The neocortex is a recurrent network of morphologically diverse inhibitory interneurons and excitatory pyramidal neurons (PYR) (Gouwens et al., 2019; Huang and Paul, 2019; Ascoli et al., 2008; Markram et al., 2004). The majority of interneurons can be assigned to biochemically defined classes, such as parvalbumin (PV), somatostatin (SST), and vasoactive intestinal polypeptide (VIP) positive cells (Tremblay et al., 2016). These neurons are distributed across layers and connected according to an intricate circuit diagram with intra- and interlaminar connections (Pfeffer et al., 2013; Jiang et al., 2015; Kätzel et al., 2011; Harris and Shepherd, 2015; Cardin, 2018). The discovery of regularities within the connectivity pattern of excitatory and inhibitory neurons prompted researchers to propose the existence of canonical microcircuits (Douglas and Martin, 2004; Beul and Hilgetag, 2014), which implement elementary computations that are repeated across the brain (Miller, 2016).

To identify such computations, research has focused on a better description of the functional role of individual neuron types by selective optogenetic activation and silencing of specific cell types (Tremblay et al., 2016; Kepecs and Fishell, 2014; Fishell and Kepecs, 2020; Maffei, 2017). These studies have not only highlighted an essential role of inhibitory neurons to balance excitation, but also recognized disinhibitory subcircuits, which release pyramidal neurons from strong inhibition (Fishell and Kepecs, 2020; Letzkus et al., 2015; Pi et al., 2013; Walker et al., 2016; Jackson et al., 2016; Fu et al., 2014). Moreover, neuronal oscillations in different frequency bands have been attributed to the activity of different interneuron types (Cardin et al., 2009; Sohal et al., 2009; Chen, 2017). While the computational properties of simplified circuits with multiple interneuron types have been investigated theoretically (Lee et al., 2017; Hertäg and Sprekeler, 2019; Garcia Del Molino et al., 2017; Lee, 2018), in the context of vision, locomotion, prediction errors, and whole-brain models (Lee and Mihalas, 2017; Dipoppa et al., 2018; Hertäg and Sprekeler, 2020; Bensaid et al., 2019), the dynamics of more complex networks comprising multiple layers with translaminar connectivity remain unexplored. Moreover, even though models have examined the emergence of oscillations in local (Lee, 2018; Domhof and Tiesinga, 2021; Veit et al., 2017) and whole-brain neuronal networks (Bensaid et al., 2019) composed of canonical microcircuits, it is unclear how firing rate descriptions of microcircuit function relate to oscillatory behavior of cortical networks, which can differ across cortical layers (Bastos et al., 2018; Adesnik, 2018; van Kerkoerle et al., 2014). This is crucial to interpret meso- and macroscopic signals from local field potential (LFP), electroencephalography (EEG) and magnetencephalography (MEG) recordings with respect to circuit function, where access to firing rate information is not possible.

To address these questions, we take a computational approach and isolate the role of different neurons in rate- and oscillation-based functioning of the layered microcircuit of the primary mouse visual cortex, for which the most comprehensive connectivity diagram to date is available (Jiang et al., 2015). Modeling permitted to go beyond of what is possible with available experimental tools and we not only characterized the effect of selective activation/suppression of different neuron types, but also perturbed specific connections and test their impact on microcircuit dynamics and response properties.

We found that the superficial and deep layers in the visual microcircuit can operate in two different states, triggered by the external activation of specific interneuron types and each with different excitation–inhibition balance: An inhibition dominated state controlled by SST neurons (SST state) and a disinhibited state that is attained by activation of PV and/or VIP neurons (PV/VIP states). By perturbing connections of different types of interneurons, we confirmed that disparities in recurrent connections within these inhibitory cell classes play a crucial role for the different EI balance in the two states. Two mutual inhibitory motifs that include SST, PV, and VIP cells serve as ultrasensitive or bistable switches with different sensitivity, which can toggle the microcircuit between the two states. Such a state change in one layer can propagate through translaminar connections to the other layer. Notably, we also found that in the inhibited regime slow beta-band oscillations were more prevalent especially in the deep layer, whereas in the disinhibited state fast gamma oscillations emerged predominately in the superficial layer, similar to experimental observations (Bastos et al., 2018; van Kerkoerle et al., 2014). We also provide a mechanistic explanation to other empirical findings such as asymmetric changes in oscillation power and frequency during state transitions as seen during the presentation of visual stimuli with increasing size (Chen, 2017; Veit et al., 2017). Thus, our results provide a comprehensive description of state-dependent effects of different inhibitory interneuron types with testable predictions and link rate- and oscillation-based accounts of microcircuit functioning.

