The Neural and Computational Architecture of Feedback Dynamics in Mouse Cortex during Stimulus Report

Detection of visual stimuli is coupled to large-scale activity patterns in the dorsal cortex

We first aimed to replicate and expand earlier reports that visual detection in mice correlates with a bimodal response pattern in V1 (Oude Lohuis et al., 2022c) and with the emergence of report-related activity across multiple cortical regions (Allen et al., 2017; Pho et al., 2018; van Vugt et al., 2018; Steinmetz et al., 2019; Yin et al., 2020; Zatka-Haas et al., 2021). To this aim, we first analyzed neuronal activity collected in head-fixed mice performing an audio-visual change detection task (Oude Lohuis et al., 2022b,c, 2024; Fig. 1A). Mice were trained to report the change in the orientation of the presented visual stimulus, by performing—for instance—a left lick, and a change in the pitch of the presented auditory stimulus by performing a right lick (with contingencies counterbalanced across mice; see Materials and Methods for details). In this report we only focus on the processing of the visual stimuli. Multi-area laminar probe recordings were performed in the primary visual cortex (V1), posterior parietal cortex (PPC), and anterior cingulate cortex (ACC; Fig. 1B). We computed stimulus-evoked spiking responses across the three areas as a function of the saliency of the visual stimulus (threshold or max change) and based on whether a stimulus was detected (hit trial) or not (miss trial). Trials from the max change condition will be referred to as “high saliency” and trials from the threshold condition as “low saliency” from here on. Of relevance, previous studies indicated that neuronal responses in both PPC and V1 did not show major deviations based on whether licking responses to full-field visual stimuli had to be done toward a detector positioned toward the left or right side of a mouse's snout (Oude Lohuis et al., 2022b,c, 2024).

In V1, we observed a bimodal pattern of activity: an early-onset wave of sensory-evoked activity, lasting until ∼200 ms after stimulus onset, followed by a late-onset wave which was mainly encoding whether a trial was a hit or miss (cf. Oude Lohuis et al., 2022c; Fig. 1C). Early sensory-evoked activity did not differ between hit and miss trials, but firing rates were positively correlated with the saliency of visual stimuli (Fig. 1C). Instead, late activity encoded both whether a trial was a hit or miss, as well as whether the sensory input was strong or weak (Fig. 1C; cf. Oude Lohuis et al., 2022c). Activity in PPC and ACC mainly encoded differences between hit and miss trials, although a generalized increase in firing rates could be observed as a consequence of the presentation of sensory stimuli (Fig. 1C; cf. Oude Lohuis et al., 2022b).

To verify that these results were not specific to our experimental protocol, we also analyzed recordings from another previously published experiment (Steinmetz et al., 2019). In this paradigm, mice had to identify which of two visual stimuli presented in the right and left hemifield had the highest contrast and rotate a wheel to move the highest-contrast sensory stimulus toward the center of the screen (Fig. 1D). We computed sensory-evoked responses as a function of both stimulus contrast (difference between the contrast of the two presented Gabor patches) and hit/miss responses, for trials in which the highest-contrast stimulus was shown in the hemifield of view contralateral to the recorded hemisphere. We analyzed neuronal responses in areas corresponding to those analyzed in the previous set of experiments [V1; VISa and VISam (data not shown), which are two secondary visual cortices spatially overlapping with PPC; ACC], as well as in a region broadly defined as the supplementary motor cortex (MOs), where report-related activity has been shown to originate (Allen et al., 2017; Fig. 1B). Results were in line with those that we observed in the first dataset. V1 showed a bimodal pattern of activity, with an early sensory-evoked response (that, however, in contrast with our dataset, did not encode stimulus saliency) followed by a report-related bump in activity (Fig. 1E). Activity in higher-order regions followed the early response displayed in V1 and was only report related. These results suggest that the spatiotemporal progression of visual- and report-related activity is mostly independent from the details of the task being performed. Report-related activity, however, could reflect several factors besides stimulus detection, such as motor correlates and reward expectation (Stringer et al., 2019; Avitan and Stringer, 2022; Bimbard et al., 2023; Pennartz et al., 2023; Oude Lohuis et al., 2024). To better understand what the late component of V1 activity reflects, we also plotted neuronal responses during false alarms—when a response is performed in the absence of a visual stimulus—and error trials, when animals perform an incorrect response (Extended Data Fig. 1-1). False alarms in general did not correlate with any clear neuronal activity, for what pertains the data we collected (Extended Data Fig. 1-1A; note that we did not observe a sufficiently high number of error trials). For the data presented in the Steinmetz et al. (2019) manuscript, both false alarms and errors correlated with an increase in firing rates in frontal and association areas (MOs, ACC, and PPC; Extended Data Fig. 1-1B) but strikingly did not display a clear late wave of activity in V1. Thus, nonsensory activity has been previously observed in V1 and has been shown to reflect several factors including corollary discharges related to spontaneous and task-related movement. However, for what specifically pertains the late wave of activity that emerges in hit trials, this predicts the upcoming report and might also correlate with other factors such as reward but does not purely reflect motor actions. Nevertheless, an in-depth assessment of this aspect is beyond the scope of this study.

