Decomposing Neural Circuit Function into Information Processing Primitives

Two dynamic regimes of response to stimulus

As presented in detail in the Models and Methods section, we model a stimulus-selective cortical region as a ring network with a “Mexican hat” connectivity profile (Fig. 2C), that is, more excitatory interactions with units (also called nodes) at nearby positions along the ring and more inhibitory with nodes farther away. In our ring model, the activity of coupled network units is characterized by their noisy firing rates. The corresponding phase diagram, that is, its parameter-dependent dynamical regimes, is shown in Figure 2D. We measure simulated responses to stimulus presentations (emulating specific tasks) in two different regimes: an SU and an SB dynamic working points (Fig. 2D, bottom).

The simplest possible task entails (correctly) responding to the presentation of stimuli with different orientations/angles S_pos in different trials. Each stimulus is spatially localized, yielding a stimulus selectivity of different units, and can be transiently presented at any chosen time. We show simulated recordings of the activity of units in a single receiving region in Figure 3A. The firing rates measured in six exemplary trials are shown in Figure 3B, three operating in the SU regime (top) and three in the SB regime (bottom). For each of the trials, we show spatial maps of activity, where the horizontal axis represents time, the vertical axis different units along the ring network, and the firing rate is color-coded. The curves below the spatial maps show the corresponding firing rates for all units over time. We highlight in color the time series of units located at specific positions (indicated by matching-color lines on the corresponding spatial maps). As anticipated, we observe a clear distinction between responses in the SU and SB dynamic working points. In the SU regime, a localized stimulus injection generates a bump-like pattern of increased activity around the injection center (red lines and curves), which disappears soon after the stimulus is switched off. The firing rates of units outside a neighborhood of the injection are either unaffected (blue trace in SU trial #n and trial #j) or, at larger distances from the injection site, decrease due to the increased lateral inhibition exerted by active units inside the bump (blue trace in trial #k). In contrast, in the SB regime, bumps of increased activity develop spontaneously, at random positions along the ring, even without any stimulation. Upon stimulation, the bump's position shifts toward the injection site, its amplitude increases, and it remains stable until the end of the stimulus. After stimulus removal, the bump amplitude relaxes back to its initial value, but the position remains stable around the injection site.

These two configurations correspond to distinct functional behaviors: in SU, stimuli are only transiently represented. In contrast, in SB, a sustained activation is observed, supporting the maintenance of the working memory of the presented stimulus after its removal. The two IPPs associated with these two simple functional behaviors are “carrying” and “buffering” information, respectively (compare Fig. 1B, top two cartoons). They can be tracked by different information-theoretical metrics. We focus first on the “carrying” IPP and address the “buffering” IPP in the next section.

IPP analysis can track the representation of a stimulus

In Figure 3C (top), we show the amount of total information that a ring unit carries as a function of time, averaged across all units and trials, provided by the entropy H(R(t)) of the activity rates R(t) as they change in response to stimulus presentation. The average entropy of activity differs between the SU and SB regimes. In SU, entropy is rather low in the absence of stimulus, due to the temporal and spatial homogeneity of baseline firing rates, fluctuating only due to a weak background noise. Entropy increases during stimulus presentation, as stimulus-evoked bumps emerge and produce differences in response rates for different stimulus positions, increasing inter-trial variance. In contrast, in SB, entropy is higher before stimulation, because of the stochasticity of the spontaneously emergent bump positions. In our simulated experiments, stimuli are presented at four discrete possible positions (a configuration often met in empirical experiments). Therefore, upon stimulation, the bump positions are quenched to only four pronounced maxima (compare spatial maps in Extended Data Fig. 3-1A), resulting in a strong entropy reduction with respect to baseline. Entropy rises again after stimulus removal, as firing rates are reduced and noisy fluctuations more evident. For both the SU and SB regimes, we furthermore observe tiny peaks and kinks of the entropy time courses in correspondence with stimulus onset and offset at times t_ON and t_OFF. These variations can be explained by the non-instantaneous response of the system to instantaneous inputs, causing fast transient dynamics (like impulse responses) to occur shortly after stimulus onset and offset (so that inter-trial variance is temporarily increased during these transients).

