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.
Perceptual rivalry is the subjective experience of alternations between competing percepts when an individual is presented with an ambiguous stimulus. It has been suggested that rivalry between neurons may be a ubiquitous property and competition between neural representations occurs throughout the brain [1]. Evidence for this includes: 1) neural correlates of visual rivalry found at multiple regions of visual processing (e. g. , V1, V4, MT, IT) [2–5], 2) most sensory modalities exhibit rivalry suggesting similar biophysical processes [6], 3) brain regions that do not receive specific sensory inputs, such as the inferior frontal and parietal lobe, exhibit activity that is correlated with perceptual switches [7], and 4) independent rivalry can occur at different spatial locations, with different senses, and under different modalities [6,8–10]. Rivalry provides a unique window into cortical function because it directly accesses an internal computation elicited by but distinct from an external sensory input. Many experiments on rivalry utilize stimuli that are always in view although possibly moving. We refer to these situations as static rivalry. In intermittent rivalry, the stimulus presentation is periodically removed while the perception alternates with a longer period. Rivalry memory refers to the return of the last dominant percept after an extended time duration without stimulus. Computational and mathematical work has shown that a neurophysiologically-constrained cortical model whose primary features are mutual inhibition between pools of neurons and a fatigue process can reproduce the basic experimental properties of static rivalry, winner-take-all behavior, normalization, and decaying oscillations induced by distractors under different input conditions [11–14]. These findings support the universality of a simple neuronal model that can be used to explain a myriad of basic cortical behaviors and as such is a candidate canonical circuit for simple cognitive functions (e. g. see [15–17] for discussion of such functions). A canonical circuit is universal in the sense that it does not imply a single function but can exhibit multiple operating regimes under a change in parameter values (including just a change in the type of stimulus). The biophysical dynamics can be inferred from behavioral observations such as rivalry, decision-making, working memory, and contrast-sensitivity [1,6, 13,18] making them potential clinical endophenotypes (simple biomarkers associated with and possibly underlying a more complex trait of interest). As such, rivalry has been suggested as a diagnostic tool for probing cognitive dysfunction such as in autism, bipolar disorder, and major depressive disorder [19–21]. The canonical circuit and similar models have been validated against a set of nontrivial observations in static rivalry including Levelt’s propositions [11,22–26]. Although mutual inhibition acting as a positive feedback has been proposed as a memory mechanism in other contexts [27], it has been argued [22,28] that a circuit with mutual inhibition and fatigue cannot reproduce intermittent rivalry nor rivalry memory because presumably there is no mutual inhibition when the stimulus is absent and the fatigue process would give the opposite result of what is observed, favoring the suppressed percept (i. e. masking not priming). The question then is whether a single circuit model can account for all of the aforementioned behaviors (including non-rivalry dynamics) or whether independent or additional circuits are required to explain all the phenomena. Here, we show that the same cortical circuit model can also be applied to time-varying inputs in intermittent rivalry and rivalry memory. We explore various possible mechanisms and show that just the inclusion of a previously neglected phenomenon—namely low, nonspecific, background activity—is sufficient to provide a unified account of static rivalry, intermittent rivalry, rivalry memory and all previously accounted for phenomena. The background activity at arbitrarily low values can provide sufficient drive to the neurons such that the memory can be held by mutual inhibition alone and withstand the effects of fatigue. The memory persists over a wide range of parameter values, is robust to noise, and does not require the inclusion of another process. The memory is topological in the sense that the total number of memory states is invariant to a range of changes to the input and network properties. Importantly this memory preserves all of the previously known behaviors of the basic model since the background activity does not play a role under the static conditions. This is in contrast to recurrent excitation models of short-term memory where neural activity is bistable between an active and inactive state, which is generally antagonistic to rivalry [29], may conflict with local balanced states [30], and relies on fine-tuning [31]. The circuit model can reproduce two main features of rivalry memory and intermittent rivalry that we observed in the ambiguous quartet illusion: 1) a dynamic Levelt’s fourth proposition (dynamic L4), where the dominance duration increases with increasing stimuli presentation intervals and 2) habituation, where the initial percept durations (epochs) decrease upon repeated stimulus presentations until a steady state is reached after several epochs. Dynamic L4 has been shown in prior work with other intermittent paradigms [32]. Habituation has also been reported for rivalry; although, not necessarily intermittent rivalry [33–35]. We provide a theoretical explanation for these behaviors. The theory suggests that for the observed habituation to occur, local fatigue such as spike-frequency adaptation or recurrent synaptic depression is the dominant form of fatigue rather than synaptic depression between pools, and that the interval between pulses is shorter than the fatigue time constant.
