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Integrative frontal-parietal dynamics supporting cognitive control

  1. Derek Evan Nee  Is a corresponding author
  1. Department of Psychology, Florida State University, United States
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Cite this article as: eLife 2021;10:e57244 doi: 10.7554/eLife.57244

Abstract

Coordinating among the demands of the external environment and internal plans requires cognitive control supported by a fronto-parietal control network (FPCN). Evidence suggests that multiple control systems span the FPCN whose operations are poorly understood. Previously (Nee and D’Esposito, 2016; 2017), we detailed frontal dynamics that support control processing, but left open their role in broader cortical function. Here, I show that the FPCN consists of an external/present-oriented to internal/future-oriented cortical gradient extending outwardly from sensory-motor cortices. Areas at the ends of this gradient act in a segregative manner, exciting areas at the same level, but suppressing areas at different levels. By contrast, areas in the middle of the gradient excite areas at all levels, promoting integration of control processing. Individual differences in integrative dynamics predict higher level cognitive ability and amenability to neuromodulation. These data suggest that an intermediary zone within the FPCN underlies integrative processing that supports cognitive control.

Introduction

While habits rigidly link stimuli to actions, cognitive control enables flexible behavior that can adapt to present conditions, prevailing contexts, and future plans (Miller and Cohen, 2001; Logan and Gordon, 2001; Egner, 2017; Badre and Nee, 2018). The human capacity for flexible behavior is thought to arise from the expansion of transmodal cortices that are synaptically distant from primary cortices (Mesulam, 1998; Margulies et al., 2016; Huntenburg et al., 2018) such that synaptic distance may untether transmodal areas from the processing hierarchies that link stimulus to action in canonical circuits (Buckner and Krienen, 2013). Such transmodal areas are prominent in the prefrontal (PFC) and posterior parietal cortices (PPC).

The relationship between cognitive control and areas of the PFC and PPC is so ubiquitous that a co-active set of PFC-PPC areas is frequently termed the ‘frontoparietal control network’ (FPCN) (Vincent et al., 2008; Braga and Buckner, 2017; Yeo et al., 2011; Dixon et al., 2018; Murphy et al., 2020). Recognizing their involvement across a diverse array of tasks, a similar constellation of areas is also referred to as the 'multiple demand network' (Duncan and Owen, 2000; Duncan, 2010; Duncan, 2013). This network is thought to implement cognitive control by flexibly coordinating activity among diverse brain systems to integrate brain-wide processing in a goal-directed manner (Murphy et al., 2020; Cole et al., 2013; Cocchi et al., 2013). The integrative capacity of these areas enables them to reconfigure the brain into difficult-to-reach states (Gu et al., 2015), thereby conferring the flexibility needed to act in an adaptive, rather than habitual manner. In this way, the integrative capacity of cognitive control is central to higher level cognition.

Mounting evidence suggests that there is not a single FPCN, but multiple networks (Braga and Buckner, 2017; Yeo et al., 2011; Dixon et al., 2018; Murphy et al., 2020). These networks are situated upon global brain gradients such that increasingly sensory-motor distal areas of the PFC and PPC are increasingly distant from areas of the brain involved in external processing (Margulies et al., 2016; Huntenburg et al., 2018). This has led to the proposal that the more sensory-motor distal aspects of the FPCN are involved in more internally oriented control processes (Dixon et al., 2018; Murphy et al., 2020). The proposal that gradients in the PFC and PPC can be classed along an external-internal axis (Sormaz et al., 2018; Buckner and DiNicola, 2019) offers a unifying perspective of the different forms of cognitive control which has remained elusive (Badre and Nee, 2018). (A ‘gradient’ refers to a change in a property along an axis. With respect to cortex, a functional gradient means that functions vary in a roughly monotonic fashion with cortical distance along a spatial axis. The resolution of the gradient, or in other words, the steps along the axes, may be discrete and areal, or approach continuity. The present study remains silent regarding the resolution of these gradients, and takes the weak position that functions change along cortical axes at some unknown rate/resolution.)

Ultimately, cognitive control is grounded in behavior. This means that internally oriented aspects of control, such as those that plan for the future, must be integrated with externally oriented aspects of control, such as those that select appropriate sensory features for processing and action. How and where such integration takes place is an open question. One possibility is that the control gradient that expands outwardly from sensory-motor cortices doubles as an integration gradient such that the most sensory-motor distal areas are the most integrative. This possibility is consistent with theories of PFC function that posit that the rostral-most (i.e. most sensory-motor distal) areas act as apex controllers that exert widespread influences that can coordinate brain-wide activity under a single goal (Badre and D'Esposito, 2009). Another possibility is that a cascade of control signals progresses from sensory-motor distal to sensory-motor proximal areas with integration of those signals progressing along the way (Koechlin et al., 2003; Koechlin and Summerfield, 2007). A third possibility is that those areas situated between externally oriented and internally oriented control are responsible for their integration. This last possibility is consistent with recent data indicating the importance of mid-lateral PFC in integrative control (Badre and Nee, 2018; Cocchi et al., 2014; Nee and D'Esposito, 2016; Nee and D'Esposito, 2017). This latter possibility would suggest a nested structure to gradients in the brain: just as the FPCN is situated in intermediary zones of the brain to flexibly guide sensation to action, so too are intermediary zones of the FPCN essential for flexibly guiding control itself.

Here, two datasets that have demonstrated macroscale gradients of cognitive control in the PFC (Nee and D'Esposito, 2016; Nee and D'Esposito, 2017) are examined to investigate dynamics in the broader FPCN. These datasets employ a Comprehensive Control Task that manipulates three forms of cognitive control across two stimulus domains to precisely map the functional underpinnings of areas within the FPCN, providing a foundation from which to interpret network dynamics. The same gradients of activation observed in the PFC are mirrored in the PPC and tied to specific control functions and behavioral timescales. Interactions among areas of the PFC and PPC are measured by examining both static and dynamic indices of effective connectivity, revealing how control integrates processing to support adaptive behavior. Finally, static and dynamic measures of integration are used to predict trait-level cognitive ability, and susceptibility of cognitive control to neuromodulation showing the importance of integration for higher-level cognition and interventions more broadly. Collectively, these analyses elucidate the integrative organization of the FPCN whose insights may be useful to understand other transmodal networks.

Results

Two independent samples (n = 24, n = 25) completed a Comprehensive Control Task that independently manipulated demands on stimulus domain (verbal vs spatial processing), sensory-motor control (associating stimuli to actions), contextual control (context-dependence of appropriate stimulus-response associations), and temporal control (planning for the future). These processes can be classed along an external-internal continuum such that sensory-motor control acts upon the sensory environment, contextual control informs those actions based upon an internalized rule, and temporal control informs the rule based upon an additional internalized representation (Figure 1). These processes can be classed by timescale such that sensory-motor control specifies an action for the present stimulus, contextual control specifies a prevailing task context, and temporal control sustains a prospective memory for the future. More generally, the processes are classed by abstraction with sensory-motor control being the most concrete and temporal control being the most abstract. A more complete description of the task can be found in the Materials and methods, and the original reports of these data (Nee and D'Esposito, 2016; Nee and D'Esposito, 2017). Behavioral data are reported in Supplemental Material.

Comprehensive control task.

On each trial, participants observed a letter at a spatial location and made a keypress in response. Keypresses mapped onto ‘yes’/'no' responses. Participants either responded ‘no’ to the stimulus without regard to the stimulus features, or made a choice response based on a pre-learned sequence to a color cued feature (T-A-B-L-E-T for letters; star trace for locations) thereby engaging sensory-motor control. The correct response was either based upon a reference stimulus for which participants responded regarding whether the present stimulus followed a reference stimulus (sequence-back), or whether the stimulus was the start of the sequence (sequence-start). Switching among these tasks engages contextual control. Finally, the reference stimulus could either be the last item presented, or a distant item. In the latter case, the reference item had to be sustained over several trials requiring temporal control to prepare for the future. Colored frames indicated relevant stimulus features (letter or location), whereas frame shapes indicated cognitive control demands which were manipulated in the middle of each block (sub-task). Stimulus domain and cognitive control demands were independently manipulated in a factorial design wherein orthogonal contrasts separately isolated sensory-motor control, contextual control, and temporal control. Refer to the Materials and methods and Nee and D'Esposito, 2016; Nee and D'Esposito, 2017 for a more complete description.

The analyses that follow proceed in two parts. First, areas within the FPCN are functionally mapped and related to behavior by contrasting activation and performance across different task conditions. Areas within the PFC have been previously described (Nee and D'Esposito, 2016; Nee and D'Esposito, 2017), and are re-depicted here to note parallels among the PFC and PPC. A prior study (Choi et al., 2018) suggested a mirrored organization of the PFC and PPC with respect to cognitive control which the analyses here seek to replicate and extend by relating activations directly to behavioral performance. These analyses are aimed to provide a functional foundation for network-based analyses to follow. Second, interactions among areas in the FPCN are examined to address the focus of the current study of how integrative dynamics within the FPCN support cognitive control. These dynamics are then related to individual differences in trait-level cognitive ability and amenability to neuromodulation to establish their importance more broadly.

Mirrored control gradients in the PFC and PPC

Figure 2A depicts the voxel-wise, whole-brain activations for each cognitive control contrast. In the lateral PFC, activations progressed in a caudal to rostral fashion as a function of abstraction of cognitive control from sensory-motor control, to contextual control, to temporal control (Nee and D'Esposito, 2016; Nee and D'Esposito, 2017). In the PPC, activations progressed in a rostral to caudo-lateral fashion as a function of abstraction of cognitive control (Choi et al., 2018). That is, in both the lateral PFC and PPC, increasingly abstract control was associated with activations increasingly distant from sensory-motor cortices of the pre/post-central gyri.

Figure 2 with 2 supplements see all
Control sub-networks.