This simple analysis illustrates how strongly the values of information-theoretical quantities depend on aspects of the neural recordings, such as signal-to-noise ratio and actual task design, which have little to do with algorithmic-level operations. Entropy is an upper bound to other metrics, for example, MI that quantifies the statistical dependence between two or more variables. Entropy variations could result in absolute MI variations, which simply reflect changes in the available informational bandwidth. For the study of primitive processing operations, we thus focus on relative metrics that are normalized by entropy. We therefore do not have to account for the additional complexity of total entropy fluctuations unrelated to the processing probed.

We show the relative amount of information that a unit's activity carries about the stimulus, disentangling two of its aspects: the stimulus time course S(t), that is, its presence/absence at specific times t and the orientation S_pos of the stimulus, which is a trial-specific property (changed every trial, see Models and Methods). This fraction of information is captured by the entropy-normalized MI between firing rate R(t) and stimulus time course S(t) (MI(R(t); S(t)) in Figure 3C, middle, or stimulus orientation label S_pos (MI(R(t); S_pos) in Figure 3C, bottom (see Extended Data Fig. 3-1B,C for the corresponding spatially resolved maps). Before stimulus presentation, no information about the stimulus can be extracted from the neural activity, since the baseline noise entropy is unrelated to the stimulus. In contrast, during stimulus presentation, activity is modulated in dependence on stimulus position (i.e., the distance between S_pos and the angle of the recorded unit).

The information about the stimulus-related time course S(t) becomes positive during stimulus presentation, in both the SU and SB regimes, saturating to a higher value in SU (Fig. 3C, middle), as the evoked bump activity configuration differs strongly from the homogeneous baseline. During stimulus presentation, some units develop much lower or higher firing rates than in spontaneous conditions, thus signatures of stimulus presence. No S(t)-related information exists before or after stimulus presentation. Similarly, MI with stimulus position S_pos (Fig. 3C, bottom) is absent before stimulus presentations and saturates to a plateau shortly after stimulus onset. It is higher for the SB than the SU regime, as SB provides a larger dynamic range of responses and sharpened bumps. Stimulus encoding is slightly delayed in SB, since the rearrangement of the bump positions is not as fast as the sudden, stimulus-evoked bump in SU. In the SU regime, all stimulus-related information vanishes shortly after stimulus offset. In contrast to SU, information about stimulus position remains present after stimulus offset in the SB regime, as the stimulus-evoked bump self-sustains itself in its (new) position. It may slowly drift away under the influence of background noise over timescales longer than the observation window considered here.

Extended Data Figure 3-1B,C show that spatial maps of MI not only depend on time but also on spatial location. Stripes are clearly visible in these “infogram surfaces,” because our design comprises only a discrete number of possible stimulus orientations (compare Extended Data Fig. 3-1A). Encoding of stimulus features is in general stronger in the bump centers as these locations have a larger dynamic range.

In summary, the normalized MI of firing rate with stimulus provides an interpretable marker of the IPP of “carrying” stimulus (un-)specific information.

IPP analysis can track the loading and maintenance of a representation in working memory

We are able to detect that the poststimulus activity in the SB regime still “carries” stimulus position information. Through which primitive processing operations can this representation be held in working memory? Answering this question requires turning to information dynamics metrics, such as AIS (see Methods), which quantifies the fraction of the information carried by a node's activity at a time t that was already carried at an earlier time t-τ, that is, MI(R(t); R(t-τ)), with delay τ = 40 δt. Plain AIS tracks the time-lagged maintenance of information by neural activity, irrespective of the origin of this information (stimulus-related or intrinsically given). The process through which this fraction of information is maintained corresponds to the IPP of “buffering” (compare the second cartoon from the top in Figs. 1B, 3D, left). Note that we focus on buffering by one node only (as we did with “carrying”). Strictly speaking, however, information about stimulus may be carried (redundantly and/or cooperatively) by more than one node simultaneously. Accounting for these more complex scenarios would require using more advanced metrics of storage that discriminate storage of redundant versus synergistic information (see Discussion), which we do not consider here, for the sake of simplicity.