In this study, we investigate the computational properties of a detailed microcircuit of the mouse visual cortex (Jiang et al., 2015; Figure 1A). This network consists of two different layers (superficial and deep), representing L2/3 and L5 of the primary visual cortex and each containing four different cell types that are connected within and between layers: excitatory pyramidal cells (PYR), and three different classes of inhibitory cells (PV, SST, and VIP). The connectivity was corrected for the different prevalence of each cell type (Jiang et al., 2015) and scaled with a global parameter (G) to approximate effective coupling changes (Deco et al., 2013; Jobst et al., 2017). This scaling was necessary, because the connectivity weights were empirically determined for individual cell pairs, whereas the effective interactions are mediated through entire cell populations for which the absolute cell count is not known. The variable G controls for the effective connectivity between cell types, such that a larger value of G implies a larger number of cells in the network. Thus, the connectivity strength between the modeled cell classes in our model also approximates the population size (Figure 1B). The population dynamics of each neuron type was given by a firing rate model (see Methods). The different excitatory–inhibitory feedback loops endowed the model with resonance properties, which was accompanied by oscillations in the presence of externally applied noise. This allowed us to study both firing rate and oscillatory behavior as measured by variations in power and frequency of the LFP, approximated by the rate of the pyramidal cell populations. We first examined spontaneous interactions across all neurons and then drove specific neuron classes, simulating input from remote cortical and subcortical sources.

Figure 1

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Origin of different firing rates and oscillations in deep and superficial layers

Next, we investigated the anatomical origin of firing rate and oscillation differences across layers by modifying specific connections. We targeted three connections, which show pronounced asymmetry across layers: PYR^sup → PYR^deep connection, translaminar projections of SST cells, and recurrent inhibition among PV neurons (PV–PV connections) (Figure 2A, Supplementary file 1d). The removal of the PYR^sup → PYR^deep connection strongly reduced the firing rate differences across the layers (Figure 2B). Removal of the translaminar SST connection, which only projects from deep to superficial layer had a smaller impact on the firing rate difference. Moreover, the disinhibitory PV–PV connections are considerably stronger in deep layer (Supplementary file 1d). When we changed the PV–PV connections such that their strength was the same in the deep and superficial layers, the firing rate difference between the two layers was also reduced. Modifying all three connections simultaneously almost completely abolished the rate inequality between layers. Likewise, differences in oscillation power in different frequency bands across layers were suppressed (Figure 2C, D, compare with Figure 1D, E). Thus, our model suggests that stronger excitation and disinhibition in the deep layer together with more inhibition in the superficial layer underlie the experimentally observed firing rate and oscillation power differences between deep and superficial layers.

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Two different states and state switching dynamics of the microcircuit

Thus far, we changed the relative prevalence of given interneuron types by scaling the connectivity matrix or silencing individual cell types or connections. Visual inspection of the microcircuit revealed two prominent mutual inhibition motifs. SST cells exhibit reciprocal inhibitory connections with PV cells and also VIP cells in each layer, which brings these cell pairs in competition with each other (Figure 1A). We hypothesized that driving one inhibitory cell type will functionally silence competing cells and toggle the circuit between different inhibitory states, which may differ in terms of PYR firing rate and their oscillation profile. To verify this hypothesis, we first tested whether input to VIP or PV cells can suppress SST activity. To this end, we enhanced the SST activity by injecting additional input to SST cells in both layers (I_ext = 5 Hz). Next, we stimulated either VIP or PV cells in both layers simultaneously, mimicking feedforward input from layer 4 to PV cells or feedback input from upstream areas to VIP cells, which may target superficial and deep layers simultaneously (van Kerkoerle et al., 2014; Pluta et al., 2019). Responses were measured from PYR and SST cells for different values of G (Figure 3A, B, see Figure 3—figure supplement 1A, B for responses of other cell types).