(A) Activations for temporal control (red), contextual control (green), and sensory-motor control (blue). Activations are depicted separately for each sample, as well as the samples combined. (B) Activations overlaid to demonstrate the gradient of cognitive control. Spheres indicate the location of regions-of-interest based upon activation peaks. (C) Overlap between activation contrasts (red – temporal control; green – contextual control; blue – sensory-motor control) and the 17-network parcellation described by Yeo et al. FPl – lateral frontal pole; MFG – middle frontal gyrus; VLPFC – ventrolateral prefrontal cortex; cMFG – caudal middle frontal gyrus; IFJ – inferior frontal junction; SFS – superior frontal sulcus; aIPS – anterior intra-parietal sulcus; IPL – inferior parietal lobule; mIPS – mid intra-parietal sulcus; SPL – superior parietal lobule; DMN – default-mode network; DAN – dorsal attention network; SAL – salience network; FPN – frontoparietal network.

Different cognitive control demands produced overlapping activations eliciting gradients along the lateral surface (Figure 2B). Although the extent of overlap depends upon preprocessing (e.g. smoothing, volumetric vs surface processing), similar gradients of activation were observed with reduced volumetric smoothing (Figure 2—figure supplement 1), as well as with minimal, surface-based smoothing (Figure 2—figure supplement 2). The mirrored gradients observed in the lateral PFC and PPC are suggestive of a mirrored functional organization extending outwardly from sensory-motor areas consistent with macroscale gradients of cortical function (Mesulam, 1998; Margulies et al., 2016; Huntenburg et al., 2018).

Previous work has suggested that the FPCN can be fractionated into sub-networks (Braga and Buckner, 2017; Yeo et al., 2011; Dixon et al., 2018; Murphy et al., 2020). In particular, it has been proposed that an FPCN network A acts as an intermediary between the FPCN and internally oriented ‘default-mode’ network (DMN). On the other hand, FPCN network B is hypothesized to act as an intermediary to the externally-oriented dorsal attention network (DAN) (Dixon et al., 2018; Murphy et al., 2020). However, precise functional descriptions of these sub-networks remains unclear. This is because prior work has fractionated the FPCN based on co-activation patterns rather than processing demands. A marked benefit of the Comprehensive Control Task is the ability to dissociate multiple control processes in a single, well-controlled paradigm. To examine how the task contrasts align with co-activation defined networks, the overlap among activations and the Yeo et al., 2011 17-network parcellation was computed. In addition to considering sub-networks of the FPCN, other relevant sub-networks were also considered including the DMN, DAN, and salience networks (SAL). Across both samples, areas activated by temporal control aligned most closely with FPCN A (Figure 2C). By contrast, areas activated by both contextual control and sensory-motor control aligned most closely with FPCN B. While areas activated by contextual control also activated FPCN A to some degree, areas activated by sensory-motor control activated the DAN more extensively. Collectively, these data suggest that the task contrasts fractionate the FPCN into sub-networks along an external (DAN -> FPCN B) to internal (FPCN A -> DMN) axis. Furthermore, these observations offer more precise functional descriptions of previously fractionated sub-networks.

To better characterize the functions of the areas within these sub-networks, spherical regions-of-interest (ROIs) were centered on activation peaks of the contrasts (Figure 2B; Table 1). Activations across the eight conditions of the factorial design are depicted in Figure 3A providing a graphical profile of the activation patterns in each area. PFC-PPC areas closer to sensory-motor cortex (blue, green) tended to be sensitive to multiple demands activating for both sensory-motor and contextual control. These areas also had a tendency to activate preferentially to one stimulus domain or the other. By contrast, areas distal from sensory-motor cortices (red) tended to be more specialized toward temporal control and did not show a preference for stimulus domain.

Figure 3 with 1 supplement see all
Activation profiles.

Activations across the eight conditions of the task design are depicted as radar plots (SB – spatial baseline; VB – verbal baseline; SS – spatial switching; VS – verbal switching; SP – spatial planning; VP – verbal planning; SD – spatial dual; VD – verbal dual). The top panel depicts idealized profiles for areas sensitive solely to temporal control (red), contextual control (green), sensory-motor control (blue), verbal stimulus domain (purple), and spatial stimulus domain (orange). Inset: results of multi-dimensional scaling of the activation profiles across regions. Colored by abstraction refers to coloring as a function of position along the control gradient (blue – sensory-motor proximal; green – intermediary; red – sensory-motor distal). Colored by stim domain refers to coloring as a function of sensitivity to stimulus domains (orange – spatial; purple – verbal; gray – neither).

Table 1
Coordinates of regions-of-interest reported in MNI space.

FPl – lateral frontal pole; MFG – middle frontal gyrus; VLPFC – ventrolateral prefrontal cortex; cMFG – caudal middle frontal gyrus; IFJ – inferior frontal junction; SFS – superior frontal sulcus; IPL – inferior parietal lobule; mIPS – mid intra-parietal sulcus; aIPS – anterior intra-parietal sulcus; SPL – superior parietal lobule.

Sample 1Sample 2
AreaXYZXYZ
FPl−44484−36520
MFG−382844−363438
VLPFC−522028−423020
cMFG−341060−30656
IFJ−38626−421024
SFS−22054−20056
IPL−54−5044−56−5242
mIPS−28−6042−26−5644
aIPS−34−4046−30−4242
SPL−14−5264−12−6058

To provide a more compact, data-driven description of these profiles, the PFC-PPC ROI data ((participants*conditions) x areas) were subjected to multi-dimensional scaling (MDS). Two dimensions accounted for 89% of the variance of the data (Figure 3B). The first dimension recapitulated the abstraction gradient, placing PFC-PPC areas proximal to sensory-motor cortices on one end of the dimension (e.g. superior frontal sulcus - SFS; anterior intra-parietal sulcus - aIPS), and areas distal to sensory-motor cortices on the other (e.g. middle frontal gyrus - MFG; inferior parietal lobule - IPL). Hence, across the different conditions of the task, this dimension collapsed abstraction of cognitive control into a single axis. The second dimension reflected sensitivity to stimulus domain with areas preferentially engaged by spatial processing at one end and areas preferentially engaged by verbal processing at the other. These patterns were also present with reduced smoothing (Figure 3—figure supplement 1). These data are consistent with the idea that the cortex is organized along two principle gradients reflecting abstraction and modality (Mesulam, 1998; Margulies et al., 2016; Huntenburg et al., 2018). Collectively, these dimensions provided a data-driven way to operationalize the factors of the task design.

Control gradient is related to present-future behavior

Next, areas were characterized as a function of their relationship to behavior in the task. Activations were assessed during the sub-task phases that manipulated cognitive control demands (Figure 1). Cognitive control behaviors were expressed as trial-wise reaction times both during the sub-task phases, as well as during return trials that immediately followed the sub-task phase. For example, temporal control requires sustaining an internal representation (i.e. a reference stimulus) during the sub-task phase to be utilized on the return trial (i.e. does the stimulus on the return trial follow the reference stimulus in the sequence?). Therefore, activations during temporal control that sustain the internal representation would be expected to relate to behavior on the return trial (i.e. return trial reaction times), but not necessarily the sub-task trials (i.e. sub-task trial reaction times). Hence, activations can be separately correlated with behavior measured at the same time as the activations (sub-task trials: present behavior) or the behavior for which the activations are preparing (return trials: future behavior; see Materials and methods).

In the PFC, increasing rostral areas were increasingly associated with future behavior and decreasingly associated with present behavior (Nee and D'Esposito, 2016; Nee and D'Esposito, 2017). This pattern was mirrored in the PPC (Figure 4A) such that sensory-motor proximal areas (aIPS, SPL) were positively associated with present, but not future behavior, while sensory-motor distal areas (IPL) were positively associated with future, but not present behavior. Areas in-between (mIPS) were associated with both present and future behavior. These patterns were confirmed with voxel-wise analyses (Figure 4B). These data are consistent with an integrative role of contextual control areas positioned between internal, future-oriented temporal control areas and external, present-oriented sensory-motor control areas.

Figure 4 with 1 supplement see all
Brain-behavior relationships.

(A) Top: Repeated measures correlations between activation and present behavior (i.e. behavior during sub-task trials; see Figure 1). Areas related to sensory-motor control (blue) and contextual control (green) showed positive associations, while areas related to temporal control (red) showed no or negative associations. Bottom: Repeated measures correlations between activation and future behavior (i.e. behavior during return trials; see Figure 1). Areas related to temporal control (red) and contextual control (green) tended to show positive associations, while areas related to sensory-motor control (blue) tended to show no associations. ** indicates Bonferroni-corrected p<0.05. * indicates uncorrected p<0.05. (B) Voxel-wise partial correlations between activation and present behavior (blue), future behavior (red), and both (green). Results are visualized at p<0.001 with 124 voxel cluster extent. (C) Linear mixed effects modeling of the activation-present behavior slope (top) and activation-future behavior slope (bottom) using the first dimension of multi-dimensional scaling (MDS) depicted in Figure 3. * indicates p<0.05; ** indicates p<0.005.

To better quantify these relationships, the abstraction dimension uncovered by MDS was used to account for areal relationships with behavior. Separate linear mixed effects models were fit for the activation-present behavior and activation-future behavior relationships across areas. Consistent with the impressions above, the more abstract the PFC-PPC area, the less it related to current behavior (sample 1: t(238) = −9.18, p=2.19e-17; sample 2: t(248) = −8.73, p=3.81e-16) and more it related to future behavior (sample 1: t(238) = 2.72, p=0.007; sample 2: t(248) = 4.39, p=0.00002). These patterns were also present with reduced smoothing (Figure 4—figure supplement 1). Moreover, the abstraction-behavior relationships were observed when each stimulus domain was treated separately consistent with domain-generality of these patterns (verbal abstraction-current sample 1: t(238) = −6.61, p=2.52e-10; sample 2: t(248) = −8.11, p=2.38e-14; spatial abstraction-current sample 1: t(238) = −10.21, p=1.55e-20; sample 2: t(248) = −7.87, p=1.07e-13; verbal abstraction-future sample 1: t(238) = 3.05, p=0.003; sample 2: t(248) = 3.77, p=0.0002; spatial abstraction-future sample 1: t(238) = 2.29, p=0.01; sample 2: t(248) = 4.23, p=3.32e-5). Hence, these analyses indicate that progressively abstract areas in both the PFC and PPC are increasingly future-oriented.

