in (E).
(E) The two CRPs corresponding to the (din, dout) pair that yielded the largest CRP shift ratio (din = 1.5, dout = 0).
See also Figure S2.
Neuron  , DOI: ( /j.neuron )
Copyright © 2012 Elsevier Inc. Terms and Conditions

5. Figure 4
Model Circuit 2: Reciprocal Inhibition among Feedforward Lateral Inhibitory Elements
(A) Conventions as in Figure 1B. Compared to model circuit 1, this circuit has one modification: reciprocal inhibition among the feedforward lateral inhibitory elements.
(B) Conventions as in Figure 1A. Schematic of key elements of the midbrain network showing Imc axon branches that, in addition to projecting broadly back to the OT (Figure 1A), terminate within the Imc as well (Wang et al., 2004). Whether these terminals form functional inhibitory synapses onto other Imc neurons is yet to be tested.
See also Figure S3.
Neuron  , DOI: ( /j.neuron )
Copyright © 2012 Elsevier Inc. Terms and Conditions

6. Figure 5
Reciprocal Inhibition among Feedforward Lateral Inhibitory Elements, Circuit 2, Can Produce Switch-like CRPs and Adaptive Shifts in CRP Switch Value
(A) Schematic of circuit 2. Recording icon indicates the unit for which responses are shown in (B) and (C).
(B) Effect of varying the parameters of the inhibitory-response function on the CRP transition range of output unit 1. Red line and arrow indicate the range of values of a parameter over which CRPs are switch like (transition ranges ≤ 4°/s). The value of the indicated parameter was varied systematically while the other parameters were held at the following fixed values: k = 10, S50 = 8, m = 5, c = 15, din = 1, and dout = 0.05; same values as in Figure 3B. The reciprocal inhibition factors rin and rout were chosen to be 0.84 and 0.01, respectively (see Results; Figures S3C and S3D).
(C) The switch-like CRP produced after choosing the values of the parameters of the inhibitory-response function to be k = 10, S50 = 8, m = 5, c = 15, din = 1, and dout = 0.05; same as in Figure 3C.
(D) CRP shift ratio (shift in CRP switch value / change in the strength of the RF stimulus) as a function of the input and output divisive normalization factors (din and dout; ranges of din and dout same as in Figure 3D). Reciprocal inhibition parameters rin and rout were set at 0.84 and 0.01, respectively (Results). All other parameter values were same as in Figure 3D. The change in the RF stimulus strength was 6°/s. The black-shaded values indicate (din, dout) pairs that yielded CRPs for which at least one of them had a maximum change in response less than the threshold of 3.9°/s (Experimental Procedures) or for which one of the CRPs was not switch like (transition range > 4°/s). Largest value of CRP shift ratio = 0.88, obtained for the (din, dout) pair = (0, 0.06), indicated by the boxed letter E. The resulting CRPs are shown in (E). Note, however, that a large range of nonzero din and dout values yielded CRP shift ratios very close to the maximal value (Figure S4A).
(E) The two CRPs corresponding to the (din, dout) pair that yielded the largest CRP shift ratio (din = 0, dout = 0.06). Inset represents normalized CRPs.
See also Figure S4.
Neuron  , DOI: ( /j.neuron )
Copyright © 2012 Elsevier Inc. Terms and Conditions