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When VIP cells were driven (Figure 3—figure supplement 1A), we found two main effects. First, VIP connections to SST cells suppressed SST rates, whereas PYR and PV cells initially increased their firing across both layers for sufficiently high G values (G > 150), because they were released from SST inhibition (Figure 3A and Figure 3—figure supplement 1A, G < 25). However, as VIP input increased, PYR and PV cells were gradually suppressed again in the superficial layer, while their firing rate was only slightly affected in the deep layer. This was caused by the inhibitory connection from VIP to PYR cells in the superficial layer and indeed its removal resulted in a response similar to the deep layer (Figure 1A, Figure 3—figure supplement 2). The presence and strength of disinhibition in the superficial layer depended on the baseline activity of SST cells, with higher SST rates, either due to high G values or caused by external drive, enhancing the PYR cell disinhibitory peak (Figure 3—figure supplement 1B). By contrast, when SST rates were too low, VIP input failed to further suppress SST activity and thus no disinhibition of PYR cells was seen.

Second, as G increased, the responses of SST cells became more switch like with sigmoidal curves in both layers, a hallmark of an ultrasensitive switch in many biological systems (Ferrell and Ha, 2014; Figure 3A). A similar sigmoidal decrease in SST firing rates with initial PYR disinhibition followed by inhibition was observed in both layers when only PV cells were driven (Figure 3B, Figure 3—figure supplement 1C). However, when PV cells were stimulated, switch like ultrasensitive responses occurred at larger G values as compared to VIP input, especially in the deep layer. By contrast, VIP cell-induced inhibition on PYR cells was weaker than PYR suppression mediated by PV cells (Figure 3A, B, Figure 3—figure supplement 1D).

In some biological systems ultrasensitivity with sigmoidal response curves is accompanied by bistable behavior (Ferrell, 2002), characterized by state transitions that are not reversed when the input is withdrawn. A telltale sign of bistability is the presence of hysteresis, that is the response curves change as a function of the direction in which the state change was triggered. To test for bistability in the microcircuit, we first applied an increasing current to VIP or PV cells in both layers simultaneously, followed by current in the decreasing direction for different values of the coupling parameter. We found that hysteresis appeared at sufficiently high G values, as visible by the appearance of noncongruent response curves for the up and down direction in all cell types of both layers for VIP (Figure 3C, Figure 3—figure supplement 3A) and PV input (Figure 3D, Figure 3—figure supplement 3B). Hysteresis in the deep layer for PV input required very strong input, even though a small hysteresis effect was observed for smaller G that was transmitted from superficial layers via translaminar connections (Figure 3—figure supplement 3C).

Inhibition-based ultrasensitivity and hysteresis commonly require strong inhibitory interactions between the components of the system (Ferrell, 2002). Therefore, we hypothesized that the enhanced mutual inhibitory connections between SST <> VIP and SST <> PV cells due to the scaling by G underlie the sigmoidal and hysteretic response curves. Indeed, selectively increasing these weights was sufficient for ultrasensitivity and hysteresis to appear in the microcircuit (Figure 3—figure supplement 4).

Next, to quantify the switching behavior of the microcircuit we fitted a Hill function to the SST firing rate response curve (see Methods) and estimated the Hill coefficient (n_H, Figure 3A), a measure for ultrasensitivity. We also estimated the area between the up and down branches of the response curves (h) to quantify hysteresis. We found that both n_H and h increased monotonically with G when either VIP cells (Figure 4A) or PV cells (Figure 4B) were stimulated. Within a limited range of G, the Hill coefficient (n_H) increased monotonically for the transition from SST to VIP or SST to PV states in both layers, while hysteresis was absent (h = 0). Hysteresis occurred at different values of G depending on the type of switch and layer, and caused an abrupt increase in n_H, which stabilized with large values of G and gave rise to a virtually binary state transition. A closer study of the bifurcation diagrams showed marked differences across switches and layers. As we increased G, the sensitivity increased rapidly for the VIP to SST switch in both layers. By contrast, a similar increase of sensitivity for the PV to SST switch occurred at higher values of G in the superficial layer and even higher G values in the deep layer (Figure 4C), as compared to the VIP to SST switch. Likewise, hysteresis onset increased from the VIP switch to the PV switch in the superficial and deep layer (Figure 4D). Note that the PV switch in the deep layer showed an early increase of h due to a propagated hysteresis effect from the superficial layer (G ~ 500, Figure 3—figure supplement 3C) and showed its own hysteresis increase later.

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Next, we tested whether the results on the VIP switch hold when external baseline input was added to both layers (Figure 4—figure supplement 1A). The same disinhibition effect was present in PYR cells and was enhanced with stronger baseline activity (Figure 4—figure supplement 1B). We also found the same sigmoidal SST suppression curve, which was shifted to higher values and displayed a larger hysteresis area with more baseline input (Figure 4—figure supplement 1C, D). However, the slope of the curve was preserved and the point of transition between ultrasensitivity and hysteresis was not altered.