We informed our model with experiments on the ambiguous quartet illusion, which is a prototypical example of intermittent rivalry and has the advantage of naturally incorporating a periodic stimulus (see Fig 1). The inputs are time dependent and the perceived motion only occurs when the frame presentation (input) is switched from one parity (e. g. dots in upper-right and lower-left corners (UR-LL) ) to the other (e. g. lower-right and upper-left corners (LR-UL) ). The motion is ambiguous because the transition has two possible interpretations. For example, in the transition from UR-LL to LR-UL, the dot located at UR could be interpreted as “sliding” vertically down to LR, while the dot at LL simultaneously slides up to UL. The alternative interpretation is that the dot at UR slides horizontally leftwards to UL, while the other dot at LL slides horizontally rightward to LR. If one imagines a bar connecting the dots then the vertical interpretation corresponds to a bar rotating clockwise from 45° to –45° (like a seesaw) while the horizontal interpretation corresponds to the stick rotating counterclockwise from 45° to 135°. Hence, the perceived motion in the quartet illusion is characterized by two degrees of freedom—orientation and direction. Orientation refers to whether the dot motion is aligned along the vertical (V) or horizontal (H) axis and direction refers to whether the motion is clockwise (+) or counterclockwise (-) (see Fig 2a). We presented the illusion to subjects with different frame presentation intervals (Tframe). We examined dynamic L4 by testing if the perception dominance duration (TD) (inverse of the percept alternation rate) was correlated with Tframe. In our first experiment we tested two subjects across a wide range of Tframe inputs. The subjects showed a dramatic response to the stimulus parameter, which occurred at different ranges for each subject (different sensitivities). In Fig 3a and 3b we plotted the TD distributions to give the qualitative picture. We also observed some evidence of a habituation effect (Fig 3c), where the dominance durations decreased to a steady state value. To verify the phenomenon we recorded dominance durations on a group of 16 hypothesis-naive subjects. We probed the system over a range of Tframe: 300,350,400, and 450 milliseconds (minimum chosen to avoid photosensitive epilepsy). Individuals were told to report on any change of motion and were trained on biased H and V motion stimuli prior to the quartet stimulus (see Methods). From our post-task survey we found that all individuals observed oscillating V motion (seesaw) and H motion (seesaw rotated by 90 degrees). For a majority of subjects, these were the only reported percepts but a subset occasionally observed rotation (H, V, H, …). There were also infrequent reports of the dots disappearing or changing size and the dots moving toward and away from the subject (three-dimensional motion). The stimulus used in the experiments can be seen in S1 Movie. To test for the presence of dynamic L4, we analyzed the pooled data across subjects and across percept-types (H, V, rotation). We observed a weak effect across subjects. The qualitative results are shown by the TD distributions and their means (see Fig 4a and 4b). We quantified the relationship with a Cox proportional hazards mixed effects model. The statistical model treats the dominance time as the survival time for a percept and evaluates the effects of factors on the survival probability (see Fig 4c). There was a significant but weak positive relationship of TD with Tframe with P = 2 × 10−4 (Wald test using 1,322 samples and 1,266 recorded switch events) and hazard ratio of 0. 996 (s. e. 0. 001). We used these preliminary findings together with previously reported effects for another rivalrous stimulus [32] as support for the dynamic L4 constraint. For the hypothesis-naive experiment we discovered a larger habituation effect of the percept durations over percept epochs. The initial percept epochs had longer TD as shown by Fig 5, and we estimated a hazard ratio of 1. 024 (s. e. = 0. 008) (P = 2 × 10−3; Wald test using 1,322 samples and 1,266 recorded switch events). We used this habituation effect as a second constraint for the model.
