Canonical Cortical Circuit Model Explains Rivalry, Intermittent Rivalry, and Rivalry Memory

Abstract

It has been shown that the same canonical cortical circuit model with mutual inhibition and a fatigue process can explain perceptual rivalry and other neurophysiological responses to a range of static stimuli. However, it has been proposed that this model cannot explain responses to dynamic inputs such as found in intermittent rivalry and rivalry memory, where maintenance of a percept when the stimulus is absent is required. This challenges the universality of the basic canonical cortical circuit. Here, we show that by including an overlooked realistic small nonspecific background neural activity, the same basic model can reproduce intermittent rivalry and rivalry memory without compromising static rivalry and other cortical phenomena. The background activity induces a mutual-inhibition mechanism for short-term memory, which is robust to noise and where fine-tuning of recurrent excitation or inclusion of sub-threshold currents or synaptic facilitation is unnecessary. We prove existence conditions for the mechanism and show that it can explain experimental results from the quartet apparent motion illusion, which is a prototypical intermittent rivalry stimulus.

Fig 1. Quartet illusion.

We presented a variant of the quartet consisting of nested quartets. A single quartet frame consists of two dots located at opposing corners of a square, across the diagonal. In the next frame the other set of opposing dots is shown. A single transition between frames is perceived as either a motion with the dots moving vertically together as an illusory bar rotating clockwise (top right frame), or horizontally as a bar rotating counterclockwise (bottom right frame).

Fig 2. Paths of motion and neural network for the quartet illusion.

(a) Each frame transition of the quartet illusion (t₀, t₁, t₂,…) induces an ambiguous percept of one of two possible motions characterized by an orientation—horizontal (H) or vertical (V)—and a direction of rotation—clockwise (+) or counter-clockwise (-). During a frame transition there is competition (mutual inhibition) between the two possible perceived motions—V+ competes with H- and V- competes with H+. In the illusion, once an orientation becomes dominant, there is an oscillation in direction on each frame presentation, e.g. V+, V-, V+, etc. Eventually, the other orientation becomes dominant and the oscillations in direction will continue, e.g. H+, H-, H+, etc. The rivalry refers to the alternation between orientations. (b) A table of the allowed transitions due to the symmetries in the illusion. Each row indicates the perceived motion at the current transition and each column the perceived motion at the next transition; a value of one in a column indicates a possible path. (c) The circuit can be reduced by averaging over the fast direction oscillations into a two pool circuit with mutual inhibition between competing neuronal pools representing H and V orientations with an intermittent drive (dashed lines).

Fig 3. Dynamic L4 and habituation.

Violin plots of percept duration (T_D in movie frames) versus the interval between changes in frame (T_frame) for author-subjects A11 (a) and A10 (b) and versus percept epochs (order of reported percepts) for A10 (c). The width of the violin plot represents the probability distribution for a dominance duration. (a-b) Increased T_D with T_frame (dynamic L4). (c) Decreased T_D across percept epochs (habituation) for pooled T_frame data.

Fig 4. Dynamic L4 survival analysis for pooled hypothesis-naive subject data.

(a) Violin plots with means (diamonds) for T_D versus T_frame. T_D is the reported uninterrupted duration of either horizontal or vertical motion (or for a few subjects rotational motion), in units of the number of presented movie frames. T_frame is the interval between movie frames. (b) Mean of the pooled data. (c) T_frame T_D-survival plots. There is a small but significant difference in survival probabilities.

Fig 5. Habituation survival analysis for pooled hypothesis-naive subject data.

(a) Violin plots for pooled data of T_D vs. percept epoch (the order of reported percepts). (b) Survival plots for the same analysis for various epochs.

Fig 6. Persistent activity maintains memory.

a) Dominance durations (T_D) as a function of percept epochs starting from rest for different T_frame intervals and fatigue time constants. A subset of the T_frame conditions tested showed habituation. When the fatigue time constant was increased there was both an overall increase in dominance durations and all of the rivalry states showed habituation. See S2 Text for model specifications. b) Like-orientated pools are bistable. When dominant (and receiving nominal inhibition from the suppressed pools) one set of like-orientated pools (H or V) can have persistent activity. Here the pools were initialized with zero activity (no input), then one of the two (green) was given a brief input (pulse), followed by no input, and then a hard reset of their activity to zero. The pulse elicited non-zero activity in both pools but was greater for the pool with direct input. Then instead of falling back to zero activity, both pools remained in an elevated state despite a lack of input. When their activity was forced to zero (reset), they then remained inactive.

Fig 7. Background-activity stabilizes memory.

a)(Top) No background activity results in fast switching between orientations for frame interval (T_frame) of 200 milliseconds. (Bottom) Inclusion of small nonspecific background input results in non-zero activity during off-states (same on-state input as in above). Orientation persists for multiple frame transitions. b) Dominance duration (T_D) increases with T_frame. All cases show habituation over percept epochs with a larger effect for short intervals. See S2 Text for model specifications.

Fig 8. Dynamic L4 for two-pool system under different assumptions.

Rate models with either fixed or noisy background input (S_off) and local or nonlocal fatigue and a conductance-based model with local fatigue all showed dynamic L4. For T_frame to the right of a curve we observed no alternations for the duration of the simulation. See S2 Text for model specifications.

Fig 9. Habituation of percept duration over percept epochs.

Simulation results using local-fatigue only or nonlocal fatigue only models with the variables initialized at resting state. For local fatigue there is a decrease in the dominance duration (T_D) for subsequent dominance periods. For example the first dominance duration (epoch one) is longer than the second. This was seen for both the rate model and the spiking model. For nonlocal fatigue in the rate model the first epoch is shorter than the following epochs. See S2 Text for model specifications.

Fig 10. u1-u2 bifurcations across static symmetric external drive S for system with nonlocal fatigue.

The pitchfork bifurcation for arbitrarily low input provides the asymmetry necessary for intermittent rivalry and rivalry memory. It allows for memory of the last dominant state by maintaining asymmetry for very small (background) input (S_off) (S_off = 0.001). A shift in the asymmetric state in the off-state by a build-up of fatigue due to larger S in the on-state (S_on) eventually leads to a shift in dominance. Although not drawn, the limit cycle extends to the red pitchfork terminating in a SNIC. A smoothed threshold was used to generate the plot. For actual simulations we used a hard threshold and zero input gives symmetric, zero activity.

Fig 11. Local versus nonlocal fatigue variables for the rested rate-model.

(a) Local fatigue variable a initialized to zero for pools i and j over percept epochs (T_frame = 105 milliseconds). (b) Nonlocal fatigue variable s initialized to one for pools i and j over percept epochs (T_frame = 150 milliseconds). See S2 Text for other model specifications.