Oscillations and switching dynamics

Next, we studied the outcome of the switching dynamics on oscillation frequency and power of the LFP. Both input to VIP and PV cells strongly increased the frequency of the dominant oscillation in superficial and deep layers, whereas the power of the oscillation peak generally decreased (Figure 5A–D). This is expected from a transition from an SST dominated state with low frequency to a high oscillation state in which the frequency is imposed by dominating PV activity (see above). Note that frequency and power show sigmoidal jumps similar to the rate transitions above (Figure 2I, J, VIP input).

Figure 5

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These results were obtained using fixed time constants ($\tau$) that were specified for each cell class according to the literature, which is based on the notion that fast and slow oscillations are generated using different interneuron populations with short- and long-time constants, respectively (Hyafil et al., 2015; Mejias et al., 2016). To examine whether the observed transition between slow and fast oscillations for the VIP switch in the superficial layer indeed depends on interneuron-specific time constants, we systematically studied different values of $\tau$ across all neuron types. To this end, we fixed $\tau$ at 10 ms for three neuron types and systematically varied the fourth type. When the SST time constant was altered, we found that the frequency difference between slow and fast oscillation states increased due to a frequency reduction within the slow oscillation state, dominated by SST cells (Figure 5E). In contrast, the frequency within the high activity state, dominated by PV cells, remained unchanged. Remarkably, a marked transition between a slow and fast oscillation state was still visible, even when the time constant across all neurons was the same. Increasing $\tau$ of PV cells had the opposite effect since the frequency of the high activity state decreased, while there was no change in frequency of the low activity state (Figure 5F). A variation of the VIP cell time constant had no influence on the oscillation frequency in either state, demonstrating again its negligible influence on oscillatory dynamics (Figure 5G). Finally, increasing the PYR time constant reduced the frequencies in both the slow and fast oscillation states (Figure 5H). The disinhibition peak was reduced, but remained at approximately double the frequency of the SST dominated baseline frequency for all tested PYR time constants. In summary, these results demonstrate that the appearance of a frequency jump during switching is independent of the time constants, even though the extent of the frequency change is modulated by differences in $\tau$.

Lateral inhibition switches the circuit to the SST state

Next, we studied switching dynamics in the microcircuit in the opposite direction, that is a transition from PV/VIP toward SST governed activity. To this end we applied input to SST cells in both layers (Figure 6A), mimicking the effect of lateral inhibition during surround suppression in the visual cortex, which was experimentally found to be mediated by horizontal pyramidal cell input from distant microcircuits within the same area to SST neurons (Veit et al., 2017; Adesnik et al., 2012). Driving SST cells resulted in a monotonic decay of activity of all other cell types in both layers for different values of G (Figure 6B), in line with several experimental studies (Chen, 2017; Dipoppa et al., 2018; Adesnik et al., 2012). Stimulation of SST cells also reduced the frequency of oscillations (Figure 6C–E). However, as we increased the input to SST cells the power of oscillations initially increased and subsequently decreased once PV cells were strongly suppressed. This finding replicates experimental results, in which stronger surround suppression is followed by a sudden transition from high frequency (gamma range) to lower frequency oscillations (high beta, low gamma range) and a concomitant increase in oscillatory power in mouse V1 (Chen, 2017; Veit et al., 2017).

Figure 6

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Input to PYR cells favors SST activity

Next, we measured the response of SST cells when PYR cells were stimulated in both layers (Figure 7A–C, Figure 7—figure supplement 1A). We studied the response of SST cells in three different scenarios. In the first scenario, we stimulated PYR cells, while VIP and PV cells received no external input. In this case, PYR input strongly increased SST activity (Figure 7A) (and to a lesser extent PV rates, see Figure 7—figure supplement 1B) in both layers, while VIP cells were suppressed (Figure 7—figure supplement 1B). Stimulation of PYR cells also increased the population oscillation frequency, whereas oscillation power decreased (Figure 7—figure supplement 1C). In a second scenario, we stimulated the PYR cells, while VIP cells received a constant external input. In this case, sufficiently high PYR input and G value caused a jump back to higher SST activity in both layers (Figure 7B) with a sudden suppression of PV and VIP activity (Figure 7—figure supplement 2A, B). In contrast to the PYR cells, stimulation of VIP cells affected the oscillations and their power in a nonmonotonic fashion: the oscillation frequency increased initially, but dropped (superficial layer) or saturated (deep layer) at the transition to the SST state, while oscillatory power declined and suddenly increased with the switch to SST activity (Figure 7—figure supplement 2C). Finally, we also stimulated PYR cells while only PV cells received a constant external input. In this scenario, we obtained results similar to those obtained in the second scenario (Figure 7C, Figure 7—figure supplement 3A–C). These findings are consistent with recent optogenetic experiments in which strong PYR drive was associated with high SST activity and comparatively low PV rates (Hakim et al., 2018).