Figure 3D shows averaged time traces of AIS computed with the ring model in Figure 3A–C. In the SU regime, AIS is positive only during stimulus presentation. It relaxes back to zero after stimulus offset as the stimulus-evoked bumps dissolve back to homogeneous baseline activation. In the baseline pre- and poststimulus presence, all entropy is due to spatially and temporally uncorrelated noise, which is by construction memory-less, thus resulting in null active storage.

The situation is different in the SB regime, in which (spontaneous) bump formation is associated with active storage and thus positive at baseline and after stimulus offset. However, AIS drops at stimulus onset and offset. These events induce changes in activity that cannot be predicted based on prior intrinsic activity and hence convey information, which is not the outcome of “buffering” but must come from outside the system. This information injection is captured by another information-theoretical metric, TE_S→R(t) from stimulus to rate (see Methods), tracking the complementary IPP of “transferring.” In general, TE identifies the information flow between time series when a given signal Y is influenced by another signal X. It is defined as the conditional MI between the present of Y and the past of X, conditioned on (i.e., factoring out) the past of Y. As shown in Figure 3E, the TE peaks match the drops in AIS visible in the middle of Figure 3D. At stimulus onset, network nodes modify their algorithmic role, reducing their implication in the IPP of “buffering” and becoming the recipients of information conveyed by the IPP of “transferring.” Transfer of information from stimulus to activity occurs also at stimulus offset, when a new information injection indicated by a second peak in TE encodes a release ,nd to either produce bump dispersion (in SU) or a decrease in firing rate together with readjustments of the bump shapes (in SB). See also Extended Data Figure 3-1D for detailed spatial maps showing the nodes that are most strongly affected by externally injected information at different times.

The information buffered at baseline in the SB regime cannot yet be stimulus-specific as the stimulus has not yet been presented (the positions of spontaneously generated bumps in SB are random). To formalize this intuition, we quantify the fraction of information about the stimulus stored by the network nodes, that is, the stimulus-specific active storage. It is the totally stored information minus the part that does not depend on the presented stimulus orientation (see Methods). The averaged time course of stimulus-specific active storage is shown in the rightmost subpanel of Figure 3D. Its trace correctly captures that there is no stimulus-specific information buffering prior to stimulus presentation, while it displays a transient increase after stimulus presentation, for SB also during the poststimulus period. Stimulus-specific active storage thus provides a valid metric to track the active maintenance of information relative to a presented stimulus.

In this single-ring example, the dynamics of “carrying” and “buffering” stimulus-related information are very similar, because all information “carried” by a node exists as a form of “buffering” well after stimulus onset and offset. However, they are not completely identical. In SB, the rebound after stimulus offset in the curve for buffering is the most obvious difference to the carrying curve. It reflects the fact that some of the transient variations in “carrying” are due to “transfer” (compare Fig. 3E). In general, compared to the IPP of carrying, buffering is always delayed, since only information already carried by the system can be buffered.

At the functional level, such stimulus-specific maintenance marks the implementation of working memory. At the algorithmic level, our IPP analyses allow a decomposition of working memory: it arises via the loading of stimulus-specific information—through the IPP of “transferring”—into the system's units. By virtue of their collective dynamics, these units are intrinsically devoted to the IPP of “buffering.” This algorithmic decomposition provides not only a narrative of how a system's dynamics translates into a function but also yields a quantitative characterization: suitable information-theoretical metrics—AIS for “buffering” and TE for “transferring”—provide a precise evaluation of when, where, and how distinct IPPs are performed.