Establishing source-target relationships

Next, interactions among PFC-PPC areas were examined. Control is embodied by source-target relationships such that controllers affect processing in controlled targets. Effective connectivity, which estimates directed influences, offers the most straightforward means to assess such source-target relationships. There are both static (stationary) and dynamic (non-stationary) interactions among the PFC and PPC (Cole et al., 2013; Cole et al., 2014; Krienen et al., 2014; Gratton et al., 2016). To examine static interactions and their directed nature, a biophysically plausible generative model of how neuronal interactions produce cross spectra in the fMRI signal was employed (Friston et al., 2014; Razi et al., 2015; Razi et al., 2017).

The method was validated in two ways. First, the method was applied to the task data of both samples and estimates of directed interactions were compared across the samples. These estimates had excellent correspondence across the samples (r = 0.96; Figure 5, top). Second, estimates of directed interactions were used to examine the putative pre-eminent role of the PFC in cognitive control (Miller and Cohen, 2001). Cognitive control is exemplified by source-target relationships such that drivers of control asymmetrically influence targets. To characterize such asymmetries on the lobular level, the magnitude of effective connectivity (i.e. deviations from zero) were separately combined for each of the 2 × 2 combinations of source-target lobe (i.e. PFC->PFC, PFC->PPC, PPC->PFC, PPC->PPC). In both samples, the magnitude of effective connectivity arising from the PFC was significantly stronger than that arising from the PPC (sample 1: F(1,23) = 7.1, p=0.0138; sample 2: F(1,24) = 6.26, p=0.0195; Figure 5, bottom). Such data are consistent with the idea that the PFC is the primary driver of PFC-PPC dynamics. Collectively, these data indicate that the method produces replicable and theoretically sensible estimates.

Figure 5 with 1 supplement see all
Estimates of static effective connectivity.

Bars are color coded by source>target lobe pairs. Top: estimates for each connection. Inset: correlation among sample averaged parameter estimates. Bottom: estimates averaged over source>target lobe pairs. Influences arising from the PFC were significantly stronger in magnitude than those arising from the PPC. * indicates p<0.05.

An intermediary integration zone of control

To examine integration of control signals, source-target relationships were assessed at the network level. Areas were assigned into networks based upon their position along the control gradient (i.e. as colored-coded in the analyses above; sensory-motor control network (blue): SFS, IFJ, SPL, aIPS; contextual control network (green): cMFG, VLPFC, mIPS; temporal control network (red): MFG, FPl, IPL). In both samples, a significant source x target network interaction was observed in effective connectivity (sample 1: F(4,46) = 25.1, p=4.56e-14; sample 2: F(4,48) = 17.81, p=5.74e-11; Figure 6). In all cases, within-network directed interactions were significant and numerically the most positive connections for each network. This is to be expected given that areas within a cortical network are assumed to excite one another, and also provides validation of the network assignment. For both nodes in the abstract, temporal control network and the concrete, sensory-motor control network, between-network directed interactions tended to be negative. Such patterns suggest that these networks dampen activity in other networks, thereby segregating processing. By contrast, between-network directed interactions arising from contextual control nodes were significantly positive (Figure 6 – top panel). Control analyses revealed that these dynamics were not driven by task-related signals since regressing out task-related activity demonstrated the same pattern of results (Figure 6—figure supplement 1). Such patterns suggest that the contextual control network elevates activity in other networks, thereby promoting integrative processing.

Figure 6 with 2 supplements see all
Static network interactions.

Top: Effective connectivity was averaged as a function of source>target network. Bars are colored as a function of the source network: TC – temporal control (red); CC – contextual control (green); SC – sensory-motor control (blue). ** denotes Bonferroni-corrected p<0.05. * denotes p<0.05 uncorrected. Middle: Effective connectivity organized by abstraction (first dimension of multi-dimensional scaling depicted in Figure 3). Circles denote positive interactions and inverted triangles denote negative interactions. Markers are scaled by the magnitude of effective connectivity. Markers are colored by the network assignments. Bottom: Data re-depicted to highlight the quadratic effect of source abstraction. Linear effects of target abstraction, source abstraction, and target x source abstraction have been regressed out to isolate the quadratic effect of source abstraction demonstrating that mean (positive) effective connectivity peaks at areas in the middle of the abstraction gradient.

Figure 6 (middle panel) depicts these patterns in a more continuous form that does not depend upon assigning nodes to networks. Source-target relationships are depicted as a function of the abstraction dimension uncovered by MDS and described by the magnitude (marker size) and sign (marker shape: circle – positive, inverted triangle – negative) of effective connectivity. At the ends of the axis, positive effective connectivity is predominant when sources and targets are at a similar abstraction level (e.g. bottom left and top right), while negative effective connectivity is predominant when sources and targets are at different abstraction levels (e.g. top left and bottom right). By contrast, positive effective connectivity is observed throughout when sources are at the middle of the axis (i.e. columns of circles toward the middle of the horizontal axis). To better quantify these effects, linear mixed effects models were fit using the abstraction dimension uncovered by MDS. The model sought to explain effective connectivity as a function of abstraction of the source area, abstraction of the target area, and the interaction among source and target abstraction. Additionally, quadratic forms of each of these effects were included to capture U shaped and inverted-U shaped relationships. In both samples, a significant source x target abstraction interaction was observed (sample 1: t(1097) = 5.08, p=4.43e-07; sample 2: t(1143) = 4.94, p=9.03e-07) reflecting that network interactions depend upon whether sources and targets are drawn from similar/different levels of abstraction. Critically, there was also a quadratic effect of source abstraction (sample 1: t(1097) = −4.51, p=7.05e-06; sample 2: t(1143) = −4.52, p=6.99e-06), which was driven by areas at mid-levels of abstraction having consistently positive outwards influences, while areas at high and low levels of abstraction demonstrated both positive and negative outward influences which yielded lower net influences when averaged (Figure 6 – bottom panel). No other effects were significant across samples. The same pattern of results was observed with reduced smoothing (Figure 6—figure supplement 2). Collectively, these patterns are consistent with the segregation/integration patterns described above and show that these patterns do not strictly depend on network assignment.

Dynamic integration by contextual control

The static directed interactions described above indicate the potential for integration/segregation of the PFC-PPC during cognitive control. Actualization of this potential would require the activation of particular networks and corresponding activity flow (Cole et al., 2016). That is, activation of intermediary, contextual control nodes should produce more integrated network interactions. To examine such actualization, psychophysiological interaction (PPI) analysis (Cole et al., 2013; Friston et al., 1997) was performed to estimate changes in effective connectivity as a function of different cognitive control demands.

Validation of the method by comparing estimates across samples (Figure 7—figure supplement 1) indicated that the context-independent effective connectivity estimates were replicable (r = 0.86), PPI’s of temporal control showed modest replicability (r = 0.32), and PPI’s of contextual control showed strong replicability (r = 0.78). PPI’s of sensory-motor control were not replicable (r = −0.06). However, those areas engaged by sensory-motor control could largely be recapitulated by contrasts of stimulus domain (Figure 7—figure supplement 2). PPI’s of stimulus domain showed strong replicability (r = 0.88). Therefore, PPI’s of stimulus domain were used as a proxy of interactions generated by activation of sensory-motor control areas.

For each cognitive control demand, source-target relationships among PFC-PPC areas were estimated. In this case, the interactions reflect the changes in effective connectivity induced by the cognitive control demands. In contrast to the stationary dynamics, within-network PPI’s were generally weak across demands (Figure 7A,B). This indicates that within-network interactions are weakly modulated by task demands, which has been previously been observed in functional connectivity (Cole et al., 2014; Krienen et al., 2014; Gratton et al., 2016). Stronger modulations were observed between networks which was especially prominent during contextual control. To quantify these effects, within- and between-network interactions were separately averaged for each PPI contrast. These were then submitted to a 2 × 3 ANOVA with factors of network connectivity (within, between) and contrast (temporal, contextual, stimulus domain; Figure 7B). This analysis revealed a main effect of network connectivity (sample 1: F(1,23) = 15.01, p=0.0008; sample 2: F(1,24) = 10.34, p=0.0037), driven by stronger between- than within-network connectivity. There was no main effect of contrast (both samples p>0.15). However, there was a network connectivity x contrast interaction (sample 1: F(2,46) = 11.84, p=0.0001; sample 2: F(2,48) = 9.86, p=0.0003). This interaction was driven by stronger between-network connectivity for the contextual control contrast relative to the other contrasts. These results demonstrate that contextual control is associated with integration across PFC-PPC networks (Figure 7C), a pattern that was also observed with reduced smoothing (Figure 7—figure supplement 3).

Figure 7 with 3 supplements see all
Dynamic Interactions.

(A) Psychophysiological interactions (PPIs) for temporal control, contextual control, and stimulus domain contrasts. Solid lines indicate positive modulations of effective connectivity while dashed lines indicate negative modulations of effective connectivity. Arrows are colored by the network of the source node. Thickness of the arrows indicates the strength of modulations. Modulations are visualized at p<0.05 uncorrected. (B) Averaged within- and between-network modulations for the temporal control (red), contextual control (green), and stimulus domain (blue) contrasts. (C) Integration indices computed by contrasting between- minus within-network modulations for temporal control (TC), contextual control (CC), and stimulus domain (SD) contrasts.