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Pyramidal cells also drive each other via recurrent excitatory connections, albeit such connectivity can be sparse (Jiang et al., 2015). To test the impact of locally recurrent excitation on the switching properties of the circuit, we systematically changed the connectivity between PYR cells in both layers (Figure 7—figure supplement 4A). With stronger weights, the sigmoidal SST response curve to VIP input was shifted to the right, while at sufficient strength network activity exploded (Figure 7—figure supplement 4B). Surprisingly, the switching dynamics was preserved even in the absence of recurrent excitation, highlighting the fact that the switch is implemented by interactions among the three inhibitory neurons types. The oscillation frequency in the high activation state of the VIP switch decreased with more recurrent excitation (Figure 7—figure supplement 4C).

State changes propagate between superficial and deep layers

Next, we addressed the question whether a state transition triggered in only one layer propagates to the other layer across translaminar connectivity. To this end, we induced the same state changes as studied above (Figures 3 and 4) by applying current to specific inhibitory neurons in only the superficial or deep layer and measured the response of pyramidal cells in the opposite layer (Figure 8). In addition, we removed translaminar connections to test their role in the state propagation (only connections with an impact are shown). When the circuit displayed high SST activity, input to VIP cells in the superficial layer showed a disinhibitory PYR rate increase in the deep layer, which was mainly due to a translaminar reduction of SST activity rather than a direct drive from superficial to deep PYR cells (Figure 8A). We obtained a similar result in the superficial layer after driving the deep layer VIP cells (Figure 8B). Likewise, input to PV cells in the superficial layer caused disinhibition in the deep layer within a certain input range which was abolished by removing translaminar SST connections (Figure 8C). Notably, translaminar PV connections reduce the disinhibition effect as their removal strongly augmented PYR activity. The same effects were found in the superficial layer after PV input to the deep layer (Figure 8D). When we set the circuit to a VIP dominated state (I_ext to VIP in both layers = 40Hz) and applied current to SST cells in the superficial layer, PYR cell activity was suppressed in the deep layer due to a direct translaminar SST connection (Figure 8E). The same results held true for SST input to the deep layer (Figure 8F). Finally, a similar suppressive effect on PYR cell rates that propagated to the other layer after input to SST cells was found in the presence of the PV dominated state (I_ext to PV in both layers = 40Hz), again due to the translaminar SST connections (Figure 8G, H). In summary, these results demonstrate that transitions between disinhibited and inhibited states triggered in one layer can propagate to the opposite layer and this interlayer interaction is primarily governed by translaminar SST connections.

Figure 8

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Feedforward and feedback input

The above model results mimic circuit responses to optogenetic stimulation of specific cell types in living neuronal networks. However, visual stimulation of mouse V1 drives local circuits through feedforward and feedback drive. Superficial and deep layers receive feedback drive from different layers in higher areas, while feedforward input to superficial layers is provided by layer 4 of V1 circuits. The extent of this drive through PYR cells is cell specific, as for instance L4 preferentially drives PYR and PV cells in superficial layers (Adesnik et al., 2012), while feedback input from the anterior cingulate cortex mostly targets VIP cells (Zhang et al., 2014; Figure 9A).

Figure 9

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To model the effects of feedforward and feedback inputs, we scaled the weight of external input to all cells according to the empirical data on feedforward and feedback inputs (Adesnik et al., 2012; Zhang et al., 2014; Figure 9A). For small G values all cell types enhanced their activity for both types of drive, while we found a gradual suppression of SST cells for larger values (Figure 9B, C). This finding was more pronounced with feedforward input indicating stronger recruitment of inhibition. As the G value increased, the rise of PYR cell activity was slowed or turned into suppression for the feedforward drive. In both input models we observed a suppression of the spontaneous low-frequency oscillation and a corresponding enhancement of higher frequency oscillations due to strong PV and VIP activation (Figure 9D). These results are consistent with the experimental literature, which reported alpha oscillation suppression and gamma oscillation enhancement upon both visual stimulation (van Kerkoerle et al., 2014) and feedback associated visual attention (Klimesch, 2012).