Earlier findings (Allen et al., 2017; van Vugt et al., 2018; Yin et al., 2020) indicated that report-related activity showed an earliest peak in the prefrontal regions, followed by PPC and V1. Our results suggest a similar picture for what pertains higher-order regions, with prefrontal areas (ACC, MOs; Le Merre et al., 2021) showing earlier indications of hit/miss differences compared with PPC. The relative timing of the appearance of report-related activity in V1 is, however, less clear (compare Fig. 1C,E) but is overall very close to that observed in the prefrontal regions (Allen et al., 2017; van Vugt et al., 2018; Yin et al., 2020). Thus, while the prefrontal regions remain the most likely candidate for the origin of report-related activity—as supported by the causal experiments performed by Allen et al. (2017)—the mechanistic pathway via which this form of activity reaches other cortical areas remains unclear.

A minimal network model reproduces the spatiotemporal propagation of visual- and report-related activity

In order to understand the possible network-level mechanisms underlying the spatiotemporal propagation of visual- and report-related activity across the cortical areas from which we analyzed neuronal activity, we developed a minimal mean-field computational model of the cortical network that: (1) uses available connectomic data (Ermentrout and Cowan, 1980; Ermentrout and Terman, 2010; Bressloff, 2014; Chaudhuri et al., 2015; Joglekar et al., 2018) and (2) is calibrated using in vivo recordings. For this reason, the model only includes the three cortical areas from which we analyzed in vivo neuronal recordings: V1, PPC, and PFC (Fig. 2A). The activity in each area is modeled with a firing rate neural mass model comprising one excitatory and one inhibitory population. Firing rate models of this type are a well-tested tool to describe macroscopic neuronal dynamics, as they average single-neuron spike rates (Ermentrout and Cowan, 1980; Ermentrout and Terman, 2010; Bressloff, 2014; Chaudhuri et al., 2015; Joglekar et al., 2018). Within each mass, the synaptic dynamic has a tunable dispersion time, and oscillatory dynamics are possible because of the coupling between the excitatory and inhibitory population (Coombes and Wedgwood, 2023). We also adopted a classical nonlinear sigmoidal firing rate for each neuronal population (see Materials and Methods for a complete description), which is standard for neural mass models in the literature (Ermentrout and Cowan, 1980; Ermentrout and Terman, 2010; Bressloff, 2014; Chaudhuri et al., 2015; Joglekar et al., 2018).

The mean field model comprises a total of six neuronal populations, two in each cortical area, which feature local as well as long-range connections. More precisely, the excitatory–inhibitory pair in each cortical area is fully connected and should be taken together as a model of a cortical area, where the excitatory node has been fitted to experimentally collected neuronal activity and therefore represents the output of an area (in terms of “firing” activity) and all other variables represent hidden state variables. In addition, there are long-range excitatory connections to and from each cortical area. Crucially, connection strengths between areas were taken from recent experimental data (Knox et al., 2019; Fig. 2B, highlighted entries). In particular, we employed values of directed connection density between V1, secondary visual areas A and AM (which are considered the mouse homologue of PPC; Driscoll et al., 2017; Pinto et al., 2019; Arlt et al., 2022; Oude Lohuis et al., 2022b), and MOs (which is considered as a component of PFC; Le Merre et al., 2021) and is thought to be the key cortical area mainly in view of generating report-related activity (Allen et al., 2017; Steinmetz et al., 2019). All other model parameters were calibrated (see Materials and Methods) to enable the excitatory nodes to reproduce patterns of activity comparable with those observed in vivo, as reported in earlier sections. During the tuning procedure all parameters in the model (characteristic rise/decay times, activation of the nonlinear firing rate functions, and local excitatory-inhibitory coupling strengths) were calibrated, while the interareal connections were kept fixed, because we had direct access to experimental data on these parameters. In this way we could test to what extent the generation and propagation of report-related activity in the three cortical areas on which we focus is shaped by corticocortical connectivity. Importantly, as our model comprises neural masses that jointly mimic the activity of whole cortical areas, all parameters except the activity of excitatory nodes do not represent measurable variables, but rather hidden state variables or input parameters that do not aim to model specific single-neuron parameters. For instance, while input currents are measured in picoampere, they reflect input to a whole cortical area and not to single neurons.

