Layered structure of cortex explains reversal dynamics in bistable perception

Abstract

Bistable perception involves the spontaneous alternation between two exclusive interpretations of a single stimulus. Previous research has suggested that this perceptual phenomenon results from winnerless dynamics in the cortex. Indeed, winnerless dynamics can explain many key behavioral characteristics of bistable perception. However, it fails to explain an increase in alternation rate that is typically observed in response to increased stimulus drive and instead predicts a decline in alternation rate. To reconcile this discrepancy, several lines of work have augmented winnerless dynamics with additional processes such as global gain control, input suppression, and release mechanisms. These offer potential explanations at an algorithmic level. But it remains unclear which, if any, of these mechanisms are implemented in the cortex and what their biological substrates might be. We suggest that the answers to these questions may lie within the laminar architecture of the cortical microcircuit. Utilizing a dynamic mean field approach, we implement a laminar columnar circuit with empirically derived interlaminar connectivity. By coupling two such circuits such that they exhibit competition, we are able to produce winnerless dynamics reflective of bistable perception. Within our model, we show that two mechanisms emerge from the layered structure that ensure increased alternation rate in response to increased stimulus drive. First, deep layers act to inhibit the upper layers, thereby reducing the attractor depth and increasing the alternation rate. Second, recurrent connections between superficial and granular layers implement an input suppression mechanism which again reduces the attractor depth of the winnerless competition. These findings suggest the functional significance of the layered cortical architecture as they showcase perceptual implications of neuroanatomical properties such as interlaminar connectivity and layer-specific activation.

Introduction

In bistable perception, the subjective experience of an observer spontaneously alternates between two mutually exclusive interpretations of the same physical stimulus^1,2. This phenomenon provides a unique window into the neural processes that underlie conscious perception, as it allows us to study how the brain constructs subjective experiences from ambiguous sensory input^3–6. It additionally offers insights into the dynamics of decision-making processes in the brain, as perceptual switches can be viewed as decisions between competing interpretations^2,6. Bistable perception illuminates the interplay between bottom-up sensory processing and top-down cognitive influences, which is a fundamental aspect of brain function^7–10. Lastly, studying bistable perception can shed light on how the brain maintains perceptual stability while also remaining flexible to new interpretations, a balance that is critical for adaptive behavior in complex environments^11–13. Behaviourally, bistable perception is typically characterized in terms of dominance duration and alternation rate. Dominance duration is the duration for which one interpretation is maintained whereas alternation rate is the number of perceptual alternations within a predefined time interval.

Statistical generalities of these behavioral measures of bistable perception have been consolidated as Levelt’s four propositions^14,15. The first two propositions pertain to dominance duration statistics and state that 1) the interpretation receiving higher stimulus drive (stronger evidence) exhibits longer dominance durations and that 2) dominance duration increases monotonically with stimulus drive (Fig. 1A). The third and fourth proposition pertain to alternation rate. Specifically, the third proposition states that alternation rate is maximal when both interpretations receive equal stimulus drive and reduces as stimulus drive diverges between interpretations¹⁶ (Fig. 1B). The fourth proposition states that when the total stimulus drive is increased but equal for both interpretations, the alternation rate increases (Fig. 1B). These rules are instrumental for validating models concerning neural mechanisms underlying bistable visual perception^15,17,18.

Fig. 1.

Conceptual illustration of Levelt’s propositions for behavioral statistics of bistable perception. (A): Dominance duration is longer for the interpretation receiving highest stimulus drive (rule 1). Dominance duration of stronger stimulus mainly increases (rule 2). (B): Alternation rate is highest when stimulus drive to both interpretations is equal (rule 3) and increases when the total drive increases (rule 4). (C): double-well diagram for a bistable attractor system; The system can occupy one of two attractor states at a time (D1 or D2). Switches between states occur through noisy jumps. Depth of the attractor determines the probability of transitions; Several mechanisms can be used to maintain shallow attractors: (D): Neural adaptation in populations inhibits its own activation; (E): A gain control mechanism suppresses neural activity when total stimulation is increased through a shared neural component; (F): Input suppression through direct suppression of the selective input.

Previous research has suggested that bistable perception results from a form of mutual inhibition between two neuronal populations reflecting the two interpretations^19–21. Strong competition between these populations will generate winner-take-all dynamics with two attractor states corresponding to the two interpretations of the stimulus. By introducing mechanisms such as neural adaptation it is possible to achieve winnerless competition dynamics where the model switches between attractor states (Fig. 1D). Dynamics of such attractor systems are commonly conceptualized using double-well energy landscapes, where the depth of a well determines the probability of transitions from one attractor state to another²² (Fig. 1C). Winner-take-all dynamics is characterized by deep wells that render transitions highly improbable. In winnerless competition, on the other hand, attractor wells are sufficiently shallow for transitions to occur regularly, albeit stochastically. Indeed, the depth of attractor states directly determines dominance duration and alternation rate²².

While models implementing winnerless competition have successfully replicated most of the key behavioral characteristics of bistable perception^15,18,20, they have faced challenges in replicating the increase in alternation rate with increased stimulus drive as posited by Levelt’s fourth proposition. A fundamental property of these models is that increasing total stimulus drive deepens attractor wells and hence reduces alternation rate^19,20. In order to address this limitation, some models introduce additional mechanisms such as global gain control, input suppression, or a release mechanism. A global gain control mechanism suppresses the total neural activity when stimulation is increased by inhibiting all neuronal populations equally²⁰ (Fig. 1E). An input suppression mechanism ensures that the currently dominant state inhibits its own input, thereby promoting transitions away from that state^17,18,23 (Fig. 1F). A release mechanism may be utilized by the suppressed population to overcome the dominant population²¹. These mechanisms serve to maintain shallow attractors when the total input received by both populations is increased and offer explanations for Levelt’s fourth proposition at an algorithmic level²⁴. However, at present it is not clear which, if any, of these mechanisms are implemented in the cortex and what might be their biological substrates.