We examined several intermittent rivalry and rivalry memory mechanisms in a canonical cortical circuit model and concluded that the inclusion of experimentally observed low-level, nonspecific background neuronal activity that induces a mutual-inhibition memory is the most plausible. The mechanism preserves all the phenomena of static rivalry as shown in previous studies [11,12,22]. Mutual inhibition has been proposed before as a mechanism for short-term memory [27]. However, it was not considered for rivalry since it was assumed that the circuit could not maintain the memory in the absence of a stimulus and the presence of fatigue would favor the suppressed percept. Even if neurons are not completely inactive during the off-states, it is not a priori obvious that an asymmetric state would exist and persist indefinitely in the presence of fatigue. We show that for reasonable conditions, this form of memory is topological (holds for a wide range of parameters) and stable for arbitrarily low input. Topological mutual-inhibition memory can exist as long as inhibition is strong enough and the gain function (i. e. , frequency-input curve) has a non-increasing slope, which is experimentally observed [36,49]. Thus, it may not be limited to rivalry and could be the mechanism for other forms of memory in the brain. The model explains the two intermittent rivalry phenomena of dynamic L4 and habituation in the quartet illusion. Dynamic L4 is similar to what Leopold et al. (2002) found for the rotating sphere (RS) stimulus using manually inserted blank periods. A habituation effect similar to what we found for the quartet has also been noted for other stimuli (e. g. , static images, motion) and sensory domains (e. g. , visual, auditory) [33–35]. However, binocular rivalry shows the opposite effect where the switch rate decreases over epochs. This has been attributed to contrast adaptation [50] and can be accounted for in the rivalry model by reducing input over time. The dynamics of our model are geometrically similar to the model proposed by Noest et al. 2007[28]. However, instead of requiring a subthreshold current with shunting adaptation, we show that the activity itself acts as the memory with the property of persisting indefinitely. There are many possible mechanisms for the background activity and perhaps the most interesting is that zero-mean noise is sufficient. While either local (e. g. , spike-frequency adaptation, recurrent synaptic depression) or nonlocal (e. g. , cross-pool synaptic depression) is sufficient to explain intermittent rivalry, local fatigue in particular reproduces habituation. Prior experimental designs of intermittent rivalry introduced the off-states by either manually removing a static stimulus or by utilizing a more complex protocol such as combining motion-induced blindness with a static stimulus, or by instructing the subject to independently attend to mixed “static, intermittent” epochs[10,32]. It is possible that some of these more complex paradigms involve higher order processing that makes replication difficult. We propose that the quartet is a robust self-contained system for the study of intermittent rivalry since periodicity in the quartet invokes natural motion processing. In retrospect, our experimental design was suboptimal for detecting dynamic L4, but the model provides guidance for future experiments. Further study is necessary to determine whether different fatigue modes are important for different rivalry stimuli. This could be predicted with the model and tested experimentally by behavioral and electrophysiological measurements, perhaps combined with pharmacological manipulation of K+-channels that modulate adaptation effects [51]. Finally, the role of background activity in the theory predicts that perturbing or suppressing the activity bias will extinguish rivalry memory.
Ethics approval for this study was granted by the NIH Combined Neuroscience Institutional Review Board under protocol number 10-M-0027 (ClinicalTrials. gov ID NCT01031407). The naive-subject study consisted of 16 adult male participants from the National Institutes of Health campus and DC metropolitan region. The data were screened such that at least two percept switches were reported in a test block. One subject did not have adequate data and was removed, leaving 15 subjects. Author data was collected on SV and PT for the quartet. Naive-subjects were tested on the standard quartet task. The standard quartet animation consists of two alternating still frames where a single frame consists of one set of dots located at opposing corners of an upright square as shown in Fig 1. The task was administered in a dark room with maximum screen and keyboard brightness (approximately 2 lux) on a 15 inch 2010 MacBook Pro with 60 Hz frame rate. Our stimulus consisted of three nested quartets centered on the viewing screen as shown in Fig 1 (also see S1 Movie); chosen to mitigate the Troxler effect and to induce motion perception over a large receptive field. The dots were outlined with the RGB color = 46,55,254 and set on a black background. For a typical viewing distance of 24 inches, although this was not rigidly enforced, the square length visual angle (dot diameter visual angle) of each nested quartet were 5. 5 (1), 3. 5 (0. 5), 1. 5 (0. 