We modeled a visual stimulus via an applied transient step current, with varying intensity, on the excitatory population of V1 (Fig. 2A; Fig. 2C–E, I_app time traces), and monitored the elicited cortical firing rate response in excitatory and inhibitory populations of V1, PPC, and PFC (whose time traces are also seen in Fig. 2C–E). To calibrate the model, we applied a visual input lasting for 500 ms to the excitatory V1 node and replicated the following experimental results. First, when subjected to a sufficiently strong stimulus, V1 activity displayed an early-onset response peaking ∼100–200 ms (before the termination of the visual stimulus) that then dropped to lower values (Fig. 2C). This reproduces the adaptation to stimuli typically observed in the visual cortex (Fig. 1; Supèr et al., 2001; Steinmetz et al., 2019; Kirchberger et al., 2021; Oude Lohuis et al., 2022c). Second, high-amplitude visual stimuli evoked a bimodal V1 response, that is, an early-onset peak of activity followed by a later peak (Fig. 2E). This second peak was absent if the stimulus had a low-amplitude (low salience stimulus) and accounts for the report-related activity observed in vivo (Fig. 1, compare hit trials). While the model itself does not include an actuator stage to perform an actual report, we consider the emergence of the late-activity bump to represent an instance of stimulus detection by the prefrontal/premotor cortical regions. This mimics the spatiotemporal time course of sensory detection, as can be observed from the neural recordings shown in Figure 1 and from the related publications (Steinmetz et al., 2019; Oude Lohuis et al., 2022c).

Following this tuning procedure, we observed that, when the network was subjected to stimuli of various intensity for 500 ms, it displayed a strongly nonlinear response for the late peak of report-related activity: for smaller inputs (Imax=1.1pA) V1 was activated, but the signal did not significantly propagate in the network and did not trigger a second, feedback-dependent bump in activity (Fig. 2C, excitatory nodes in row 2–4). For higher input strengths (Imax=2pA) , the network displayed the late activity bump in many, but not all, realizations (compare Fig. 2D,E). To run the model, we first set the initial value of the firing rate in each of the excitatory and inhibitory population; that is, we set initial conditions prior to the initiation of the stimulus. In the simulation, each population is set to a random initial state with a small variance. In particular, we found that initial conditions varying within 10⁻² spikes/s, simulating noisy initial data, trigger or suppress the occurrence of the late activity bump.

This is in line with experimental findings showing that, when subject to a sufficiently large stimulus, large late-latency activity arises with high probability, but not with certainty (van Vugt et al., 2018). The probabilistic nature of this response is analyzed in detail in later sections. Before addressing this aspect, we observed the dynamics in each neuronal population and noted that the occurrence of a late-latency activity bump appears to be feedback-induced. The external stimulus activated V1 which, in turn, following a feedforward chain, activated PPC and PFC. The activity in the latter areas reached a peak (Fig. 2D,E, vertical time marker) before decaying owing to local (intrapopulation) inhibition. The time marker aligned remarkably well with the small late-latency activity in V1, signaling the onset of a feedback mechanism (from PFC and PPC back to V1; Fig. 2A, schematic). In realizations in which the late activity bump occurred, it was again PFC and PPC that displayed a peak preceding the late, report-related activity in V1, in line with a feedback mechanism. This claim will be further substantiated in the following sections.