We suggest that the answers to these questions lie within the principal architecture of the cortical microcircuit. The cortex is characterized by a multi-layered structure with complex interlaminar connectivity^25–27. The horizontal organization of the cortex into columns is characterized by responses to specific sensory features²⁸ while the vertical organization into layers is marked by a canonical connectivity pattern that is consistent across the cortex^29–31. As such, mutually exclusive interpretations of the same physical stimulus are represented in distinct cortical columns (c.f.³²) that compete via layer-specific horizontal connections located primarily in superficial layers 2 and 3 (L23;^26,33–35).

Like several previous studies (e.g.,^18,20,36), we hypothesize that bistable perception is a form of winnerless dynamics, where an adaptation mechanism ensures shallow attractors and random noise causes transitions between attractor states. However, in classical winnerless competition models, the stimulus input directly drives the populations engaged in mutual inhibition. In contrast, the layered cortical circuitry in our model separates the input from the mutual inhibition mechanism. More specifically, feedforward input primarily arrives in layer 4 (L4;^27,37–40). In contrast to L23, L4 selectively targets intra-columnar populations with similar preferred features, thus lacking lateral connectivity to surrounding cortical columns^37,41,42. Nevertheless, L4 projects to L23^40,43 and hence provides input to winnerless dynamics between cortical columns. Finally, L23 excitatory neurons also project to L4 inhibitory neurons^44,45. Through these projections L23 effectively inhibits its own input. We therefore hypothesize that an input suppression mechanism is inherent in the recurrent connections between L4 and L23.

We hypothesize that the implementation of shallow attractors is further supported by a gain control mechanism implemented by the deep layers of the cortex. Activation of layer 6 (L6) in mouse cortex has been shown to strongly suppress neural activation of the upper layers^46–48. Similarly, deep layer 5 (L5) suppresses activity in superficial and granular layers L23 and L4, respectively⁴⁹. We suggest that L4 activates L23, next L23 activates deep layer L5, and finally deep layers L5 and L6 inhibit superficial and granular layers L23 and L4 (c.f.⁴⁰) to adjust their sensitivity to input. Given that both L5 and L6 also receive feedforward thalamic input^{27,43,50–53}, this gain control mechanism is also responsive to stimulus drive.

We thus propose three key hypotheses: (1) bistable perception is a form of winnerless dynamics that arise from mutual inhibition between columns in superficial layers, (2) input suppression is implemented through recurrent connections between superficial and granular layers, and (3) gain control is mediated by deep layers modulating activity in upper layers. We test these hypotheses in silico using a biologically-derived layered columnar model (Laminar Column Model). The model comprises two columns of four layers (L23, L4, L5, L6), representing the two competing interpretations of a bistable stimulus (e.g., horizontal and vertical motion in an ambiguous motion paradigm). Each layer consists of one excitatory and one inhibitory population. Estimations of layer specific sizes of neuron populations are taken from a macaque brain atlas⁵⁴. Moreover, we used empirically derived interlaminar connectivity^40,43,55. Inspired by a recent study demonstrating that two mutually exclusive interpretations of an ambiguous motion stimulus, horizontal- and vertical motion, were reflected by distinct cortical columns in (human) MT³², we report results for interlaminar connectivity specifically of (macaque) MT. However, our results generalize to other cortical areas as well (See Appendix D). Dynamics of each population are described by a set of dynamic mean-field equations⁵⁶. Mutual inhibition between columns is implemented within L23 to promote competition. Noise and adaptation are included to promote state reversals between attractors (see Laminar Column Model diagram in Fig. 2).

Fig. 2.

Laminar Column Model diagram. (A): Two layered columns mutually inhibit each other through lateral connections in L23, from excitatory (blue triangles) to inhibitory (red circles) populations. and scale the lateral inhibition and the local self-excitation weights, respectively (arrows: excitatory connections; black circles: inhibitory connections). L23 populations are recurrently connected to deeper layers according to the empirically derived interlaminar circuit connectivity from⁴⁰. Each column consists of four layers (L23, L4, L5, L6). The two columns receive selective input in layer L4 reflecting the strength of the stimulus for the two interpretations (D1 & D2; e.g. horizontal or vertical apparent motion). (B): The local dynamic mean field model. Each population in the network is simulated using a set of non-linear differential equations to obtain the synaptic input, the membrane potential and eventually the firing rate.

We show that the layered architecture allows for replication of all four of Levelt’s propositions. Specifically, we show that the recurrent interlaminar connectivity between superficial layer L23 and granular layer L4 implement an input suppression mechanism. This results in a suppression of L4 by L23 for strong feedforward activation of L4 and hence maintains shallow attractors. Furthermore, we show that deep layers L5 and L6 indeed implement a gain control mechanism on the upper layers. This additionally contributes to maintaining shallow attractors. Both input suppression and gain control mechanisms in the empirically derived columnar model ensure full replication of Levelt’s propositions.

These findings provide evidence for the functional significance of the layered cortical architecture. We show that lateral connectivity between columns enables winnerless competition and that the laminar structure of cortex provides two additional mechanisms to ensure shallow attractors in spite of strong stimulus drive. This model sets the stage for future research endeavors that aim to elucidate the functional role of laminar cortical circuits for perception²⁷.

Results

The Laminar Column Model reflects empirically observed Bistable Perception Dynamics

It has previously been shown that self-excitation of L23 excitatory neurons controls the dynamical stability of the columnar model⁵⁷. We extend these findings and show that self-excitation in L23 is also important for the competitive dynamics of the column. Specifically, the dynamic range of the model is primarily determined by the strength of self-excitation within L23 of one column and the strength of lateral inhibition between L23 across columns Feedforward stimulation of L4 enables competition between columns (Fig. 3A). Higher values of both self-excitation and lateral-inhibition promote competition between the columns (Fig. 3A). To simulate winnerless competition dynamics, in the following we take parameter values within the winnerless regime that are biologically realistic (see Methods for details).