Recurrent inhibitory connectivity differentiates inhibited from disinhibited states

The connectivity between different interneuron types and pyramidal cells allows the microcircuit to switch between a disinhibited state with high PYR cell firing and an inhibited state with reduced PYR activity, as we show above. However, for a deeper understanding of this switch one important question remains: Why are PYR cells more inhibited in the SST dominated regime as compared to the PV governed regime? To this end, we examined the mouse V1 connectivity matrix and found that there is a strong asymmetry between recurrent connections among PV and SST cells. While connections between PV cells in each layer are the strongest within the entire matrix, recurrent connections among SST cells are entirely absent (Figure 10A, Supplementary file 1d). Thus, we hypothesized that the strong self-inhibition of PV cells effectively reduces their inhibitory effect on PYR cells, while SST cells can elicit comparatively stronger inhibition on PYR cells due to the absence of self-inhibition. If this was true, exchanging the recurrent connections, that is removing PV self-connections and add them to SST cells may invert their role in microcircuit state switching (Figure 10A). In simulations with the inverted connectivity scheme we found that input to SST cells indeed created a disinhibition peak in the PYR cell response (Figure 10B, left), similar to VIP input in the original connectivity scheme (Figure 3A, Figure 4—figure supplement 1B), while PV and VIP cells showed a monotonic suppression (Figure 10B, right, Figure 10—figure supplements 1 and 2A). Likewise, driving VIP or PV neurons was followed by inhibition of all the other cell types, similar to the effect of SST input in the original case (Figure 10C, D, Figure 10—figure supplement Figure 10—figure supplements 1 and 2B, C). A notable exception is disinhibition in deep layer after PV input (Figure 10—figure supplement 2C). These results indeed suggest that inhibitory state-dependent alterations in excitation–inhibition balance, which are at the core of the switching properties of the microcircuit, are due to large differences in PV and SST self-connectivity (Figure 10E).

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In this study, we showed that superficial and deep layers of the mouse V1 microcircuit are endowed with two switch mechanisms that can toggle the pyramidal cells (output of the microcircuit) between high (disinhibited) and low activity states (inhibited) across superficial and deep layers (Figure 10F). The underlying switching mechanics are realized by the interactions among the three interneuron types (PV, SST, and VIP), which compete for inhibitory influence on pyramidal cells. In the inhibited state, SST cells dominate inhibition which serve as ‘master regulators’ by strongly connecting and inhibiting activity of pyramidal cells and other interneurons in the circuit (Jiang et al., 2015; Chen, 2017; Fino and Yuste, 2011; Urban-Ciecko and Barth, 2016; Naka et al., 2019). In the disinhibited state, excitation is mainly balanced by PV cells (Ferguson and Gao, 2018) and to a lesser extent by VIP neurons (Garcia-Junco-Clemente et al., 2017), whereas SST activity is reduced.

The current manuscript is a computational study and thus no data have been generated for this manuscript. The empirical connectivity matrix of the microcircuit is provided in Supplementary File 1d. Modeling code is uploaded as Source Code Files 1 and 2.

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Author details

1. Gerald Hahn

   Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain

   Contribution

   Conceptualization, Software, Formal analysis, Investigation, Visualization, Methodology, Writing - original draft, Writing – review and editing

   For correspondence

   gerald.a.hahn@gmail.com

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-7069-0639

2. Arvind Kumar

   Computational Science and Technology, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden

   Contribution

   Conceptualization, Investigation, Methodology, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-8044-9195

3. Helmut Schmidt

   Brain Networks Group, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany

   Contribution

   Conceptualization, Methodology, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-2264-0821

4. Thomas R Knösche

   1. Brain Networks Group, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
   2. Institute of Biomedical Engineering and Informatics, Department of Computer Science and Automation, Technische Universität Ilmenau, Ilmenau, Germany

   Contribution

   Conceptualization, Supervision, Funding acquisition, Methodology, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-9668-3261

5. Gustavo Deco

   1. Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain
   2. Institució Catalana de la Recerca i Estudis Avançats, Barcelona, Spain
   3. Department of Neuropsychology, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
   4. School of Psychological Sciences, Turner Institute for Brain and Mental Health, Monash University, Melbourne, Australia

   Contribution

   Conceptualization, Supervision, Funding acquisition, Writing – review and editing

   Competing interests

   No competing interests declared

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