7. Figure 6
Comparison of Model Predictions with Experimental Data from the Owl OTid
(A–G) Simulated data calculated for output unit 1 in circuit 2 (Figure 4A).
(A–E) Simulated loom speed-response functions obtained from model circuit 2 using different sets of parameter values to illustrate the range of effects of a fixed-strength competing stimulus, described in the Results. The values of the parameters used to generate these curves are listed in Table S1. Black represents target-alone response profiles, orange shows target-with-competitor response profiles, dashed vertical lines indicate the location of the half-maximum response speeds, and solid horizontal lines indicate the dynamic ranges. Error bars indicate SEM.
(F) Scatterplot of dynamic ranges. Diagonal line represents line of equality.
(G) Distribution of the difference between the half-maximum response speed (L50) of the target-with-competitor response profile and the strength of the competitor.
(F and G) 135 pairs of target-alone response profile and target-with-competitor response profile were generated by varying the half-maximum response speed (S50) of the output units systematically over nine values (from 4°/s through 12°/s) and by varying the half-maximum response speed of the inhibitory units (from 7°/s through 9°/s) while holding all other parameter values constant. The strength of the competitor was always 8°/s.
(H–O2) Experimental results based on measurements of loom speed-response functions from 51/71 OTid units for which (1) both response profiles (target-alone response profile and target-with-competitor response profile) were correlated with the strength of RF stimulus, (2) they were well fit by sigmoids (r2 > 0.8), and (3) there was an effect of the competitor (Experimental Procedures). Median strength of competitor = 8°/s.
(H–L) Loom speed-response functions measured without (black) and with (orange) a competitor stimulus located 30° to the side of the RF. The strength of the competitor in each case is indicated by the position of the black triangle on the x axis. Dashed vertical lines indicate the location of the half-maximum response speeds (L50). Solid horizontal lines indicate the dynamic ranges.
(M) Scatterplot of dynamic ranges of target-with-competitor response profiles (TcRPs) versus those of target-alone response profiles (TaRPs), showing several neurons that had narrower dynamic ranges in the presence of the competitor (Experimental Procedures). Diagonal line represents line of equality. Similar to model predictions in (F).
(N) Scatterplot of the amount of suppression (spikes/s) of responses to the strongest RF stimulus (22°/s) versus suppression to the weakest RF stimulus (0°/s), showing several neurons with greater suppression of the responses to the weakest RF stimulus. Diagonal line represents line of equality.
(O1) Scatterplot of half-maximum response speeds (L50) of TcRPs versus those of TaRPs, showing that TcRPs are typically right shifted with respect to TaRPs. Diagonal line represents line of equality.
(O2) Plot of the difference between the half-maximum response speed (L50) of the TcRP and the strength of the competitor, showing that the distribution is centered around 0 (p > 0.05, t test against 0). Similar to model predictions in (G).
See also Table S1.
Neuron  , DOI: ( /j.neuron )
Copyright © 2012 Elsevier Inc. Terms and Conditions

8. Figure 7
Comparison of the Performance of Alternative Circuit Implementations of Feedback Lateral Inhibition
(A–D) Alternatives to model circuit 2 (Figure 4) that also implement adaptive, competitive lateral inhibition.
(A) Feedback lateral inhibition by output units; inset represents equivalent circuit.
(B) Same as (A), but with additional recurrent excitatory loops to output units.
(C) Feedback lateral inhibition to input units.
(D) Same as (C), but with additional recurrent excitatory loops to input units.
(E and F) Comparison of settling times for circuit 2 (orange) and the next-simplest circuit, circuit 3 (green), shown in (A).
(E) Examples of time courses of responses to an RF stimulus strength of 9°/s and a competitor stimulus strength of 8°/s. Top: circuit 2. Bottom: circuit 3. Dashed lines represent settling time (Experimental Procedures).
(F) Settling time as a function of relative stimulus strength (RF stimulus strength − competitor strength). Competitor strength was held constant at 8°/s. Orange represents circuit 2, and green indicates circuit 3.
(G and H) Comparison of the reliability of the two circuits.
(G) Monte Carlo simulation was used to generate 100 estimates of the Fano factor (a metric that is inversely related to response consistency; Experimental Procedures) for the steady-state response (at t = 100 time steps) with an RF stimulus strength of 9°/s and a competitor strength of 8°/s (Experimental Procedures). Orange represents circuit 2, and green indicates circuit 3.
(H) Ratio of the mean Fano factor yielded by circuit 2 to that yielded by circuit 3, as a function of the relative stimulus strength (RF stimulus strength − competitor strength). Competitor strength was held constant at 8°/s. Filled circles indicate p < 0.05 (pairwise rank-sum test between Fano factor distributions at each value of relative stimulus strength followed by Holm-Bonferroni correction for multiple comparisons); open circle indicates p > 0.05.
(E)–(H)For the simulations, the parameter values of circuit 2 were the same as in Figure 5E. The parameters for circuit 3 were chosen to be optimal (minimum model error; Figure S5 and Experimental Procedures): din = 1.1, dout = 0.005, m = 1, h = 21, S50 = 9, and k = 5.
See also Figure S5.
Neuron  , DOI: ( /j.neuron )
Copyright © 2012 Elsevier Inc. Terms and Conditions