Fig. 3.

Exploring winnerless competition dynamics. (A): Feedforward stimulation is applied to granular layer L4. (B): Variance of L23E firing rate within trials for different combinations of local self-excitation () and lateral-inhibition strengths () without (top) and with (bottom) stimulus drive in L4. Variance of the firing rate reveals the winnerless competition regime (WL) because firing rates in the non-competing (NC) and winner-take-all (WTA) regimes do not change over time while firing rates in the WL regime alternate between high and low rates. Local self-excitation and lateral-inhibition in L23 both facilitate competition. The model can occupy 3 states: non-competing (NC), winnerless dynamics (WL) and winner-take-all (WTA). Without feedforward stimulation in L4 the model does not compete (NC) (top). Applying an input of 20 Hz reveals a bistable regime where the variance increases (WL; bottom). The red dot indicates the parameter settings used in further simulations. (C): Dominance duration for different combinations of feedforward input in L4 to the two columns. right: Dominance duration per column when changing input to one column while keeping input to the other column constant. (D): Alternation rate for different combinations of feedforward input in L4 to the two columns. right: Increasing total input decreases alternation rate. Alternation is highest when columns are equally stimulated.

We expect the model to align well with all four of Levelt’s propositions. We first test whether the first three propositions are reproduced by the winnerless competition resulting from applying stimulation to L4 of both columns. Specifically, we expect the dominance duration to primarily increase for the column receiving stronger stimulation. Furthermore, we expect the alternation rate to be maximal when both columns are equally stimulated. Each column receives an external input applied through 300 and 188 synapses to the excitatory and inhibitory populations of L4, respectively (ratio derived from⁴⁰), resulting in a net excitatory stimulation. We simulate 10 trials for each condition with 100 seconds per simulation. From each simulation we extract the dominance duration per column and the alternation rate. The winner is the column whose excitatory L23 population exhibits the highest firing rate. We define a dominance duration interval as the time between two successive switches of dominance. Increasing the stimulus drive to one column mainly increases the dominance duration of that column (Fig. 3B). In line with our hypotheses, the alternation rate is maximal when stimulation of the columns is equal and decreases when the difference in stimulation is increased (Fig. 3C). The alternation rate is decreased with stronger total stimulus drive, compared to the behaviorally observed increase. The alignment of the model with the first three propositions shows that feedforward stimulation of L4 affects the mutual-inhibition mechanism in L23 by increasing the depth of the attractor receiving the highest stimulation. Without input to deep layers, the model does not account for the fourth proposition. Indeed, as was found for other winnerless competition models, the alternation rate is not enhanced with higher stimulus drive because it increases competition between L23 populations and deepens the attractors, lowering the probability of transitions (Fig. 3D). Up to now we only applied feedforward stimulation to L4. However, applying no stimulation to deep layers is not biologically realistic^{27,43,50–53}. Therefore, in the next section we discuss the influence of deep layers on winnerless competition dynamics.

External input to deep layers explains Levelt’s fourth proposition

We expect that deep layers 5 and 6 implement a gain control mechanism on the upper layers^46–49. Such a gain control mechanism would promote shallow attractors and enhance the alternation rate with increased stimulus drive. We apply external input to L5 and L6 through all external synapses (see Table 1) to excitatory and inhibitory populations, (Fig. 4A), resulting in a net excitatory input. We systematically vary the stimulus drive to deep layers L5 and L6 and obtain the alternation rate and dominance duration are for each combination. Externally stimulating L5 or L6 both increases the alternation rate (Fig. 4B) and decreases the dominance duration (Fig. 4C) of the winnerless column model. Externally stimulating L5 and L6 simultaneously further enhances this effect. These results indicate that layer-specific stimulation of deep layers during bistable perception result in output matching Levelt’s fourth proposition: increased alternation rate in response to increased stimulation. Effects are generally larger for stimulation of L5, but robust for stimulation of L6 as well. External input can target either or both excitatory and inhibitory populations within a layer. To show how the excitation-inhibition balance of the layer-specific input affects the alternation rate we systematically apply different levels of input to the excitatory and inhibitory populations of the layers in question, L5 (Fig. 4D) and L6 (Fig. 4E). For both layers we find that more excitation increases higher alternation rate. More inhibitory input would not affect the alternation rate significantly. Interestingly, for L6 there is a slight decrease before the alternation rate starts increasing when the layer is excited more. Together these results suggest that deep layers modulate the winnerless dynamics. Stimulation of excitatory populations in these layers causes an increase in alternation rate which aligns the winnerless dynamics of the model with all of Levelt’s propositions for bistable perception, including the fourth.

Table 1.

Model structure.