Static and dynamic integration relates to higher level cognitive ability

The analyses above indicate that a PFC-PPC network involved in contextual control statically integrates processing among PFC-PPC networks, and that PFC-PPC networks are also more dynamically integrated when contextual control is required. Next, the relationship between individual differences in these network interactions (Figure 8A,B) and higher-level cognitive ability was examined. Each participant completed several tasks measuring short-term memory, working memory, and fluid intelligence. These measures were combined using principle components analysis (PCA) to form a composite measure of higher-level cognitive ability (Figure 8C). Measures of static and dynamic integration were then used to predict higher-level cognitive ability using two-fold cross-validated ridge regression. The static integration measure was intended to capture individual differences in the degree to which contextual control areas integrate PFC-PPC processing in a stationary manner. In other words, this measure captured the general integration of the FPCN without regard to specific demands. By contrast, the dynamic integration measure was intended to capture individual differences in the degree to which the FPCN became more integrated when contextual control was required. That is, this measure reflects integration 'on demand'. The data were separated by sample with one sample used to estimate regression weights, and the estimated regression weights used to predict higher-level cognitive ability in the other sample.

Figure 8 with 3 supplements see all
Integration predicts higher level cognitive ability.

(A) Static integration was computed by contrasting between minus within-network effective connectivity of the contextual control network while controlling for (regressing out) the same contrast of the temporal control network and sensory-motor control network and individual differences in head motion. (B) Dynamic integration was based upon the integration index of the contextual control PPI’s while controlling for (regressing out) the integration indices of the temporal control and stimulus domain PPI’s and individual differences in head motion. (C) Higher level cognitive ability was computed as the first principle component of a battery of cognitive tests measuring capacity. (D) Cross-validated ridge regression was used to predict cognitive capacity based upon static and dynamic integration. The scatterplot depicts correlations between the predicted cognitive ability and actual cognitive ability. (E) Correlations among static integration, dynamic integration, and cognitive ability.

A significant prediction effect was observed (r = 0.32, p=0.029; Figure 8D) indicating that individual differences in integration dynamics are related to higher level cognitive ability. While static integration was associated with lower cognitive ability, dynamic integration was associated with higher cognitive ability (Figure 8E). These data indicate the importance of control network integration for higher level cognition.

It could be the case that network integration measures are superior to, redundant with, or complementary to activation-based measures for the purpose of predicting cognitive ability. To examine this question, factors were created to summarize activation-based metrics of temporal control (first principle component of the temporal control contrast in FPl, MFG, and IPL), contextual control (first principle component of the contextual control contrast in VLPFC, cMFG, and midIPS), sensory-motor control (first principle component of the sensory-motor control contrast in IFJ, SFS, antIPS, and SPL) and stimulus domain (first principle component of the stimulus domain contrast in IFJ, SFS, antIPS, and SPL). Similar to the integration measures, activation measures were able to predict individual differences in higher-level cognitive ability (r = 0.37, p=0.01; Figure 8—figure supplement 1). However, activation-based measures were complementary to network integration measures as evidenced by insignificant shared variance amongst the measures (activations explained ~3% of variance in the integration measures, adjusted R-square <0). Moreover, adding activation measures to the network integration measures significantly improved prediction accuracy (r = 0.50, p=0.002; nested model comparison using ordinary regression: F(4,42) = 2.84, p=0.048). Interestingly, whereas integration measures focused on static integration of the contextual control network, and dynamic integration during contextual control, activation during contextual control was the least informative of the activation-based measures (<1% explained variance; see Figure 8—figure supplement 1). Such data indicate that both network-based and activation-based measures can be useful for explaining cognitive ability, but do so in complementary manners.

The same analyses were repeated with reduced smoothing. Although dynamic integration was again positively associated with cognitive ability, with reduced smoothing, no relationship was observed among cognitive ability and static integration. As a result, integration measures could not be used to predict cognitive ability (r = 0.03; p=0.44; Figure 8—figure supplement 2). On the other hand, activation based measures remained significantly predictive (r = 0.31, p=0.04; Figure 8—figure supplement 3) and significantly improved prediction when added to models containing integration measures alone (r = 0.32, p=0.03; nested model comparison using ordinary regression: F(4,42) 3.05, p=0.04). I return to the implications of the non-replication with reduced smoothing in the Discussion.

Static and dynamic integration relates to transcranial magnetic stimulation susceptibility

The fMRI data for sample two was used to localize targets for transcranial magnetic stimulation (TMS). TMS was performed on nodes in each sub-network: FPl – temporal control; VLPFC – contextual control; SFS – sensory-motor control, as well as a control site (S1). As previously reported (Nee and D'Esposito, 2017), we anticipated behavioral effects on temporal control following FPl stimulation, stimulus domain processing following SFS stimulation, and a contextual control x stimulus domain processing interaction following VLPFC stimulation. These expectations were observed (Nee and D'Esposito, 2017). However, individuals varied in their susceptibility to these effects. To examine whether such susceptibilities were related to the organization of cognitive control networks, the static and dynamic integration measures described above were used to predict TMS effects.

A PCA on the TMS effects was performed to derive a general susceptibility of cognitive control to PFC TMS (Figure 9A). Static and dynamic integration measures were used to predict the cognitive control TMS effect using leave-1-out cross-validated ridge regression. This analysis revealed that TMS effects on cognitive control could be predicted by static and dynamic integration (r = 0.56, p=0.01; Figure 9B). In particular, those individuals with stronger static integration tended to show increased TMS-induced cognitive control impairments, while those individuals with stronger dynamic integration tended to show decreased TMS-induced cognitive control impairments. These results were replicated with reduced smoothing (Figure 9—figure supplement 1). Such data indicate that integration of control networks is related to susceptibility to neuromodulation. Follow-up analyses suggested that only domain-general, but not domain-specific susceptibilities to TMS could be predicted (see Supplemental results).

Figure 9 with 4 supplements see all
Integration predicts transcranial magnetic stimulation (TMS) effects.

(A) Previously reportedNee and D'Esposito, 2017 cognitive control impairments induced by continuous theta-burst TMS were combined using principle components analysis to derive a general susceptibility to PFC TMS. (B) Correlations between cognitive control TMS effects and static and dynamic integration. Leave-one-out cross-validated ridge regression was used to predict TMS effects using static and dynamic integration. Scatterplot depicts the correlation between predicted and actual TMS impairments.

Next, additional relationships among TMS susceptibility, cognitive ability, and activation were examined. TMS susceptibility and cognitive ability showed a non-significant negative relationship (r = −0.33, p=0.13). To examine whether integration measures predicted TMS susceptibility over-and-above cognitive ability, cognitive ability was regressed out of measures of static and dynamic integration. The resultant measures could be used to predict TMS susceptibility (r = 0.46, p=0.02; Figure 9—figure supplement 2). These data suggest independence between prediction of cognitive ability and TMS susceptibility. Next, activation-based measures were used to predict TMS susceptibility similar to the procedures detailed above. Unlike cognitive ability, activation-based measures could not predict TMS susceptibility (correlations among predicted and observed TMS effects all <0; Figure 9—figure supplement 3). Moreover, after regressing out both cognitive ability and activation measures from static and dynamic integration, integration measures continued to predict TMS susceptibility (r = 0.47, p=0.02; Figure 9—figure supplement 4). These effects were all replicated with reduced smoothing (Figure 9—figure supplements 24). Hence, these data suggest that network integration is useful for predicting susceptibility to neuromodulation over-and-above cognitive ability and control-related activations.

Discussion

The FPCN is thought to support cognitive control through integrating diverse networks (Murphy et al., 2020; Cole et al., 2013; Cocchi et al., 2013). However, evidence that the FPCN itself is not unitary, but fractionates into multiple sub-networks (Braga and Buckner, 2017; Yeo et al., 2011; Dixon et al., 2018; Murphy et al., 2020) leaves open questions of the functional roles of these sub-networks, and how their interactions support cognitive control. Here, functional mapping of the FPCN was established by contrasting multiple forms of control within a single paradigm. This revealed a mirrored organization in the PFC and PPC. More concrete forms of control that placed demands on stimulus-action selection (sensory-motor control) activated areas proximal to sensory-motor cortices. Increasingly more abstract forms of control which guided stimulus-action selection based upon prevailing contexts (contextual control), and temporally extended internal representations (temporal control) activated areas increasingly distal from sensory-motor cortices. Through correlating activation magnitudes with behavioral reaction times, it was observed that activations in areas responsive to sensory-motor and contextual control rose with reaction times in the moment, consistent with the idea that these areas are engaged commensurate with externally driven demands. By contrast, activation in areas sensitive to contextual and temporal control rose with future behavioral reaction times, consistent with a role of these areas in sustaining internal representations to prepare for future demands. Collectively, these data suggest that the FPCN is organized along a present/external to future/internal axis extending from sensory-motor proximal to sensory-motor distal areas.

Analyses on effective connectivity (directed interactions) examined network dynamics supporting cognitive control. These analyses revealed the existence of an integrative set of control areas whose dynamics relate to higher level cognitive ability and amenability to neuromodulation. These integrative areas were situated in an intermediary zone of the mirrored PFC-PPC gradient. Networks on either end of this control gradient acted in a segregative manner, exciting within-network nodes, while suppressing between-network nodes. Such dynamics may support selective processing of one time horizon (present/future) or medium (external/internal) at the exclusion of another. By contrast, the integration of both external/present-oriented and internal/future-oriented control networks may support hierarchical control wherein appropriate behaviors are jointly contingent on external and internal representations. The broader importance of such integrative processing was underscored by the relationship of individual differences in integrative dynamics and higher-level cognitive ability on the one hand, and amenability to neuromodulation on the other. Hence, the dynamics may be useful to specify optimal cognitive function, and predict responsivity to interventions.