IPP analysis can track the propagation of representations through a multiregional hierarchy

We now tackle the algorithmic decomposition of the function of activity propagation. As detailed in Models and Methods, we simulated a feed-forward chain of three-ring modules, representing three hierarchically ordered regions (e.g., V1, V2, and above; Fig. 4A, bottom). The bottom ring R1 represents a sensory cortical area. It receives an input stimulus, which is sent to hierarchically higher cortical areas (R2 and R3). Each unit in the bottom and middle rings (R1 and R2) is coupled to the corresponding unit (and its local neighbors) in the subsequent rings (R2 and R3), respectively.

Figure 4B shows a representative example of single-trial firing rate traces (together with the associated spatial maps of activity) for all three rings, for both the SU (top) and SB regimes (bottom). Red lines and curves indicate units at the position of stimulus injection, blue units far from it, and magenta lines and curves indicate the initial bump position in SB simulations. All panels show the propagation of activity bumps through the hierarchy of rings. Again, bumps are purely stimulus-evoked in the SU regime, while they emerge spontaneously (and are persistent) in the SB regime. The bump’s maximum amplitude decreases, and its peak latency is delayed when propagating from the bottom to the top ring. This effect is more pronounced in the SU regime than in the SB regime, where self-amplification via local recurrent excitation acts as a facilitator for propagation. In SB, the effect of forward coupling is already observable without any stimulation: the intrinsic bump positions (magenta lines and curves before stimulus onset) are very similar in the three rings, whereas they would be completely decorrelated if rings were uncoupled.

As for the one-ring model, we study whether bump activity performs the basic IPP of “carrying” information about the stimulus. The encoding dynamics revealed by the MI analyses in Figure 4C closely mirror the dynamics of firing rates in Figure 4B. The peak amount of information carried about stimulus position is larger in the bottom ring (black curve) and weaker in the top ring (dotted curve). Furthermore, the rise of encoded information is slower and delayed in rings R2 and R3, particularly in the SB regime where the realignment of bump positions is slow and continues in higher-order rings even after stimulus offset. Our model thus successfully captures the propagation of sensory representations.

The obvious IPP algorithmically mediating this propagation is that of “transferring” (compare Fig. 3E). In Figure 4D, we show the time series of interregional information transfer evaluated via TE (again, see Discussion for some limitations of this metric). TE quickly rises after stimulus presentation, reaching a peak when MI with the stimulus saturates at its maximum plateau value (compare Fig. 4C). Transfer is stronger and faster from R1 to R2 than from R2 to R3, again in agreement with the firing rate dynamics in Figure 4B. After the peak, transfer drops to a plateau level, which slowly decays after stimulus offset. The profile of transfer is more complex for the SB than for the SU regime. Firstly, in SB, there is inter-ring transfer of information prior to stimulus onset, since the bump positions in R1 and R2 influence those in R2 and R3, respectively (compare Fig. 4B). Secondly, SB curves are broader with marked secondary peaks, associated with the rearrangement of bump positions. Their rearrangement takes longer than their mere creation. The spatial maps of TE in Extended Data Figure 4-1A show that substantial transfer occurs even to units far from the stimulus centers as the generation or drift of bumps at locations misaligned with the stimulus must be actively controlled (another interregional functional interaction that TE is able to track).