Thus the model, using a set of nominal parameters, was able to qualitatively reproduce the types of activity we observed in vivo. While the model was specifically tuned to reproduce V1 activity, we also obtained comparable patterns of activity in PPC and PFC, indicating that the model could be used to study the mechanisms underlying the propagation of activity across cortical areas during sensory motor transformations. In particular, we focused on studying the role of feedback connections in the genesis of the late activity bump, i.e., of report-related activity.

We highlight that the time courses of the activity of excitatory nodes are strongly determined by the inhibitory ones: in Figure 2D,E, it is visible that inhibitory nodes in each cortical area activate after the corresponding excitatory node, and this determines the rise-and-fall behavior in the latter. It is known that neurotransmitter release in excitatory and inhibitory populations are affected by timescale separation between signals (Rodrigues et al., 2016). Our model achieves the delayed inhibitory activation using timescale separation between excitatory and inhibitory rising times (see discrepancies in the parameters τE and τI in Materials and Methods). However, we also must point out that, for the purposes of this study, we did not calibrate the dynamics of inhibitory nodes to match experimental results, but only tuned their parameters so that excitatory nodes would show realistic behaviors. For this reason, we will only focus on excitatory nodes in the rest of the manuscript.

The likelihood of late activity bumps is influenced by variations in internal state

As we have seen above, when the network is in the nominal setup and the visual stimulus is sufficiently high, a late activity bump occurs with a given probability, upon perturbing the initial state of the system. We investigated systematically this scenario by running 100 simulations during which the initial state of the excitatory V1 population was picked randomly and uniformly between 0 and 0.05 spikes/s, thereby imposing a small variance in the internal state (Fig. 3A) that is in line with experimental observations linking cortical state fluctuations to perception (Supèr et al., 2003; McGinley et al., 2015a,b; Speed et al., 2019; Samaha et al., 2020). We observed that early V1 responses elicited by either small (Imax=1pA) or large (Imax=3pA) input currents were not affected by such small variations, as trajectories were grouped together as simulation time progressed. On the other hand, intermediate currents (Imax=1.8−2pA) considerably propagated the initial uncertainty: a late activity bump occurred often, but the fine details of the trajectory could differ. These findings further support the conclusion that the network in the nominal setup supports robustly self-generated late-latency activity bumps. However, more delicate questions arise: given a fixed set of network parameters, how often does the network generate such a bump? And further: how do changes in the network parameters affect this likelihood? To address these questions, we developed first a mathematical index to track late-latency V1 activity.

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Figure 3.

Network activity as a function of initial conditions and input currents. A, Examples of activity trajectories (random initial conditions) for different input currents, in the nominal setup of parameters. B, Distributions of integral quantity S for the trajectories in A. A late-activity bump is detected when the integral of V1 firing rate S lies in the interval [0.2, 0.35], highlighted in green. C, Frequency distribution of S for different values of applied current I_app. Red columns highlight the values displayed in B. The statistics is obtained over 100 different realizations for every value of I_max, with initial conditions sampled from a uniform, random distribution u_i(t = 0) ∈ [0, 0.05] spikes/s.

We therefore introduced a cumulative (integral) spiking measure S, with the view of determining the likelihood of late-latency activity in V1. For each of the V1 traces seen in Figure 3A, we counted the average cumulative number of spikes occurring after the early activity bump in V1 (Materials and Methods). More precisely, we disregarded the trajectory before the reference time tinit  = 250 ms, because this is the characteristic time in which the early activity bump occurs (Del Cul et al., 2007; Oude Lohuis et al., 2022c), and then we calculated the area under the curve (proportional to the average number of population spikes) between tinit and the end of the simulation, tend=1,000ms , during which the late activity bump may occur. We expected trajectories with Imax=1.1pA (Fig. 3A) to have a very small cumulative spike number S, because they did not display a late activity bump. Indeed, the histogram in Figure 3B with Imax=1.1pA shows that, in all such trajectories, fewer than 0.05 spikes were observed in V1, on average, after the early activity bump, in the time interval [250, 1,000 ms]. On the contrary, a fully saturated response, in which firing rate reach the maximum value allowed by the model's equations (Fig. 3A; Imax=3pA ), is characterized by a large S, and indeed the histogram in Figure 3B (with Imax=3pA ) shows that all such trajectories had >0.35 spikes after the first bump, on average. Finally, a late activity bump was characterized by an intermediate value of S: with Imax=1.8−2pA we observed a clear separation in the histogram of S. Therefore, we can use the value of S to define, empirically, the occurrence of a late activity bump (Fig. 3B). We thus classified a V1 activity trace by the corresponding value of S: we labeled traces with 0<S<0.2 , as displaying only the early activity bump, traces with 0.2≤S≤0.35 (Fig. 3B,C, green band) as displaying both the early and late activity bumps and those with S>0.35 as displaying an overshoot (Fig. 3A).