Beyond the PFC: toward a network view of cognitive control

A substantial body of work has focused on the functional organization of the lateral PFC and interactions therein that support cognitive control. Despite long-standing recognition that cognitive control is supported by areas distributed across the frontal and parietal lobes (Vincent et al., 2008; Yeo et al., 2011; Duncan, 2010; Cole et al., 2013; Cole and Schneider, 2007; Power and Petersen, 2013; Fedorenko et al., 2013; Warren et al., 2014; Duncan et al., 2020), much work, particularly in the domain of hierarchical cognitive control, has centered narrowly on how processing varies along the rostral-caudal axis of the PFC (Badre and Nee, 2018; Badre and D'Esposito, 2009; Koechlin et al., 2003; Nee and D'Esposito, 2016; Nee and D'Esposito, 2017; Badre and D'Esposito, 2007; Badre, 2008). Although a number of insights have been gained by focusing on the PFC, such a narrow focus ignores the broader networks in which the PFC participates. Choi et al., 2018 recently demonstrated that the same rostral-caudal organization for control observed in the PFC is reflected in the PPC consistent with the idea that the PFC and PPC are comprised of ordered networks for control. The data here replicate those findings while also linking PFC-PPC activations with behavior along distinct timescales. Hence, it appears to the case that many functions that have been attributed to the PFC are also present in the PPC. This necessitates expanding the study of cognitive control beyond the PFC to network and brain-wide levels.

Macroscale gradients and cognitive control

There has been a recent surge of interest in macroscale gradients across the cortex (Margulies et al., 2016; Huntenburg et al., 2018; Wang, 2020). This interest stems from the thought that gradients provide a scaffold for functional processing thereby offering a window into how large-scale networks support cognition. Following Mesulam, 1998, Margulies et al., 2016 proposed the existence of two macroscale axes upon which gradients are built with the first reflecting connectivity distance from primary cortices and the second reflecting modality. Huntenburg et al., 2018 further proposed that the first gradient matches a temporal gradient reflecting the fundamental timescale over which a cortical area operates (Hasson et al., 2015; Chaudhuri et al., 2015; Murray et al., 2014), and the abstractness of the mental representations processed by the cortical area. These ideas are similar to those proposed by Fuster, 2001 who hypothesized that mirrored frontal and posterior abstraction gradients support the temporal organization of controlled behaviors. However, within these frameworks, it is unclear exactly whether or how control should be distinguished from processing. That is, if the cortex can be organized along a principle axis of abstraction, does control emerge at the far end of that axis, all throughout, or in-between?

The position of the FPCN with respect to macroscale gradients of cortex is intermediary between canonical circuits involved in modality-specific processing, and the default-mode network involved in internal mentation (Buckner and DiNicola, 2019; Raichle et al., 2001). The intermediary positioning of the FPCN may be optimal for the orchestration of diverse brain regions in the service of adaptive behavior (Cole et al., 2013). Consistent with prior data (Braga and Buckner, 2017; Yeo et al., 2011; Dixon et al., 2018; Murphy et al., 2020), the data here indicate that the FPCN is not unitary but itself has a gradient organization. In particular, the data suggest that an intermediary zone of the FPCN, which itself is an intermediary zone of macroscale cortical gradients, is involved in the integration of control networks for adaptive behavior. Such data suggest the importance of examining gradients at multiple scales to understand brain-wide function. For example, the default-mode network has also been revealed to be comprised of multiple networks (Braga and Buckner, 2017; Yeo et al., 2011; Buckner and DiNicola, 2019). Extrapolating from the findings here, default-mode network B may act as an intermediary between the memory-related default-mode network A and the FPCN, positioned to integrate memory with control to guide internally-oriented cognition. Consistent with this idea, although the areas engaged by temporal control most closely aligned with FPCN A, there was some overlap with default-mode network B, suggesting some shared function among FPCN A and default-mode network B. Further investigation of the interactions among these networks would be an interesting future endeavor.

One question that remains open is the putative functions of FPCN sub-networks. Prior data that have fractionated the FPCN into sub-networks have done so based on co-activation patterns (Braga and Buckner, 2017; Yeo et al., 2011; Dixon et al., 2018; Murphy et al., 2020) which leave open the precise functional role of FPCN sub-networks. On the one hand, the overlap of areas sensitive to temporal control and FPCN A is suggestive that FPCN A acts upon internal representations to prepare for future controlled processing. These internal representations are likely to be relayed from areas in the DMN (Dixon et al., 2018; Murphy et al., 2020) potentially providing abstract schematic representations that are useful for organizing control processes toward a goal (Badre and Nee, 2018). On the other hand, areas sensitive to sensory-motor control overlapped most strongly with FPCN B. FCPN B is thought to coordinate with the DAN (Dixon et al., 2018; Murphy et al., 2020). This relationship with the DAN is consistent with the idea that attentional selection is necessary to guide action toward task-relevant stimuli at the exclusion of task-irrelevant stimuli – processes that support sensory-motor control.

However, alignment between task activation contrasts and previous co-activation based parcellations was mixed such that each putative control process examined here activated multiple sub-networks. To some extent, this is to be expected given that task contrasts are rarely process pure. On the other hand, areas can shift network allegiances as a function of task demands (Salehi et al., 2020a), which is further compounded by the finding that what constitutes an area/parcel itself shifts as a function of task demands (Salehi et al., 2020b). Indeed, the variable connectivity of the FPCN is thought to be the essence of its control capacities (Cole et al., 2013). Moreover, control, by definition, denotes a source-target relationship. Hence, it may make little sense to consider any sub-network in isolation as representative of a control process. Instead, constellations of network activations and connectivities may be the unit of function when considering cognitive control. Commensurate with this idea, temporal control was profiled by activations most strongly in FPCN A, but also in DMN B, indicative of control acting on internal representations. Sensory-motor control was profiled by activations most strongly in FPCN B, but also in DAN, indicative of control acting on external representations. Finally, contextual control was profiled by activations most strongly in FPCN B, but also in FPCN A indicative of a co-operation of internal and external control processes. Collectively, these data serve to functionally ground the sub-networks that have been identified through co-activations.

One question that remains open is the spatial resolution of macroscale cortical gradients. The gradients depicted here appear somewhat continuous (Figure 2). However, the appearance of such continuity could be the result of any number of processing steps including spatial interpolations, smoothing, and averaging. For example, discrete individual variability can appear smooth and continuous after group averaging (Braga and Buckner, 2017; Gordon et al., 2017). When examined in an individual, connectivity profiles have been demonstrated to abruptly shift along spatial axes (Wig et al., 2014) suggesting that the cortex is best considered to be composed of discrete areas. Moreover, a recent study examining the scale of gradients in the PFC of non-human primates also concluded that such gradients vary in an areal rather than smooth fashion (Tan et al., 2020). Such data are consistent with the longstanding idea that discrete cortical areas perform discrete functions (Brodmann, 1909; Amunts and Zilles, 2015). Because of the processing and spatial resolution of the data here, the present dataset is unable to speak to finer gradations that may exist below the areal level, and is not inconsistent with the idea that the resolution of macroscale gradients is the areal level.

Integration and cognitive control

Previous work has indicated the presence of an integrative core of regions important for multiple tasks (Duncan and Owen, 2000; Duncan, 2010; Duncan, 2013; Cole et al., 2013; Cocchi et al., 2014; Cole et al., 2012; Shine et al., 2019a; Dosenbach et al., 2008; Dubois et al., 2018). For example, Shine et al., 2019a recently performed a spatiotemporal principle components analysis across multiple tasks of the Human Connectome Project. The first principle component of this analysis rose and fell in cadence with task demands across multiple domains with greater rising associated with greater fluid intelligence. Similarly, Cole et al., 2012 found that the global brain connectivity of a region in mid-lateral PFC predicted individual differences in fluid intelligence. Cocchi et al., 2014 found that a similar region showed enhanced dynamic coupling with a diverse set of brain areas as the complexity of reasoning demands increased. Collectively, these data indicate the need for integration across tasks and demands for higher level cognition. Our data situate the areas associated with such integration in an intermediary zone of the FPCN.

In contrast to the integrative dynamics of intermediary areas, sensory-motor proximal and distal areas acted in a segregative fashion. Segregation is likely to be important to select relevant information while suppressing irrelevant information. Consistent with the data here, Shine, 2019b posited that rostral areas of the PFC are involved in segregation while mid-lateral areas are involved in integration. He theorized that segregation is mediated by cholinergic modulations while integration is mediated by noradrenergic modulations. Further research into the influences of distinct PFC-PPC networks on neuromodulatory mechanisms would be fruitful to elucidate such effects.

The data demonstrated both static and dynamic forms of integration. Areas involved in contextual control tended to excite other control networks, providing a potential substrate for integration through binding. Moreover, demands on contextual control increased inter-network communication producing a dynamic form of integration. Both static and dynamic integration were related to individual differences in higher level cognitive ability. Interestingly, the different forms of integration tended to be associated with opposite effects. On the one hand, increased static integration was associated with decreased higher level cognitive ability. It has been posited that an appropriate balance of segregation and integration into distinct networks or modules is important to optimize brain efficiency (Sporns, 2010). In particular, it has been observed that more segregation between networks, and integration within networks (i.e. modularity) at rest is associated with memory capacity (Stevens et al., 2012). Therefore, integration across networks in a stationary manner may be sub-optimal for cognition. On the other hand, increased dynamic integration was associated with increased higher-level cognitive ability. These data are consistent with previous studies that have shown that integrative reconfigurations of brain networks from rest to task are related to improved performance on complex tasks (Cohen et al., 2014; Braun et al., 2015; Cohen and D'Esposito, 2016). These data suggest that the brain’s ability to integrate ‘on-demand’ is beneficial to cognitive processing.

Areas and networks that bind together processing of multiple brain systems are integral to multimodal processing. A potential cost of such an organization is that integral processing hubs convey a vulnerability to cognitive processing such that damage to key areas/networks will have widespread impacts (Warren et al., 2014; Gratton et al., 2012). The data here suggest that in the domain of control processing, static integrative dynamics provide increased susceptibility to TMS-induced control deficits. The form of TMS explored here was aimed to be inhibitory (Huang et al., 2005) to cause deficits in control processing. Many therapeutic approaches to TMS utilize excitatory protocols in order to enhance irregular hypo-function (e.g. Blumberger et al., 2018). It would be interesting to see whether the widespread impacts of stimulation to integrative nodes can enhance therapeutic effects when excitatory protocols are employed.