Since the wiring of the multiregional circuit is purely feed-forward, there should not be any significant feedback information transfer. In the SU regime, the backward TE from higher-order toward lower-order rings is close to zero. However, in the SB regime, a finite backward TE is detected. It is clearly smaller than the forward TE, allowing it to correctly capture the dominant direction of transfer. This spurious backward transfer is due to the misestimation of joint probability density given the finite amount of data, as well as to systematic biases of our simple “plug-in” estimators. Since the wiring of the multiregional circuit is purely feed-forward, there should not be any significant feedback information transfer. In the SU regime, the backward TE from higher-order toward lower-order rings is close to zero. However, in the SB regime, a finite backward TE is detected. It is clearly smaller than the forward TE, allowing it to correctly capture the dominant direction of transfer. This spurious backward transfer is due to the misestimation of joint probability density given the finite amount of data, as well as to systematic biases of our simple “plug-in” estimators. It can be reduced by using a longer delay in estimating TE (Extended Data Fig. 4-1B), and it vanishes almost completely when using multivariate delay coordinate embeddings as originally prescribed for TE (Schreiber, 2000; see Extended Data Fig. 4-1C). Both approaches allow limiting the impact of fast transients not properly captured by our quantized estimation of joint activity distributions (see Methods). The spurious backward transfer occurs primarily in the particular case of three coupled rings in the SB state: here, the changes in the internal dynamics (bump displacement) are very slow compared to the fast change in the external input (stimulus onset), because the reformation of bumps inside each ring takes a certain amount of time and is even more delayed in rings 2 and 3. In this case, a multi-delay estimator of TE can be used to substantially reduce the bias. In all presented cases, the conclusions reached by more sophisticated (and computationally costly) estimators are qualitatively equivalent to the ones of simpler single-delay TE. Single-delay TE, furthermore, despite its simplicity, already allows a clearer detection of the dominant direction of information propagation than plain time-lagged MI (Extended Data Fig. 4-1D), in line with previously published theoretical analyses (Kirst et al., 2016).

In summary, all estimators were able to correctly detect the existence of dominantly feed-forward information transfer. The “transfer” IPP is always the main component in the algorithmic decomposition of the propagation of a sensory representation.

IPP analysis can track the integration of bottom-up and top-down information flows

Our last model configuration is specifically designed to reproduce another important cognitive function: selective attention and the involvement of working memory in its implementation. An attentional effect is depicted as boosting responses to stimuli with attended features and suppressing responses to stimuli with features far from the attended ones (feature–gain–similarity principle, Maunsell and Treue, 2006). Seminal modeling work by Ardid et al. (2007) has first shown that the attentional effects on sensory responses can be explained as a byproduct of the nonlinear integration of sensory bottom-up inputs and top-down inputs from a higher-order region with working memory. This is in line with earlier hypotheses that working memory could be a fundamental component of mechanisms mediating attentional modulation (Desimone and Duncan, 1995). In the following, we will show that this merging of bottom-up and top-down influences can be tracked by the IPP of “integrating,” quantified by synergistic information modification (Fig. 5A). In the model proposed by Ardid and co-workers, two ring networks are reciprocally coupled (2RC architecture; see Methods). The lower-order ring R1 represents a sensory area tuned in SU, thus generating stimulus-driven bumps upon stimulus injection. The higher-order ring R2 represents the prefrontal cortex, conditionally set to be in the SU or SB regime, respectively, depending on the attention state “off” (att-OFF) or “on” (att-ON). With att-ON, the second ring is enabled to sustain an induced representation of a presented stimulus, even after the stimulus is removed (i.e., it can act as working memory).

Following Ardid et al. (2007) in the main aspects, we simulate a classic delayed match-to-sample task (Fig. 5B). This virtual task mimics actual experiments probing the response of cells recorded in the MT cortex to drifting dot patterns. Cells in MT show a strongly selective response to stimuli drifting in their preferred angular direction (Albright, 1984), resulting typically in bell-shaped tuning curves with a marked unique peak. In our computational model, this selectivity is captured by the heterogeneous responses of units along the sensory ring, resulting in the response profile given by the black curve in the top panel of Figure 5C. In the virtual task design of Figure 5B, two types of trials exist. The “att-OFF” trials correspond to an empirical condition in which the subject actively attends to a stimulus presented outside the receptive field of the recorded cells [called “unattend” in Treue (2001)]. The “att-ON” trials conversely correspond to the empirical “attended” condition where the attentional spotlight is in the receptive field of the recorded cells. In both conditions, a first cue stimulus is shown and then removed (Fig. 5B, red stage), followed by a delay period of a certain length (Fig. 5B, black stage) with no stimulus. Then, a second stimulus is presented, whose direction can be close to or far from the direction of the initially cued stimulus (Fig. 5B, match stage, magenta). Individual simulated trials for different cue and match stimulus configurations are shown in Figure 5D, in both the att-ON (top) and att-OFF (bottom) conditions.