Based on the fraction of trajectories whose S value falls in each of these three bands, we estimated the probability of having only the early activity bump as P_1b, both the early and late activity bumps as P_2b and overshoot as P_ov. For example, from the histograms in Figure 3B with stimulus Iapp=2pA , we estimated that the nominal network displays both an early and late activity bump with probability P2b=71% , an overshoot with probability Pov=5% , and an early activity bump only or inactivity with probability P1b=24% .

Late-latency activity relies on network feedback

Armed with a quantitative index to inspect the likelihood of late-latency activity, we investigated how this likelihood changes upon variations in the network topology. As we shall see below, this analysis revealed that the late-latency activity is feedback induced. We performed two different experiments which transform the connectivity matrix. In the first one, we perturbed the connectivity matrix at the initial time and kept the matrix constant thereafter. In the second experiment, we dynamically perturbed the matrix to explore the effects of abrupt changes to the topology of the network.

With the view of imposing changes in the network connectivity, we introduced a morphing parameter α (see Materials and Methods). When α=1 , the network is in its nominal state (the one studied so far); when α>1 , selected network links are strengthened; when α<1 , those links are weakened; finally, when α=0 , the links are absent. The name morphing parameter suggests that with this index, we can continuously transform the nominal network to intensify weaken or even suppress certain links. Therefore, we introduced a tool to causally study to what extent the specific strength of an interarea connection enables the emergence of a regime in which a sensory input to V1 can (with a certain probability) determine the occurrence of a late, report-related bump in activity.

We first used the morphing parameter to vary the strength of selected networks links from the starting time onward, beginning with the feedback link from PFC to PPC (Fig. 4A), signposted with a red arrow in the network schematic (mathematically, the PFC→PPC connection was scaled by factor α). We repeated the experiment of Figure 3A,B for various values of the morphing parameter ( α between 0 and 1.5) and recorded the probability of a single early bump P1b , both early and late bumps P2b , and overshoot Pov . We used P2b to derive the heatmap showed in Figure 4A: the lighter colors correspond to a higher probability of a late activity bump, while darker colors denote lower probability thereof. We also used isolines to indicate where the probability of a single bump P1b crosses 99% (green isoline) and where the probability of overshoot Pov crosses 99% (orange isoline).

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Figure 4.

Probability of observing a late-activity bump, in the plane of parameters (α, I_max), for the sets of connections considered. In each panel, heatmaps show the probability of observing both an early and late activity bumps P_2b as a function of applied input current I_max and morphing parameter α, applied to a different set of connections. The green and orange lines represent isolines of P_1b= 99% and P_ov= 99%, respectively, which border regions dominated by single bumps/inactivity and overshooting (see gray labels on the top-left panel). A white, dotted line marks the nominal setup (α = 1). For each panel, morphed connections are colored in red on the respective network scheme. For each couple of (α, I_max) values, we considered 50 random initial conditions (see Materials and Methods).

The overall information we gathered from the heatmap in Figure 4A can be summarized as follows. First, the network produced a late activity bump robustly with respect to changes in the PFC→PPC feedback link: light yellow areas (late-bump probabilities close to 100%) were found in a variety of network configurations (for various values of α). Second, there are regimes, labeled “ov” and “1b,” where the feedback bump was absent, but either an overshoot (ov) or an early bump only (1b) were found with probability >99%, respectively. Third, the network could produce a late activity bump even when the feedback link PFC→PPC was weakened with respect to the nominal condition, provided that the strength of the impinging stimulus was increased; this can be deduced from the yellow area in Figure 4A “curving upwards” toward higher values of Imax . Finally, the feedback pathway PFC→PPC was an important player in triggering late-latency activity. While the network could compensate for the weakening of this link with a higher input to produce a late-latency bump, network configurations in which that link was either too weak or too strong failed to produce a late activity bump.