Although I have suggested an integrative role of areas positioned in the middle of the FPCN, other accounts are plausible. For example, the excitatory influences of the mid-positioned areas in the FPCN on areas at either end of the FPCN could be considered a form of top-down modulation which may serve to strengthen or sharpen representations (Miller and Cohen, 2001; Miller and D'Esposito, 2005). This perspective could entail a more focal or localist influence of the mid-positioned areas of the FPCN than the integrative role that has been suggested. While tenable, I favor an integrative view given the global impact on network architecture observed when hub-like areas are damaged (Gratton et al., 2012). Moreover, top-down control by the FPCN has typically been document by long-range connections upon those areas responsible for stimulus representation (Feredoes et al., 2011; Miller et al., 2011). However, this does not preclude a top-down biasing role of the FPCN upon itself. Resolving this matter would likely require additional data that can identify the distinct representations of different areas of the FPCN and how those representations are modified by network dynamics.

The FPCN is not the only network important for integration and cognitive control. Extensive work has indicated the importance of the cingulo-opercular network (Cocchi et al., 2013; Dosenbach et al., 2008; Cohen et al., 2014; Marek et al., 2015) . Moreover, a cognitive control organization that parallels the PFC has recently been observed in the cerebellum (D’Mello et al., 2020). In the cerebellum, as in here, intermediary areas involved in contextual control showed an integrative role, mediating relationships among control areas at either end of the external/internal, present/future axis. Detailing interactions among the FPCN and these other networks would provide valuable insights into the brain-wise basis of cognitive control.

Limitations

Several limitations should be considered to properly contextualize the findings reported here. First, positive effective connectivity has been posited as an excitatory influence while negative effective connectivity has been posited as an inhibitory influence. However, such interpretations should be taken with caution. Although spDCM models the translation of synaptic activity to the blood-oxygenation level dependent (BOLD) signal, it does not attempt to model more specific cellular and molecular processes. Moreover, estimates of effective connectivity depend upon the areas modeled. That is, an estimated direct influence among areas A and B could potentially be mediated by an un-modeled area C. In particular, it could well be the case that negative influences among areas in the FPCN are mediated by interactions with other structures such as the thalamus and basal ganglia (Frank and Badre, 2012; Frank et al., 2001; Badre and Frank, 2012). Hence, these observations should be taken as a starting point from which more complex and biologically plausible networks can be expanded.

Second, conclusions regarding the relationships among individual differences in FPCN network integration and cognitive ability/susceptibility to neuromodulation should be tempered by the sample sizes studied. Estimated effect sizes can be inflated at small sample sizes giving the impression that more variance is explained by a given measure than is actually the case (Yarkoni and Braver, 2010). Moreover, estimates of brain-phenotype relationships can be unstable at small sample sizes leading to poor replicability (Marek, 2020). The use of multi-variate, cross-validated methods here should improve replicability and generalizability (Kragel et al., 2020). However, replication with larger samples is needed to draw firm conclusions regarding the relationships among FPCN network integration, cognitive ability, and susceptibility to neuromodulation.

Third, multiple steps have been taken to ensure the replicability of the findings here including replicating results across independent samples, and repeating the analyses with different preprocessing choices. All but one reported finding replicated across analyses: the use of FPCN network integration measures to predict cognitive ability did not replicate with reduced smoothing. In light of the many replicated results, this non-replicated result warrants consideration. The lack of replication could indicate that the original finding was a false positive and/or that power is insufficient in the present sample to produce a stable effect size. Another possibility is that reduced smoothing limited the ability of brain-derived FPCN integration measures to predict behavior. Behavior arises from population-level dynamics such that considering more of the relevant population-level signals should facilitate better explanations of behavior. Hence, although less smoothing makes the signals more focal, which is good for dissociating nearby areas, it may be that pooling across nearby areas makes the signals more representative of the population-level dynamics that explain behavior. Toward this possibility, in all the analyses that used neural data to predict behavior, prediction accuracy, even when significant, was universally diminished with reduced smoothing. Whether the lack of replication of FPCN integration measures predicting cognitive ability with reduced smoothing indicates that the original result/analysis was a false positive/had insufficient power or whether this is a reflection of a true result varying as a function of preprocessing choices requires future investigation. For the time-being, this result should be taken with some measure of caution.

Fourth, the analyses presented here have focused exclusively on the left hemisphere. This is in keeping with prior work with these data (Nee and D'Esposito, 2016; Nee and D'Esposito, 2017) and is consistent with the preponderance of work in the domain of abstraction and hierarchical control showing more marked recruitment of the left hemisphere (Badre and Nee, 2018; Badre and D'Esposito, 2007; Nee and Brown, 2012; Nee and Brown, 2013; Nee et al., 2014; Bahlmann et al., 2014; Bahlmann et al., 2015; Jeon and Friederici, 2013; Jeon et al., 2014). The reason for this left lateralization is unclear, but may relate to the presumed development of internalized control structures via interactions with the language system (Luria, 1959; Baddeley, 2012). However, some control processes, such as those responsible for the inhibition of motor responses tend to be more right lateralized (Aron et al., 2004; Aron, 2007). Future work would do well to compare and contrast network integration of the left and right FPCN.

Materials and methods

Participants

Twenty-four participants (13 female; age 18–28, mean 19.9 years) formed sample 1, previously described (Nee and D'Esposito, 2016). Twenty-five participants (16 female; age 18–27; mean 20.6 years) formed sample 2, previously described (Nee and D'Esposito, 2017). Collectively, the total sample size was forty-nine.

All participants were screened to be right-handed, native English speakers or fluent by the age of 6, and had no reported history of neurological or psychiatric disorders. Informed consent was obtained in accordance with the Committee for Protection of Human Subjects at the University of California, Berkeley.

The targeted number of participants was based upon previous work with related paradigms. The empirical replicability of univariate activations from these data has been previously established (Nee, 2019) indicating that power is sufficient for the estimation of cognitive control networks at the group level at the collected sample sizes. To ensure replicability of more complex analyses, bi-variate, and effective connectivity analyses in the present study are reported separately for each sample when possible, providing indications of replicability and power sufficiency.

Experimental design and statistical analyses

Comprehensive control task

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The Comprehensive Control Task was adapted from prior work (Koechlin et al., 1999; Charron and Koechlin, 2010), and designed to manipulate multiple forms of cognitive control within a single, well-controlled paradigm. These different forms of control can be classed by different levels of abstraction with concrete processing acting on external stimuli in the present moment, and abstract processing supporting the maintenance of internal representations to guide future behavior. At the lowest level, sensory-motor control selects relevant stimulus features and associated actions. At the mid-level, contextual control selects the rules that guide the appropriate stimulus-response associations. Finally, at the highest level, temporal control supports temporally-extended representations that prepare for future control demands.

On each trial of the task (Figure 1), participants were presented with a letter at one of five spatial locations surrounded by a colored shape. Each stimulus required a choice decision indicated by a left or right keypress. Choice-to-keypress mappings were counter-balanced between participants. The correct decision depended upon a combination of (1) a stimulus feature, (2) a contextual rule, and (3) a temporal epoch.

Stimulus feature: choice decisions were based either on the letter (verbal task) or spatial location (spatial task). Participants pre-learned a sequence of letters (t-a-b-l-e-t) and locations (trace of a star, starting at the top position). Choice decisions were based upon these sequences.

Contextual rule: for a given stimulus feature, participants determined either whether the present stimulus was the first item of the relevant sequence (‘t’ for the verbal task; top position for the spatial task; sequence start task) or whether the present stimulus followed a reference stimulus in the sequence (sequence back task).

Temporal epoch: for the sequence back task, the reference stimulus was either the immediately preceding stimulus, or a stimulus that appeared multiple trials ago.

Loads on each of these factors were orthogonally varied to form a 2 × 2 × 2 factorial design. Trials were grouped into blocks wherein each block sampled one cell of the 2 × 2 × 2 design. In each block, the relevant stimulus feature, either letter or location, was cued by the color of the frame. The relevant stimulus feature remained constant throughout a block. Participants performed the sequence start task on the relevant stimulus feature on the first trial of a given block. Thereafter, each block was divided into three phases: a first baseline phase, a sub-task phase, and a second baseline phase. Transitions among these phases were indicated by the shape of the colored frames. In all blocks, the baseline phases were cued by square frames. Sub-tasks were cued by triangle, diamond, or cross frames with shape-to-sub-task mappings counter-balanced across participants. For ease of exposition in what follows, we will assume the following associations: circle-switching, triangle-planning, diamond-dual. Only one sub-task was cued in a given block.

In Baseline blocks, participants continued to perform the sequence back task throughout the block thereby keeping the contextual rule and temporal epoch constant. On Switching blocks, shape-switches (i.e. from square to circle or from circle to square) indicated the need to switch tasks (i.e. from sequence back to sequence start). Thus, these blocks placed demands on responding based upon the appropriate contextual rule engaging contextual control. On Planning blocks, triangle shapes indicated that the presented stimulus could be ignored. Participants acknowledged the presence of each triangle-framed stimulus with a ‘no’ keypress. All the while, the last square-shaped stimulus had to be retained as a reference for the next square-shaped stimulus. Hence, Planning blocks minimized processing of present stimuli, but placed demands on planning for the future in order to respond according to the correct temporal epoch thereby requiring temporal control. Finally, on Dual blocks, diamond frames indicated the need to both switch contextual rules, and plan for the future. That is, participants started and continued a new sequence on all diamond framed stimuli, but backwards-matched to the last square-framed stimulus when the frame reverted to a square. Hence, Dual blocks required both contextual and temporal control.