When simulating neural responses in the att-OFF condition (prefrontal area ring R2 tuned to SU), the response profile of the sensory ring to the match stimulus is unchanged with respect to the one during the cue stage. The presentation of match stimuli with different directions simply produces rotated response profiles (Fig. 5C, black and dashed gray lines). Inspecting the responses in individual trials, we see that all match stage activity bumps in the sensory ring look similar and that the activity in the prefrontal ring R2 has a smaller rate and a worse signal-to-noise ratio compared to R1 (Fig. 5D, bottom).

In contrast, in the att-ON condition (a copy of the cue has been held through the delay period by R2 switched to SB), the response profile at match stimulus is differently modulated depending on the relative difference of orientation between cue and match stimuli (Fig. 5C, ΔΘ). If cue and match stimuli have identical orientations (ΔΘ = 0), the response of the direction-selective units in R1 is boosted, while the response of units selective to stimuli far from the attended one is reduced. This can be seen in single-trial responses (Fig. 5D, top), where the match bump is slightly darker for identical cue and match configuration (trial #n). It is clearer in the red activation profile in Figure 5C whose peak at ΔΘ = 0 is higher than the black one obtained for att-OFF. If cue and match stimuli have different directions, the difference in Δθ modulates the corresponding response profile (Fig. 5C, purple curves) in the att-ON condition. The net amount of (simulated) attention-induced modulation can be quantified by computing the percent difference ratio between the response profiles to a stimulus in att-OFF and ON conditions as shown in the bottom panel of Figure 5C. In our virtual task, the positive modulation can be as large as +15% for responses to identical cue and match stimuli and down to between −10% and even −45% for stimuli, which are ∼45° displaced. We now study the algorithmic effects of these nonlinear dynamics.

We focus specifically on the IPP of “integrating,” occurring here at the match stage when the sensory response (Fig. 5D, R₁) is the byproduct of nonlinearly merged bottom-up stimulus-related input (S_pos2) and top-down attention-related input (R₂). The information-theoretical quantity, we use to track this IPP is synergistic information modification (Lizier et al., 2013). As graphically depicted in the information Venn diagram of Figure 5E, the two bottom-up S_pos2 and top-down R₂ inputs carry together (when considered jointly) a certain amount of information MI_tot = MI((R₂, S_pos2); R₁) about what is going to be the output sensory response R₁. A fraction of this total information is contributed uniquely by each of the two considered inputs. At match stimulus onset, only the bottom-up input S_pos2 can convey information about the direction of the newly shown match stimulus, while only the top-down input R₂ can carry information about the previously presented cue stimulus. Both inputs contribute to determining the final output response, and they comprise two unique information fractions conveyed exclusively by each of the two inputs (Fig. 5E, green and blue areas). Some additional information may be shared between the two inputs—including noise entropy—as captured by the redundant information fraction (Fig. 5E, cyan intersection). Yet, the sum of unique and redundant contributions could be smaller than the total information MI_tot. Some information necessary to determine the response could be conveyed by the two inputs in combination but by neither of them in isolation. This surplus contribution—“more than the sum of the parts” (Anderson, 1972)—is the synergistic fraction of the total information (Fig. 5E, white area), and its extraction by the output nodes is termed the synergistic modification operation. We estimate these unique, redundant, and synergistic contributions, quantifying when and where along the virtual task (Fig. 5B) the activity of the interacting rings implements the IPP of “integrating.”