Populations	16 populations; 2 columns, 8 per columns
Num. Synapses	K, within, between columns, stimulus drive
Weights	J, within and between columns
Population size	N, area and population specific
	L23E	L23I	L4E	L4I	L5E	L5I	L6E	L6I
Population sizes
	20683	5834	21915	5479	4850	1065	14395	2948
	30303	8547	14101	3525	7088	1556	7918	1621
Number of external synapses
	1600	1500	2100	1900	2000	1900	2900	2100
	0	0	295	186	0	0	0	0
	300	255	300	255	300	255	300	255
	1.5	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Columnar connectivity
	source:
target:	L23E	L23I	L4E	L4I	L5E	L5I	L6E	L6I
L23E	0.1009	0.1689	0.0880	0.0818	0.0323	0.0000	0.0076	0.0000
L23I	0.1346	0.1371	0.0316	0.0515	0.0755	0.0000	0.0042	0.0000
L4E	0.0077	0.0059	0.0497	0.1350	0.0067	0.0003	0.0453	0.0000
L4I	0.0691	0.0029	0.0794	0.1597	0.0033	0.0000	0.1057	0.0000
L5E	0.1004	0.0622	0.0505	0.0057	0.0831	0.3726	0.0204	0.0000
L5I	0.0548	0.0269	0.0257	0.0022	0.0600	0.3158	0.0086	0.0000
L6E	0.0156	0.0066	0.0211	0.0166	0.0572	0.0197	0.0396	0.2252
L6I	0.0364	0.0010	0.0034	0.0005	0.0277	0.0080	0.0658	0.1443
	0.0878	-.3113	0.0878	-.3512	0.0878	-.3998	0.0878	-.4287
Lateral inhibition parameters
	0.1
	0.172
	0.13
P: connection probabilities; J: synaptic strength (mV); : adaptation strength

Fig. 4.

External input to deep layers. (A): A net-excitatory external input is applied to deep layers L5 and L6. Combinations of input to L5 and L6 increase alternation rate, (B) and reduce dominance duration, (C) y-axes and x-axes indicate the amplitude of the external input to L5 and L6, respectively. Alternation rate increases for higher input to both L5 and L6, or separately. External input to excitatory and inhibitory populations in L5 (D) and L6 (E), separately. y-axes and x-axes indicate input to excitatory and inhibitory populations, respectively. More excitatory input mainly increases the alternation rate in both layers. F: A slice from (D) highlighting a realistic range of alternation rates, dominance times, and external stimulation using only excitatory stimulation to L5. G: Same for L6 taking a slice from (E).

External input to granular layer explains Levelt’s fourth proposition

Several models of bistable perception suggest a form of input suppression to account for Levelt’s fourth proposition^17,18,23. Such architectures generally consider a two-level hierarchy where the input components are isolated from the decision making components. The decision making components then inhibit the input components and thereby sustain shallow attractors. The laminar structure of our model naturally provides such a split structure. Granular layer L4 generally receives stimulus input while L23 implements a decision making mechanism through the lateral mutual-inhibition mechanism between two columns. To test whether the interlaminar connectivity between L4 and L23 implements an input suppression mechanism we examine various combinations of external stimulation of L23 and L4 and their effect on the alternation rate and dominance duration. We apply external input to L23 and L4 through all external synapses (see Table 1) targeting excitatory and inhibitory populations (Fig. 5A), resulting in a net excitatory input. We systematically vary the external input to superficial L23 and granular L4 used in simulations and record the corresponding alternation rates and dominance durations. Injecting external input to the decision layer L23 generally decreases the alternation rate (Fig. 5B) and increases the dominance duration (Fig. 5C). This reflects a deepening of the attractors, which is common in simple mutual-inhibition network models of bistable perception which consists of only a decision layer²². For external input to the granular layer L4 the results are less straightforward. For weak inputs to L4 the alternation rate decreases (Fig. 5B) and dominance duration increases (Fig. 5C), just as it does for inputs to L23. Interestingly, increasing external input to L4 further reverses the effect and causes the alternation rate to increase again. This non-linear relation between the external input and the alternation rate reflects first a deepening and than a diminishing of the attractor for increasing stimulus drive. This suggests a suppression of L4 activity when external input to L4 is strong. To explore how the excitation-inhibition ratio of the layer-specific input affects the alternation rate we perform a grid search applying different levels of input to the excitatory and inhibitory populations of the layers in question, L23 (Fig. 5D) and L4 (Fig. 5E). We find that more inhibitory input to superficial layer L23 increases the alternation rate, which is expected as inhibitory input would diminish the competition between columns by reducing the attractor depth. For granular layer L4 we find that it is particularly unbalanced input (i.e., more excitatory or more inhibitory) which increases the alternation rate while for balanced input (i.e., similar excitatory as inhibitory input) the alternation rate is at its lowest point. This confirms again that more excitatory input diminishes the depth of the attractors, but in addition shows that predominantly inhibitory input to L4 has a similar effect. Feedforward stimulation between areas is generally of excitatory nature and generally targets L4. Our results suggest that such unbalanced excitatory input could very well cause an increase in the alternation rate.

Fig. 5.

External input to superficial and granular layers. (A): A net-excitatory input is applied to layers L23 and L4. (B): Alternation rate decreases with increasing excitatory input to L23. For relatively strong L23 input, alternation rate is decreased for weak input to L4 as well. (C): Dominance duration increases with increased excitatory L23 input. Dominance duration increases for weak input to L4 but decreased for strong stimulation of L4. B, C y-axes and x-axes indicate the amplitude of the external input to L23 and L4, respectively. (D): External input to excitatory or inhibitory populations in L23. y-axes and x-axes indicate input to excitatory and inhibitory populations, respectively. More inhibitory input mainly increases the alternation rate. (E) External input to excitatory or inhibitory populations in L4. More unbalanced input increases the alternation rate. The effect is more pronounced for strong excitatory input. (F): A slice from (D) highlighting a realistic range of alternation rates, dominance times, and external stimulation using only excitatory stimulation to L23, (G): Same for L4 taking a slice from (E).

Additional simulations with a single layer circuit of superficial L23 populations show that without inter-laminar mechanisms the alternation rate only decreases upon increasing stimulation strength (Appendix C). Furthermore, the contributions of the layer specific input to the reversal dynamics is robust against changes adaptation strength, noise and self-excitation (Appendix B).

Interlaminar mechanisms underlying Levelt’s Fourth proposition

Our results from simulations wherein we apply varying amounts of external input to different layers support the hypotheses that deep layers implement gain control while superficial and granular layers conjointly implement an input suppression mechanism. We argue that these mechanisms critically depends on the interlaminar connectivity profile we derived from biological datasets. Here, we explore this further and elucidate the specific interlaminar circuits of the columnar model that contribute to gain control and input suppression.