Different cognitive control process can be detailed through orthogonal contrasts of the factorial design. At the highest level, temporal control is isolated by contrasting blocks that require planning with those that do not (Dual + Planning > Switching + Baseline). At the middle level, contextual control is isolated by contrasting blocks that require switching with those that do not (Dual + Switching > Planning + Baseline). At the lowest level is sensory-motor control which can be examined through the contrast of (Dual + Baseline > Planning + Switching). To understand this contrast, consider that the Dual condition is effectively Switching + Planning. Then, using subtraction logic, what remains after subtraction is the Baseline condition which consists of the demands of selecting the appropriate feature and responding to it. The utility of using the contrast over-and-above simply examining the Baseline condition alone is that it better controls for ancillary demands, and it keeps all of the main contrasts of interest statistically orthogonal to one another. Finally, those areas involved in sensory-motor control can be further fractionated by contrasting stimulus features with one another (i.e. verbal > spatial or spatial > verbal), thereby emphasizing verbal articulatory processes (verbal > spatial) or spatial attention processes (spatial > verbal).

Participants in sample 1 completed 24 blocks of each cell of the 2 × 2 × 2 design over the course of two fMRI sessions. These blocks consisted of 1920 total trials with each block containing 7–13 trials. Participants in sample 2 completed 12 blocks of each cell of the 2 × 2 × 2 design during a single fMRI session. These blocks consisted of 864 total trials with each block containing 7–11 trials. In both samples, the task was split across 6 runs of 16 blocks each in each session.

Each stimulus was presented for 500 ms followed by a variable inter-trial interval of 2600–3400 ms. At the end of each block, feedback indicating the number of correct trials in the block out of the total number of trials in the block was presented for 500 ms. A variable 2600–3400 ms interval separated each block. Self-paced breaks were administered in-between runs.

Within a week prior to scanning, participants performed a practice session to learn the task. During the practice session, participants received extensive written instruction and clarification from an experimenter. Given the numerous rules and complexities of the task, instruction was broken up such that participants first learned the verbal sequence, then the spatial sequence, and then the sub-tasks. Participants continued to repeat instruction and practice under experimental supervision until they were comfortable with the rules. Thereafter, participants completed three runs of the task on their own. During each scanning session, participants completed one additional practice run in the scanner prior to fMRI data collection.

Cognitive battery

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To obtain trait-level measures of cognitive ability, participants performed computerized versions of letter span, spatial span, operation span, and symmetry span. Operation span and symmetry span provide measures of working memory capacity (Turner and Engle, 1989). Letter span and spatial span provide simple measures of short-term memory capacity. Participants also performed a paper version of Raven’s Advanced Progressive Matrices (http://www.perasonassessments.com), wherein Set I was used as practice, and Set II was used to measure fluid intelligence. As previously reported (Nee and D'Esposito, 2016), performance across these measures were correlated. Therefore, the measures were combined using principle components analysis with the first principle component providing an index of general higher-level cognitive ability.

Image acquisition

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As previously reported (Nee and D'Esposito, 2016; Nee and D'Esposito, 2017), brain imaging data were acquired at the Henry H. Wheeler, Jr. Brain Imaging Center at the University of California, Berkeley using a Siemens TIM/Trio 3T MRI equipped with a 32-channel head coil. Stimuli were projected to a coil-attached mirror using an MRI-compatible Avotec projector (Avotec, Inc; https://avotecinccom). Experimental tasks were created using E-Prime software version 2.0 (Psychology Software Tools, Inc; https://pstnet.com/). Eye position was monitored using an Avotec system (RE-5700) and Viewpoint software (http://www.arringtonresearch.com/). Response data were collected on an MR-compatible button box (Current Designs, Inc; https://curdes.com).

T2* weighted fMRI was performed using gradient echo planar imaging (EPI) with 3.4375 mm2 in-plane resolution and 35 descending slices of 3.75 mm thickness. TR = 2000 ms, echo time = 25 ms, flip angle = 70, field of view = 220 mm2. The first three images of each run were automatically discarded to allow for image stabilization. Field maps were collected to correct for magnetic distortion. High-resolution T1-weighted MPRAGE images were collected for anatomical localization and spatial normalization (240 × 256 × 160 matrix of 1 mm3 isotropic voxels; TR = 2300 ms; echo time = 2.98 ms; flip angle = 9). Each session included a 6 min eyes open resting state run in addition to six task runs. In sample 1, the resting-state run was collected prior to the task in the first session, and after the task in the second session. In sample 2, the resting-state run was collected prior to the task.

Behavioral data preprocessing

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Behavioral data was preprocessed using custom MATLAB code (MathWorks; https://www.mathworks.com). Data were sorted by phase (first baseline, sub-task, second baseline). Transitions between phases were considered separately. Of primary importance in this report are the sub-task trials (i.e. all trials in the sub-task phase excluding the first trial of the phase) and what are referred to as ‘return’ trials which mark the transition from the sub-task phase to the second baseline phase. For example, in Planning blocks, the sub-task trials themselves require minimal processing since all stimuli during this phase require a ‘no’ keypress. On the return trial, participants perform sequence back with reference to the stimulus feature that preceded the sub-task phase. Thus, the sub-task trials reflect a combination of cognitive control in the moment and preparing for the future, while the return trials reflect actualization of sub-task preparation. Sub-task and return trials were separately sorted for each cell of the 2 × 2 × 2 design. Reaction times were computed on trials with a correct response only. Reaction times less than 200 ms were discarded as anticipatory and reaction times greater than 2000 ms were discarded as inattentive. Furthermore, reaction times greater than 2.5 standard deviations of the mean of a given condition were removed as outliers. These procedures resulted in the removal of 0.76% of the trials in sample 1, and 0.65% of the trials in sample 2.

Image preprocessing

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Unless otherwise specified, preprocessing was performed using SPM8 (http://www.fil.ion.ucl.ac.uk/spm/). Raw data was converted from DICOM into nifti format. Origins for all images were manually set to the anterior commissure. AFNI’s 3dDespike function (http://afni.nimh.nih.gov/afni) was applied to the functional data to remove outlier time-points. Correction for differences in slice-timing and spatial realignment were performed next. Images were then corrected for magnetic distortion using the FieldMap toolbox implemented in SPM8 Andersson et al., 2001. Functional data were co-registered to the T1-weighted image. Segmented normalization was performed on the T1-weighted image. Spatial normalization parameters were subsequently applied to the functional task data. This step also resampled the functional images to 2 mm3 isotropic. Task data were subsequently smoothed using an 8 mm3 full-width/half-maximum isotropic Gaussian kernel. To ensure that smoothing did not artifactually influence the results, all analyses were also repeated with 4 mm3 smoothing. Prior to spatial normalization, resting data underwent additional preprocessing using custom-written MATLAB scripts. Resting data were high-pass filtered at 0.009 Hz using SPM8’s spm_filter function. Next, nuisance signals from white matter and cerebrospinal fluid were extracted and regressed out of the data along with linear, squared, differential, and squared differential motion parameters (motion parameters were estimated during spatial realignment described above). The residualized data were low-pass filtered at 0.08 Hz using a second-order Butterworth filter. The filtered, artifact-corrected resting data were then spatially normalized and smoothed as described above.

The bulk of the report focuses on data that were preprocessed in the manner described above. However, large volumetric smoothing kernels can blur and obscure activation gradients. To ensure that the observed activation gradients were not artifactually caused by these processing choices, the data were re-processed using Freesurfer version 6.0 (https://surfer.nmr.mgh.harvard.edu/). The T1-weighted image was registered to the fsaverage surface using recon-all. Despiked, slice-timing corrected, realigned, unwarped functional data described above (i.e. before spatial normalization) were sampled onto the fsaverage surface using preproc-sess (note, motion correction was omitted using the –nomc flag since motion correction was previously performed). Four mm smoothing was performed on the surface and then the functional data was returned to the volume using surfsmooth-sess. In this case, returning the data to the volume enabled the same model estimation procedures to be performed on both the volume smoothed and surface smoothed data, providing a well-matched comparison.

Univariate image analysis

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Univariate modeling of task activation has been previously described (Nee and D'Esposito, 2016) and was implemented using SPM8. Of main interest are the sub-task phases which were separately modeled for each cell of the 2 × 2 × 2 design as epochs starting after the first sub-task trial through the end of the final sub-task trial. The first and second baseline trials were also modeled as epochs, separately for each phase and stimulus domain, also starting from the second trial of the epoch through the last. Transient regressors were included to model the first trial of each block, separately for each stimulus domain, the first trial of each sub-task, separately for each cell of the 2 × 2 × 2 design, and the first trial of the second baseline (also known as the ‘return’ trial), separately for each cell of the 2 × 2 × 2 design. Additional transient regressors were included to model left and right keypresses, as well as error trials. All regressors were convolved with the canonical hemodynamic response function implemented in SPM. Each run was modeled separately containing a separate intercept term, high-pass filter at 128 s, AR(1) modeling to account for temporal autocorrelation, and scaling such that run-wide global signal averaged 100. For participants demonstrating greater than 3 mm/degrees of motion over the course of the session or a single framewise movement greater than 0.5 mm/degrees, 24 motion regressors were included reflecting linear, squared, differential, and squared differential to remove motion-related artifacts (Lund et al., 2005; Satterthwaite et al., 2013).