This extraction of the synergistic information is tracked and quantified by the information modification surfaces shown in Figure 5F, for both att-ON (left) and att-OFF (right) conditions (compare Extended Data Fig. 5-1 for details on the individual terms contributing to its computation). In addition, Figure 5G shows the profile of a section of the modification surface at the beginning of the match stage (Fig. 5F, averaging range delimited by the dotted black rectangle). Clearly, sensory ring units perform information modification at specific task-related locations and times in the att-ON condition while there is nearly no synergistic modification for att-OFF.

The most prominent involvement in information modification occurs in the match stage, particularly at the immediate onset of the match. This is precisely when attentional modulations of stimulus response occur. As visible when comparing the profiles of attentional modulation (Fig. 5C, bottom) and information modification (Fig. 5G), the participation of a node in information modification is stronger for the prominent bump in attentional modulations. Specifically, modification is enhanced at the bump flanks, where the most attentional depression is observed. Modification at the bump center position is weaker, because here, the strong net drive helps the recurrent excitatory connectivity within the sensory ring to sustain the boosted activity.

For att-ON, information modification can be seen to occur during different virtual task stages. Modification stripes preceding the match stage occur during the delay stage with a much weaker intensity. They are related to the fact that some small-intensity activity is top-down transferred from the bump in R2 (compare Fig. 5F). These nonlinear interactions between the working memory bump during the delay and its “sensory shadow” effectively reduce the variability of the sensory ring activity in att-ON versus att-OFF. This is another type of nonlinear phenomenon beyond rate modulations that can result in modification (see Discussion). Other modification events occur during the cue stage, probably due to the transient reshaping dynamics of activity bumps caused by the parameter changes for R2 to switch from SU to SB regime.

In the att-OFF state, information modification is close to zero and possibly estimated to small positive values, because of numeric estimation artifacts. As detailed by Extended Data Figure 5-1, the surfaces shown in Figure 5C are the sum of several other surfaces corresponding to the different terms in the expression for the synergistic information part (see Methods). Numerical errors could thus be more important, as more steps are involved.

In conclusion, the function of selective attention admits an algorithmic decomposition involving the IPP of “integrating,” a much more complex function than the IPPs of “carrying,” “buffering,” or “transferring” described in previous sections.

Information dynamics in a large-scale model of the cerebral cortex

The ring models we have studied so far represent generic coupled brain regions with only stylized notions of hierarchical connectivity (Fig. 4, feed-forward propagation; Fig. 5, top-down integration). Detailed information about interregional cortical connectivity is, however, available and large-scale models of cortical activity have been constructed, embedding empirically derived multiregional connectomes (Deco et al., 2011). In these models, the local activity of individual regions is modeled with simple neural mass equations. Each region receives inputs from other regions, scaled by the relative strength of connections within a connectome matrix. In addition, the distinct fiber tract lengths of the connections can be represented by different propagation delays. To validate our IPP approach beyond generic and ad hoc constrained ring model architectures, we now consider the case of stimulus-evoked activity in a large-scale model of macaque monkey cortex with realistic connectivity (Fig. 6).