Gain control by deep layers

Potjans & Diesmann⁴⁰ identified a feedforward flow of activity resulting from the interlaminar connectivity of the circuit: L4 excites L23, which in turn excites L5. Layer 5 then excites L6. Finally, L5 and L6 inhibit L23 and L4, respectively. Deep layers balance the circuit by directly targeting the superficial and granular layers with interlaminar connections. We explore whether these connections are also directly responsible for modulations in alternation rate and dominance duration by manipulating their strength. We control the connection strength of all connections from deep layer populations L5 and L6 onto superficial and granular layers, L23 and L4 respectively (Fig. 6A). Completely uncoupling the deep layers from the upper layers decreases the alternation rate (Fig. 6A). That is, without the inhibiting effects of the deep layers, the dominant attractor state becomes deeper, resulting in increased dominance duration and less alternations between states (Fig. 6A, B). Increasing the connection strength from deep layers to upper layers increases the alternation rate and suppresses the dominance duration in a linear fashion. Together, these results show that it is the direct interlaminar connections of deep layers onto upper layers L23 and L4 which affect the winnerless dynamics and give rise to statistical regularities summarized in Levelt’s Fourth proposition. Consistent with empirical findings^46–49, the deep layers within this columnar model exhibit an inhibitory effect on the upper layers. We establish a direct connection between these biological findings and behavioral observations of statistics related to bistable perception.

Fig. 6.

Exploring interlaminar mechanisms. (A): Alternation rate is increased by increasing connection strength of deep layers to upper layers. (B): Dominance duration is decreased by increasing connection strength of deep to upper layers. (C): Population specific latency relative to switching attractor states in L23E. Lower latency indicates an early detection of switching states compared to population L23E. Latency measured for all decision reversals for 100s simulations for 10 trials. Black horizontal bars indicate standard deviation. (D): Effect of L23 to L4 connections on the alternation rate in a superficial-granular sub-circuit. Increasing weak feedforward connectivity (L4E to L23E, ) decreases the alternation rate in both the circuit with L23 to L4 connections (dashed) and the circuit without these connections (solid). Increasing stronger feedforward connectivity () leads to an increase in the alternation rate of the circuit with L23 to L4 connectivity while the alternation rate of the other circuit does not. (E): Effects of L23 to L4 connections on the mean rate of L23E (red) and L4E (black) populations. Rates are normalized per population.

To further investigate the causal role of deep layers in decision reversals we compare the timing of state switching in the deep and superficial layers. Specifically, for each decision reversal from one attractor state to the other we take a 400ms interval around the time-point where the reversal took place in L23E (i.e., when the rate of L23E in the dominant column first dropped below the rate of L23E in the other column). The population rates in this interval are then used to obtain the population specific reversal point (i.e., when the rate of a particular population in the dominant column first dropped below the rate of the same population in the other column). Interestingly, L5 populations show a particularly early onset of switching decision compared to L23 (Fig. 6C). This suggests a causal influence of L5, and in particular the inhibitory population, in bringing about decision reversals. An early review on the laminar and lateral structure of cortical circuits assigns a central role to L5 in decision making²⁵. According to the authors, L5 would confirm the decision after it was made by superficial layers and prepare the cortical output. However, our results suggests that L5 might causally affect the decision process in the superficial layers and play an important role in reversing rather than confirming a decision. We suggest that L5 ensures that attractor states remain shallow, thereby promoting exploration of the attractor landscape. The switches in L6 excitatory population are relatively late compared to decision layer L23. L6 inhibitory neurons switch at similar times as L23. We suggest these results on the population-specific latency of switches only provide information on whether a population is involved in causing particular jumps across the attractor separatrix and are independent from the effects of constant input, as this mainly affects the attractor depth during the simulation.

Input suppression in superficial-granular circuits

We find that weak input to granular layer L4 deepens the attractors while strong input renders them more shallow, promoting reversals between states. We hypothesize that L23 and L4 implement an input suppression mechanism where L23 suppresses L4 ⁴⁵. To inspect whether interlaminar connections from L23 onto L4 are indeed capable of causing the observed increase in alternation rate for strong input to L4, we first uncouple the deep layers (L5 and L6) from the superficial and granular layers. Next, we compare two implementations of this superficial-granular sub-circuit: One with and without L23 connections targeting L4. We then systematically manipulate the feedforward connection from L4E to L23E which controls the feedforward input to the decision layer L23. We keep the external input fixed. For weak feedforward connectivity () the alternation rate strongly decreases for both versions of the circuit, indicating a deepening of the attractors (Fig. 6D). However, for strong feedforward connections () the circuit implementing direct feedback connections from L23 onto L4, the alternation increases. This suggest connections from L23 onto L4 ensure shallow attractors and promote reversals. To show that L23 is suppressing its own input, we investigated the effect that the feedback connections from L23 to L4 have on the mean firing rate of these populations. Specifically, we implement two versions of a full column model. One with and one without connections from L23 to L4. As before, we manipulate the feedforward connection strength, L4E to L23E, while keeping the external input fixed. We compare the normalized rates of L23E and L4E in both versions of the column. Without connections from L23 to L4 it is mainly the rate of L23E which is increased while the rate L4E is not much affected (Fig. 6E). With L23 to L4 connections the increase in rate of L23E is much weaker. Interestingly, the rate of L4E is now strongly affected by an increase in feedforward connectivity. The L23 to L4 connections cause a strong decrease in L4E rate. These results show that L23 and L4 in the cortical column model implement an input suppression mechanism through direct feedback connections from L23 to L4 within the same column.