25) degrees. There was a fixed orange, central dot with RGB color = 255,127,0. This was the instructed focal point for the subject. These parameters were arbitrarily chosen. During the task, subjects were instructed to maintain fixation on this central dot and report a change in motion by pressing the Return-key. To give feedback that a switch was recorded, the central dot briefly changed color from orange to green (RGB = 0,255,0) to orange when the subject reported a change. The task consisted of 7 blocks: a tutorial, a task-comprehension block, and 5 frame-period (Tframe) blocks with a two second black screen period between blocks. Participants were told that the task would test their ability to detect changes in motion and were not informed that the motion was ambiguous. They were also shown examples of the types of motions to expect: horizontal or vertical, consisting of unbiased apparent motion animations, where a set of three frames was repeatedly presented such that the dots progressed from corner, to center, to corner, to center. This was done for vertical and horizontal orientations of motion. The task-comprehension block used this same biased motion stimulus and the direction was changed at fixed intervals that were known to the experimenter. The first frame-period block was set to 300 millisecond frame intervals and lasted six minutes (we refer to this as the practice block). This was followed by four blocks with frame periods (and block durations) of 300 (5), 350 (5), 400 (6), and 450 (8) ms (minutes). The order of the last four blocks was shuffled between participants. Author-data was collected on the quartet task. The quartet task was similar to the above but without the tutorial, task-comprehension, or practice blocks. These sessions consisted of randomized Tframe with 2–3 sampled frame periods and the duration was based on reporting 11 switches (some Tframe were repeated in separate sessions). Data from the naive-subject group was analyzed using a Cox proportional hazards model (see [52,53] for review). It is a semi-parametric model that is robust to the distribution of the data, which was non-normal for our case. The analysis calculates statistics across all time points and accounts for right-censored data. We chose this approach since it accounts for percept duration that may extend beyond the test block, including those that may span the majority of a block. The frequency of percepts that remained dominant after TD dotted frame presentations were fit to a baseline survival model for each test condition (e. g. , Tframe) and normalized (the non-parametric component of the model). The hazard ratio is the exponential adjustment to the baseline survival for the conditioned effects, which is the parametric component. An increased hazard ratio means there was an increased probability of percept extinction over a time period as the parameter was increased. To be considered a valid model fit, there were two statistical tests: 1) test whether the estimated coefficient for the effect is non-zero, and 2) that the distribution of the residuals has zero slope across time (is flat). We used the coxme mixed effects R function to estimate the hazard ratios. The mixed effects model was used so we could account for subject- or Tframe- specific deviations. A Wald test was used to estimate a P-value for the hazard ratio. The coxme library does not have a test for the residuals. To check this we calculated a noise vector (z) from the coxme fit given by z = ŷ − θx, where ŷ is the linear model prediction, θ is the estimated coefficient, and x is the predictor vector. The noise vector z was used as an offset in the R function coxph and the residuals from this were checked with cox. zph. We used a criterion of no significant deviation of the residual slope from zero (i. e. , P>0. 05), in order for the proportionality assumption to apply. Bifurcation analysis was performed in XPPAUT [54]. Rate models were simulated using Python. Conductance-based model simulations were performed with circuit of two mutually inhibiting neuron pools with a calcium activated spike frequency adaptation-like current and synaptic depression. This model was simulated in XPPAUT and the output was analyzed in Python. All code used for simulations and numerical analysis including parameters are attached as S2 Text.
When the brain is presented with an ambiguous stimulus like the Necker cube or what is known as the quartet illusion, the perception will alternate or rival between the possible interpretations. There are neurons in the brain whose activity is correlated with the perception and not the stimulus. Hence, perceptual rivalry provides a unique probe of cortical function and could possibly serve as a diagnostic tool for cognitive disorders such as autism. A mathematical model based on the known biology of the brain has been developed to account for perceptual rivalry when the stimulus is static. The basic model also accounts for other neural responses to stimuli that do not elicit rivalry. However, these models cannot explain illusions where the stimulus is intermittently switched on and off and the same perception returns after an off period because there is no built-in mechanism to hold the memory. Here, we show that the inclusion of experimentally observed low-level background neural activity is sufficient to explain rivalry for static inputs, and rivalry for intermittent inputs. We validate the model with new experiments.
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Canonical Cortical Circuit Model Explains Rivalry, Intermittent Rivalry, and Rivalry Memory