A markedly different behavior was observed when we perturbed the feedback link PPC→V1 (Fig. 4B). From Figure 4B, it can be seen that the likelihood of a late activity bump was strongly affected by changes in this feedback link. Small deviations from the nominal value of the link caused the late activity bump to disappear quickly. While the network could tolerate a weaker PFC→PPC link (Fig. 4A), even the slightest weakening of the PPC→V1 link caused a complete suppression of the feedback bump. This data revealed that the experimentally derived anatomical connectivity used in the nominal conditions (α=1) was crucial to obtain a late activity bump.

On the contrary, the network's activity was only minimally affected by changes to the feedback link PFC→V1. Figure 4C shows that feedback bumps could be produced with high probability even when this link was absent (α=0) , in case the strength of the input was increased (compensating for the reduced PFC→V1 link).

For the experiments in Figure 4A–C, we perturbed one link at a time, but the morphing parameter can also be varied on multiple links simultaneously. In Figure 4D, for instance, we strengthened or weakened all the feedback pathways at once. These manipulations showed that late-latency bumps cannot exist without (or with too much) feedback. Therefore, it is the interplay between the various feedback pathways that generates the late-latency bump. This was further confirmed by the results displayed in Figure 4E,F, showing that a network in which the PFC or PPC nodes were progressively isolated (transforming the architecture into a two-node network) did not display robust late activity bumps.

The previous experiment modulated the strength of feedback connections over the whole simulation period. However, we expect that, if the network receives a shock in the form of instantaneous removal of certain links during sensory processing (rather than from the initial time), this will also have an impact on late-latency activity. We investigated this scenario in a further experiment: we selected initial states which, in nominal conditions, would lead to late-latency activity; we then ran this network up to a chosen time T*, at which we instantaneously set selected links to zero (see Materials and Methods). In Figure 5A.1, the PFC→V1 link is removed for different values of T* in the range 50–450 ms, when applying a value of I_max= 1.8 pA. We found that inactivating the link at any time resulted in a quick decay in V1 activity, preventing the feedback bump to occur. In Figure 5B.1, analogous results are found when PFC is instantaneously isolated from the rest of the network. We found similar results when we removed network links from the initial time (Fig. 4).

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Figure 5.

Effects of instantaneous link inactivation on feedback bumps. A, We selected initial states and nominal conditions leading to late-latency activity (dashed line, T* = none). We ran this network up to a chosen time T* and then instantaneously set the PFC→V1 link to zero. For I_max= 1.8 pA (A.1) the instantaneous inactivation prevented (T* = 50–300 ms) or suppressed (T* > 300 ms) the feedback bump in V1. Conversely, when a higher value of I_max is used (A.2, I_max= 3.0 pA), feedback activity can be restored in V1 despite the inactivation of the PFC→V1 link. B.1–2, Same as A.1–2 but for the isolation of PFC from the network. Note how the feedback bump is always prevented or suppressed irrespective of the value of I_max (compare Fig. 4). Similar results were obtained for all other set of connections (compare Fig. 4).

However, as we discussed earlier, the amplitude of the external stimulus to V1 (i.e., I_max) influences the genesis of the feedback bump. We thus repeated the previous experiments using a larger value of I_max= 3 pA in order to establish whether sufficiently large inputs can compensate for instantaneous inactivation of the network links. In all cases, except for the PFC→V1 link, we found that large stimuli cannot overcome instantaneous inactivation of a set of links, hence impairing the generation of a feedback bump. In Figure 5B.2, representative of most cases, it can be seen that a second bump is not formed, irrespective of the value T*. On the contrary, a feedback bump is still visible when inactivating the PFC→V1 link with a T* between 150 and 300 ms, showing that feedback activity can be restored by sufficiently large external drive in spite of the inactivation of this specific link.

In summary, the analyses performed using the morphing parameter shed light on the fact that the late activity bump is dependent on feedback connections. Upon external stimulation, V1 is activated and a feedforward pathway excites PPC and PFC. From these two areas, a late-latency activity bump appears in V1, mainly owing to an indirect pathway from PFC to PPC and then to V1. It turns out that direct feedback from PFC to V1 is instead not crucial for feedback bumps to be observed in V1, because the impact of reducing this link can be easily compensated by increasing stimulus strength.