Discussion

We test the significance of the layered structure of the cortex for bistable perception. Using a dynamic mean field model of two cortical columns with empirically derived interlaminar circuit connectivity of macaque area MT, we find that the architecture of the cortical microcircuit provides the neurobiological substrate required for winnerless competition dynamics supplemented with gain control and input suppression mechanisms. We show that these mechanisms are robust to parameter changes (Appendix B) and are absent in a single layer implementation of the dynamic mean field model (Appendix C). Two columns in our model compete for dominance through mutual-inhibition in superficial layers L23. We find that the first three of Levelt’s propositions are directly accounted for by the model through systematically applying feedforward stimulation to the main input layer L4 of both columns (Fig. 3 and Appendix A). Furthermore, we establish that concomitant input to deep layers increases the alternation rate as a function of stimulus drive. This shows that feedforward input to deep layers accounts for Levelt’s fourth proposition using a mechanism grounded in biology. In line with theoretical work on bistable perception²⁰, we suggest that deep layers implement a gain modulation mechanism on the upper layers through interlaminar inhibition. This requires that deep layers receive stimulus-related feedforward input, which is supported by several studies that have shown that deep layers are important targets for thalamic axons (both matrix and core thalamic nuclei) in many brain areas^43,50–53. Our model further shows that relatively weak inhibition of the upper layers is already sufficient to increase the alternation rate, however several studies have highlighted that inhibitory effects of layer 6 on the upper layers are rather strong^46–49. These studies are based on mouse cortex while our model implements connectivity derived mainly from cat. Furthermore,^47,48 have shown that the mechanism responsible for such gain modulation involves a more complex inhibitory circuit than currently implemented in our Laminar Column Model. The wide variety of cell types and projections suggest a variety of layer 6 dependent circuits with different roles. Further research is needed to delineate how layer 6 is involved in the implementation of gain control ⁴⁶. We suggest that extending our model to include a more sophisticated inhibitory circuit in layer 6 would amplify the importance of this layer in modulating the winnerless competition dynamics and in maintaining shallow attractors. Nevertheless, our model is capable of implementing gain control due to weak inhibitory connections from deep layers to superficial and granular layers. Because empirical and modelling work suggests that deep layers inhibit upper layers we hypothesize that projections from deep to upper layers are responsible for maintaining shallow attractors required for high alternation rates. By systematically modulating the connectivity from deep to upper layers we show that it is indeed these connections that are responsible for increasing the alternation rate.

Theories of bistable perception have postulated forms of input suppression to explain Levelt’s fourth proposition^17,18,23,58. We hypothesize that local recurrent feedback from L23 to L4 implements such a mechanism. We find that applying weak input to L4 ( to L4 and no input to L23) reduces the alternation rate, but when stronger input is applied () the alternation rate starts to increase again. By systematically modulating the recurrent feedforward and feedback connections between L23 and L4 we show that it is indeed the feedback from L23 onto L4 which causes this increase in alternation rate during strong stimulation of L4. With this we show that the columnar circuit implements a form of input suppression that can account for the increase in alternation rate when the stimulation is strong. Interestingly, one study has shown a potential deviation from Levelt’s fourth proposition as formulated in¹⁵. By alternating the contrast and motion strength separately in a random dot motion experiment⁵⁹, these authors found a decrease of alternation rate for weak motion strength (but not for weak contrast levels) and an increase in alternation rate for strong motion. Importantly, unlike previous models, our model accounts for this deviation from Levelt’s fourth proposition at weak stimulus drives. We show that weak feedforward stimulation to L4 reduces the alternation rate and strong stimulation increases the alternation rate matching the experimental observation in⁵⁹.

Our findings have implications for a systems-level perspective on bistable perception as well. The layer-specificity of the gain control and input suppression mechanisms in conjunction with characteristic laminar patterns of feedforward, lateral and feedback projections in the cortex, allows us to draw inferences and make predictions on how cross-regional interactions affect bistable perception. For example, top-down feedback selectively targets deep layers during viewing of ambiguous figures⁶⁰. Furthermore, activity in frontal areas is associated with higher alternation rates⁶¹. Together with insights gleaned from our model, these observations support the hypothesis that increased top-down feedback from higher cortical areas targeting deep layers in visual cortex serves to inhibit the upper layers in order to maintain shallow attractors and increase the alternation rate. Through such a mechanism the frontal areas, known to be important for executive control and voluntary action^62,63, may actively induce switches. When more anatomical data on feedforward and feedback connectivity between MT and frontal areas becomes available these can be incorporated in the model to test this hypothesis. Moreover, many theoretical studies highlight the importance of top-down and bottom-up interactions for bistable perception without specifying the neural substrate that would implement these mechanisms^17,18,23,58. The model by¹⁸ takes perceptual inference as a starting point and incorporates an input-suppression mechanism in an hierarchical two-level model, suggesting that suppression of evidence from a decision-level to an evidence-level is central to predictive theories of brain function. We show that the empirical interlaminar circuit implements mechanisms which explain all of Levelt’s propositions and thus provides a possible neural substrate for bistable perception locally within a brain region. We predict that input-suppression from L23 to L4 might be a form of suppression of evidence, similar to the predictions made by^17,18 but interpreted within a local circuit instead of between different brain areas. How much local and inter-area mechanisms each contribute to bistable perception and coordinate perceptual inference remains an open question, but our work highlights the importance of the local inter-laminar circuitry. Further extensions of our model to encompass additional brain regions are warranted to gain a more comprehensive understanding of the interplay between local and inter-area inhibitory effects and how these align with theories of perceptual inference. Specifically, it would be interesting to explore the dynamics and hierarchical nature of a multi-area model including lower sensory areas such as V1 and V2, and higher-areas such as LIP using the available neuroanatomical data^64,65. This would materialize the predictions about the origins of feedback and feedforward input to the decision making circuit, and allow testing theories of perceptual inference.