Specifically, we re-implemented a model previously published by Joglekar et al. (2018), embedding a directed and weighted connectome derived from systematic tracer experiments (Markov et al., 2014; Fig. 6A). The “bow-tie” architecture of such a connectome introduces a barrier to the free propagation of externally injected stimuli. As shown in Figure 6B, the application of a brief transient input to region V1, mimicking the presentation of an external visual stimulus, leads to a very limited propagation of activity along the visual stream. However, a GBA mechanism can be introduced, in which lr excitatory connectivity is enhanced, while simultaneously strengthening local inhibition (to excitatory populations within each region; Fig. 6B, top right). In this way, propagation is facilitated by stronger connections, while the increased amount of excitation is controlled by a modified inhibitory-to-excitatory balance. Figure 6B compares a scenario of weak (left) versus strong GBA (right), revealing that stimulus-related activity volleys can reach higher-order regions only in the latter case. Following Joglekar et al. (2018), higher-order regions are endowed with stronger excitability and correspondingly longer time constants. Thus, once a stimulus-related volley has reached a higher-order region (e.g., region 46d), the stimulus-evoked activity will last well beyond the offset of the applied stimulus. Adoption of a strong GBA regime and hierarchy-scaled excitabilities allows thus to implement in the large-scale model a scenario reminiscent of the att-ON condition in Figure 5, where the top ring, after being cued to attend a stimulus direction, is switched in the SB regime, sustaining bumps in absence of a stimulus.

We performed simulations of stimulus propagation in this large-scale cortical model and extracted its algorithmic decomposition, revealing “buffering,” “transferring,” and “integrating” IPPs. Figure 6C shows raster plots of IPP metrics, computed in the strong GBA regime, whereas Figure 6D shows an alternative representation of these IPPs, time-averaged radar charts, where blue lines indicate strong and red lines weak GBA regimes. The results of analyzing (stimulus-unspecific) AIS are reported in the first column on the left. We observe that sensory regions (e.g., V1 and V4) and (pre-) frontal regions (e.g., 46d, 8) have very different storage dynamics. The raster plot (Fig. 6C) shows that in sensory regions, AIS drops relatively quickly after stimulus offset, while in higher-order regions, it persists for a longer time span, an effect of the longer intrinsic time constants. Areas 46d and 8 display positive AIS before stimulus presentation, reminiscent of ring networks in the SB regime (compare Fig. 3B). However, when additionally computing stimulus-specific storage (Fig. 4E, area 46d), we see that the fraction of storage imputable to stimulus is zero before stimulus onset and increases thereafter. In the low GBA condition, only a limited set of regions displays noticeable AIS (Fig. 4D).

The IPP of transfer is shown in the second and third columns of Figure 6, C and D. Here, we consider the forward TE from V1 to other areas and the backward transfer to V1. In the strong GBA regime, V1 transfers information to a variety of other regions, mostly in the ventral (e.g., V4) or dorsal (e.g., MT) visual stream. Backward transfer is weaker and arises mostly from nearby low-level visual regions (e.g., V2 and V4). Again, a transfer is considerably disabled in the low GBA regime (Fig. 4D).

Finally, we consider V1 as a target node integrating the bottom-up stimulus-related input and top-down inputs from other regions in the large-scale cortical circuit and compute the amount of synergistic modification performed by V1 (Fig. 6C,D, rightmost columns). Strong stimulus-related synergies exist with a variety of regions through the entire cortical hierarchy, particularly strong with frontal and prefrontal regions (areas 8 and 46d). Similar to the IPPs of “buffering” and “transferring,” a strong GBA regime is needed to establish substantial synergistic modification. In Figure 6F, we study in detail the latencies with which synergistic integration arises. Figure 6F (left) shows the synergistic information in the stimulus-induced V1 response due to the integration of top-down inputs from region 46d. As expected, the V1 response peak precedes the peak in the 46d response, which lasts longer than the V1 response. Synergy starts growing in parallel with the increase of activity in the area 46d region, and the synergy peak occurs very close to the area 46d response peak, indicating a fast integration of top-down signals by V1. Remarkably, as shown by the scatter plot in Figure 6G, synergistic integration is achieved first with top-down inputs from regions hierarchically distant from V1. Indeed, a significant anticorrelation (R = −0.66, p = 0.0002) exists between distances in the matrix of Figure 6A (right) and the peak of the synergy time course. This finding is nontrivial and reveals how the bow-tie topology of the corticocortical connectome supports a fast-“forward” transfer of stimulus-related information followed by a “backward” integration of top-down influences, initiated by the top-most regions (see Discussion).