Our model has been constructed based on empirical data of cortical circuitry^40,43,54,55 and we have not explicitly fit to the behavioral statistics of bistable perception experiments reversal dynamics, except for the mean dominance duration to be similar to the durations found by³². This means that the input dependent reversal dynamics we observe are an emergent property of the connectivity. We show the robustness of the input suppression and gain control mechanisms to a range of parameters B. Furthermore, we also confirm the presence of these mechanisms using cell counts and connectivity adapted to different visual areas (Appendix D⁵⁴). This speaks to the transferability of the model to different stimuli⁶⁶. While this is a strength of the model, a limitation is that we do not have a quantitative fit to empirical data from behavioral experiments. Animal data on bistable or ambiguous perception is limited because of the challenges that come with capturing the perceptual reversals. We suggest that a next step in validation of the model could be to obtain behavioral data from humans and animals perceiving the ambiguous motion quartet from³² and fit model parameters to the observed reversal statistics.

Future work on layer specific responses and connectivity during bistable vision could help to further constrain our model. For example, the advent of ultra-high field fMRI allows us to investigate neural correlates of human cognition at columnar and laminar resolution^67,68. Using this technique in combination with behavioral measures we can test whether deep layer activity and alternation rate correlate across individuals and trials in area MT⁶⁹. Furthermore, laminar multi-unit arrays can be used to record layer-specific activity in animal models with high spatial and temporal resolution^70,71. This technique can be used to investigate the layer-specific population activity changes around the perceptual reversal. In particular, our model predicts changes in activity in the deep layers preceding the reversal in superficial layers L23 and a suppression of L4 activation upon following increased L23 activation. A future experiment could test this prediction using a similar bistable motion stimulus and monkeys trained on reporting perceptual reversals⁷². Laminar probes could be used to investigate the laminar specificity of activity and latency with respect to measured and reported reversals. Direct testing of the presence of a gain control and input suppression mechanism affecting the reversal dynamics requires simultaneous layer-specific stimulation⁴⁶, mapping of synaptic activity⁷³, and reporting on perceptual reversals using in vivo multi-photon imaging ⁵¹. The model predicts that in such an experiment stimulation of deep layers L5 and L6 would suppress activity in L23⁴⁶ and simultaneously increase the alternation rate. Optogenetic techniques allow layer-specific manipulation of neural activity^34,74,75, which can be used to probe the correlation between alternation rate and deep layer activation by directly controlling the activation level of these layers. For example, by activating layer 6 we would expect the gain-control mechanism to suppress superficial layers⁴⁶, and in turn increase the alternation rate. Ideally, one would lesion specific inter-laminar synaptic pathways to test these predictions but such technology is not yet available⁵¹.

In our model we chose the mean firing rate in L23 to represent the decision variable^20,76. Interestingly, recent findings suggest correlations between population activity, or mean firing rate, and decision variables in perception^71,77–80. Specifically,⁷¹ found laminar differences in decision related activity in pre-motor cortex. Using laminar probes it would be interesting to explore the significance of the laminar specificity of population activity in sensory areas under perceptual ambiguity. We expect laminar differences in population activity and reversals timings with respect to a decision variable.

There are several notable open questions regarding mechanisms of bistable perception we will discuss shortly. First, we currently include a slow adaptation variable in our model, which is a common mechanism in winnerless dynamics models to promote bistability^20,81. Interestingly, ^81,82 note a perceptual stabilization under intermittent presentation of the stimulus. We do not explicitly take these experiments into account but would like to explore the dynamics of the model under such conditions in future studies. In particular, as discussed above, a multi-area implementation of the model could explore the relative contributions of local adaptation and inter-areal interactions on the stabilization of the percept. This would be of interest, because both local adaptation^20,81 and multi-stage integration^18,58 have been proposed as candidate mechanisms to stabilize percepts. Second, our stimulus is represented by a simple input variable, similar to other models ^18,20. While there is evidence supporting a similar mechanism underlying different bistable perception phenomena⁶⁶, the spatial and temporal structure of visual stimuli is well known to affect the bistable dynamics^83,84. Finally, we do not model excitatory-excitatory lateral connections between different columns. Empirical evidence suggests a patchy organization of feature-tuned horizontal connections in area MT^64,85,86. In particular, neurons in L23 target patches with similar tuning for motion direction. Recently, it has been shown that such long-range feature-selective horizontal connections selectively increase activity and perceptual sensitivity in area MT⁸⁷. Modeling work has shown that clustered excito-excitatory connections drive slow dynamics and introduce multi-stability^88,89. Exploring how inter-laminar and lateral connectivity patterns affect each other and the reversal dynamics can be an interesting extension to the model. Receptive fields in MT cover a large part of the visual field⁹⁰, therefore it is likely that many similarly tuned columns receive similar input. We hypothesize that through lateral connectivity the different patches coordinate their reversals as observed in³². Non-specific feedback to MT might also play a role in coordinating the synchronized reversals. It would be interesting to explore how a model with more information rich visual stimuli and lateral connectivity would behave. Areas like MT or V1 could be modeled as a as set of columns which have spatial- and tuning-dependent horizontal- ^18,91 and inter-areal⁹² connectivity.

In conclusion, previous work has provided important insights how bistable perception may possibly be implemented algorithmically^{17,18,20,23,58}. Our work advances beyond this in several key ways. First, we incorporate a biologically realistic layered cortical architecture, allowing us to investigate how specific laminar circuits contribute to bistable perception. Second, our model integrates both gain control and input suppression mechanisms within a single framework, providing a way to study how both mechanisms affect the winnerless dynamics. Third, we demonstrate how these mechanisms emerge naturally from the cortical microcircuit, rather than being imposed as designer choices. Our work thus provides a step towards an understanding which and how these algorithms are implemented by the neurobiological hardware of the cortex^24,93. Lastly, our model makes specific, testable predictions about the role of different cortical layers in perceptual switching, opening new avenues for empirical research.

Methods

Dynamic mean field

We use a dynamic mean field (DMF) implementation which simulates neural populations of the cortical column. A single column consists of 8 populations divided across 4 layers: L23, L4, L5 and L6 (Table 1). Each layer contains an excitatory and an inhibitory population. The intra- and interlaminar connectivity is derived from⁴⁰ which base their connectivity scheme on empirical research reviewed in^43,55. We adjust the population sizes to fit with area MT of macaque using estimated population sizes computed by⁵⁴. The empirical nature of our model necessitates that we implement a column of a specific cortical region. We chose MT because a recent study showed that two mutually exclusive interpretations of an ambiguous motion stimulus were reflected by distinct cortical columns in (human) MT. However, the mechanism we identify generalize to other cortical regions (see Appendix D for layer specific input using connectivity of other visual system areas). We implement two columns, each representing an axis-of motion column in MT, one for each direction of motion (horizontal (H) or vertical (V)). The firing rate dynamics of each population are modelled using a set of differential equations. Each population has five state variables: the synaptic current, the membrane potential, noise, an adaptation variable and the firing rate. The change in current to each population in the DMF model is given by the stochastic differential equation:

1

Where is the synaptic time constant, W and the recurrent connectivity strength and the recurrent input from other populations, respectively. and are the external weight and input to population i. Finally, the noise n(t) is an Ornstein-Uhlenbeck process⁹⁴ with zero mean and deviation :

2

Where is a white noise process with zero mean and variance 1. The current is passed through a linear temporal filter to obtain the change in population membrane potential:

3

Where is the membrane time constant and R is the membrane resistance given by . Adaptation is modelled by updating an rate-dependent variable (w) with a slow time-constant:

4

Where , and are the adaptation time constant and population specific adaptation strength and firing rate, respectively. Finally, the membrane potential and the adaptation variable are passed through a non-linear threshold function⁷⁶ to obtain the population firing rate:

5

6

Where a, b and d are the gain, threshold and noise factor, respectively. These parameters are fitted such that the DMF and LIF implementation of the microcircuit model have similar firing rates (see Table 1). Code for simulating the dynamic mean field is available at github.com/ccnmaastricht/LCM-BS

Network connectivity

We obtain the intra- and interlaminar recurrent connection probabilities from⁴⁰. The feedforward connection probability from L4E to L23E is doubled as in to compensate for the decrease in firing rate in L23E due to the lateral inhibition (c.f.^45,95). We subsequently compute the number of synapses between populations:

7

Where P, and are the connection probabilities between the pre- and post-synaptic populations and the number of neurons in the pre- and post-synaptic populations, respectively. The layer-specific excitation-inhibition ratio is obtained by dividing the number of excitatory neurons by the inhibitory neurons. The inhibitory synaptic weight is then the multiplication of this ratio with . The final connectivity matrix is obtained by multiplying the number of synapses by the synaptic weight:

8

External input is applied by defining a number of synapses and an input frequency and multiplying the these with the standard excitatory weight . Each population in the network receives a background input with a frequency of 8 Hz via a population specific number of synapses with weight . The number of background synapses are taken from⁴⁰. Lateral mutual-inhibition is modelled by symmetric connections from population L23E in one column to L23I in the other column. and control the self-excitation of L23E and lateral-inhibition strength, respectively. Feedforward stimulation of L4 excitatory and inhibitory populations is applied through 295 and 186 synapses, respectively (with the same E/I-ratio as⁴⁰). The number of external connections of net excitatory external inputs in layers L4, L6 and layers L23, L5 are 300 and 255 for excitatory and inhibitory populations, respectively. The full list of model parameters are provided in Tables 1 and 2. Figure 2 shows a diagram of the implemented model.

Table 2.

Model parameters.

Dynamic mean field parameters
Name	Value	Description
	0.02 nA	Noise amplitude
	0.5 ms	Synaptic time constant
	20.0 ms	Membrane time constant
	250.0 mF	Membrane capacitance
	48	Function gain
	981	function threshold
	0.0089	Function noise factor
	8 Hz	Background rate
	10 s	Adaptation time constant

Simulation

All simulations of the stochastic differential equations describing our model are performed in Python 3.8.10 using the Euler-Maruyama method with a simulation time of 100.0s and a time step of 0.1ms. Simulations are executed on the PizDaint CSCS Supercomputer cluster.

Analysis

Our main analyses focus on the distribution of the dominance duration and alternation rate. The dominance duration is defined as the length of the time intervals the model occupies one of the attractors (i.e. L23E rate of column D1 is high and D2 is low, or vice versa). To obtain the distribution of dominance durations, we extract the reversal time-points of L23E populations by comparing their rates. The difference between consecutive reversal time-points quantifies the dominance duration.

The alternation rate is here defined as the number of reversals per second per simulation (in Hz). Thus, every instance of a simulation has a single value for the alternation rate. Distributions for the alternation rate are obtained by running multiple trials using different random noise realizations.

Author contributions

Conceptualization: Kris Evers, Mario Senden. Investigation: Kris Evers. Methodology: Kris Evers, Mario Senden. Project Administration: Kris Evers, Judith Peters, Rainer Goebel, Mario Senden. Software: Kris Evers. Supervision: Mario Senden, Judith Peters. Visualization: Kris Evers. Funding Acquisition: Rainer Goebel Writing - Original Preparation: Kris Evers. Writing - Review & Editing: Kris Evers, Judith Peters, Rainer Goebel, Mario Senden

Data availability

The code generated during the current study is available at github.com/ccnmaastricht/LCM-BS. The current study does not use datasets from other sources.

Competing Interests

The authors declare no competing interests.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-20811-2.