At the first level, contrasts were created to isolate the sub-task phase of each cell of the 2 × 2 × 2 design by averaging parameter estimates across runs. These first level parameter estimates were then carried forward to a second level 2 × 2 × 2 ANOVA. Second-level contrasts were calculated as t-tests within the ANOVA framework. Five orthogonal contrasts of interest were considered: Temporal Control (Dual + Planning > Switching + Baseline), Contextual Control (Dual + Switching > Planning + Baseline), Sensory-Motor Control (Dual + Baseline > Planning + Switching), Verbal Stimulus Domain (Verbal > Spatial), and Spatial Stimulus Domain (Spatial > Verbal). Note that the contrasts with the ‘Control’ modifier collapsed across Stimulus Domain (e.g. Dual is a combination of Verbal Dual and Spatial Dual), while contrasts with the Stimulus Domain modifier collapsed across the Control conditions (e.g. Verbal is a combination of Verbal Dual, Verbal Planning, Verbal Switching, and Verbal Baseline). In keeping with previous reports on these datasets (Nee and D'Esposito, 2016; Nee and D'Esposito, 2017), whole-brain voxel-wise activation maps were thresholded at p<0.001 at the voxel level with 124 voxel extent providing correction for family-wise error (FWE) at p<0.05 according to AlphaSim.

Network overlap

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For each activation contrast, the overlap with the Yeo et al., 2011. 17-network parcellation was examined. For each of the 17 networks, the percentage of significant voxels for a given activation contrast that overlapped with the network was tabulated.

Regions-of-interest

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The five contrasts of interest produced wide swaths of activation throughout the PFC and PPC. To examine the activations in a more granular manner, regions-of-interest (ROIs) were created as 6 mm3 spheres centered on peak activation coordinates. PFC ROIs have been previously described (Nee and D'Esposito, 2016; Nee and D'Esposito, 2017). Given that the contrasts produced partially overlapping activations, distinct peaks were defined as local maxima that were distanced at least 1.5 cm from another peak. The location of PFC peaks was determined by sample one and peaks similar in location revealed by the same contrast were identified in sample 2. This ordering was due to the temporal ordering of data collection and analysis (i.e. sample one was collected and analyzed first and sample two was analyzed in an effort to replicate findings in sample one as detailed previously [Nee and D'Esposito, 2016; Nee and D'Esposito, 2017]). This resulted in six PFC ROIs detailed in Table 1: lateral frontal pole (FPl), middle frontal gyrus (MFG), ventrolateral prefrontal cortex (VLPFC), caudal middle frontal gyrus (cMFG), inferior frontal junction (IFJ), and superior frontal sulcus (SFS).

ROIs in the PPC were defined separately for sample 1 and sample 2, again using the five contrasts-of-interest. Again, distinct peaks were identified as local maxima distanced from other peaks by at least 1.5 cm. This procedure results in four PPC ROIs detailed in Table 1: inferior parietal lobule (IPL), mid intra-parietal sulcus (midIPS), superior parietal lobule (SPL), and anterior intra-parietal sulcus (antIPS).

In both the PFC and PPC, some peaks could be identified by two or three contrasts (i.e. local maximum within 1.5 cm from one another were observed across multiple contrasts). The contrast chosen to define a given peak was done with consideration of the contrast that most unambiguously identified the peak in individual subjects. This choice was made since the effective connectivity analyses detailed below were tailored to each individual’s activation peaks, providing individual-specific parcellation. The end result of this analysis choice was that the least expansive contrast (where expansive refers to the number of activated voxels of a contrast) tended to be chosen to define an ROI for a given peak.

Functional profiling and multi-dimensional scaling

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Since ROIs could respond to multiple demands, we sought to quantify each ROI’s activation profile. Because the ROIs were formed from peaks of a particular contrast in a particular sample, simply plotting the activation profile of the ROIs defined above constitutes circularity that biases the profile toward the ROI-defining contrast (Kriegeskorte et al., 2009). To provide unbiased estimates, the ROIs from sample one were used to functionally profile sample two, and vice versa. Hence, data used to define ROIs and test ROIs were independent. Within these unbiased ROIs, statistics for the five contrasts-of-interest were calculated using repeated-measures 2 × 2 × 2 ANOVAs. For each sample, statistical significance was Bonferroni corrected for the number of ROIs.

To further characterize each ROI, the ROI data were submitted to multi-dimensional scaling. The data for each individual and each ROI were z-scored across the eight conditions-of-interest. Then, for each ROI, the individual-level data were stacked, resulting in a two-dimensional matrix wherein one-dimension was composed of individuals x conditions, and the other dimension was composed of ROIs. Dissimilarity among ROIs was computed using 1 – r, where r is the Pearson’s correlation. This dissimilarity matrix was submitted to MATLAB’s cmdscale function. Each ROI was then plotted as a point in the space defined by the first two dimensions wherein the first two dimensions captured 89.2% of the variance in the data (71.0% for the first, 18.3% for the second, 0.04% for the third). As explained in the Results, the first dimension appeared to map well onto an abstraction axis, and the second dimension appeared to map well onto a stimulus domain axis.

Brain-behavior relationships

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To better understand how activation in each ROI relates to cognitive control, relationships between behavioral performance in the Comprehensive Control Task and activation were calculated similar to previous reports (Nee and D'Esposito, 2016; Nee and D'Esposito, 2017). Three differences between the analyses reported here and those reported previously is that here, (1) each ROI is considered separately (pairs of ROIs were combined previously), (2) ROI data were extracted to ensure independence as explained above (i.e. sample one defined ROIs for sample two, and vice versa), and (3) repeated measures correlations were computed using the rmcorr package in R (previously correlations were computed by regressing out subject-specific terms). Mean RT for the eight conditions of interest were calculated for each individual separately for the sub-task trials and return trials, as described above. The eight element vector was then z-scored separately for each phase. The sub-task trial RTs were regarded as ‘Present Behavior’ since the RTs reflect behavior at the time that the fMRI signal was estimated (i.e. activations of interest were drawn from the sub-task phase). The return trial RTs were regarded as ‘Future Behavior’ since the RTs reflect the time directly after the fMRI signal was estimated. Future Behavior reflects the behavior that is being prepared for during the sub-task phase, which might not be reflected in the sub-task trial RT per se (e.g. Planning blocks have fast Present RTs, but slow Future RTs). For each ROI, a repeated measures correlation was used to assess the relationship between activation and Present Behavior (controlling for Future Behavior), and activation and Future Behavior (controlling for Present Behavior). These procedures were performed separately for each sample. Statistical significance was assessed after Bonferroni correction for number of ROIs. Correlations that did not survive multiple comparisons correction, but were present at uncorrected levels are also noted.

Linear mixed effects models were fit in order to quantify how ROIs differ in terms of their relationships to Present and Future Behavior. For each individual and ROI, Present and Future Behavior were simultaneously regressed onto the activations. Parameter estimates reflecting the slope relating activation to Present and Future Behavior, respectively were submitted to the linear mixed effects models. For each ROI, the loading of the ROI on the first dimension of the multi-dimensional scaling described above was used as a continuous, objective measure of abstraction. Separate linear mixed effects models tested whether the relationship between Present RT and activation varied as a function abstraction, and whether the relationship between Future RT and activation varied as a function of abstraction. That is, these analyses tested whether the slope estimates varied by abstraction. Models of the form: Present Behavior Slope ~ Abstraction + (Abstraction|Subject), and Future Behavior Slope ~ Abstraction + (Abstraction|Subject) were estimated. These analyses were performed separately for each sample.

ROI analyses offer an incomplete picture of brain-behavior relationships. To better visualize whole-brain patterns, voxel-wise partial correlations were performed. The data were stacked across individuals. For each voxel, the partial correlation between activation and Present Behavior, controlling for Future Behavior and individual, as well as the partial correlation between activation and Future Behavior, controlling for Present Behavior and individual were calculated. The resultant maps were thresholded at p<0.001 at the voxel-level, and clusters of 124 voxels or more were retained for visualization.

Resting-state functional connectivity

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Of main interest in this report is effective connectivity which estimates directed relationships among areas. To constrain these analyses, seed-based functional connectivity was performed on the resting-state data in order to identify ROI’s that may be connected to one another (and prune connections that are likely to not be present). For each ROI, voxel-wise correlations were computed between the ROI time-series and each voxel time-series. This was done separately for each resting-state run in sample 1 (note, only sample 1 was used here to maintain compatibility with the connectivity matrix defined previously [Nee and D'Esposito, 2016]). For a given seed ROI, the correlation values of each voxel were ranked after excluding voxels within 1.5 cm of the seed ROI. A correlation value r at cost c was computed wherein r reflects the correlation value of voxel at the cth percentile. Here, c was set to 18 as detailed previously (Nee and D'Esposito, 2016). Then, four counts were made: whether ROI 1 was connected to ROI 2 when ROI 1 was the seed in run 1, whether ROI 1 was connected to ROI 2 when ROI 2 was the seed in run 1, whether ROI 1 was connected to ROI 2 when ROI 2 was the seed in run 2, and whether ROI 1 was connected to ROI 2 when ROI 2 was the seed in run 2. A pair of ROIs were considered ‘connected’ if the average correlation value in the target ROI exceeded r. If at least 3 of the 4 counts were tallied, the connection between the areas was considered a candidate for future consideration. The resultant candidate connectivity matrix was utilized for effective connectivity analyses. The intent of this procedure was to be somewhat liberal, and allows the effective connectivity modeling to further prune connections. Hence, this procedure should be considered a scaffold for analyses to follow rather than an attempt to determine the true connectivity structure of the data.

Spectral dynamic causal modeling

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Time-invariant effective connectivity was estimated using spectral dynamic causal modeling (spDCM) implemented in SPM12 and DCM12.5. spDCM inverts a biophysically plausible generative model of the fMRI cross-spectral density (Friston et al., 2014; Razi et al., 2015; Razi et al., 2017). The model estimates the effective connectivity among hidden neural states and includes a hemodynamic forward model that accounts for how synaptic activity translates into regional hemodynamics and observed connectivity in the fMRI signal. spDCM estimated the effective connectivity among the six PFC and four PPC areas that are the focus of this report. Previously, ‘classic’ deterministic dynamic causal modeling (DCM) (Friston et al., 2003) was performed on the six PFC areas (Nee and D'Esposito, 2016; Nee and D'Esposito, 2017). ‘Classic’ DCM differs in numerous algorithmic and practical ways from spDCM (see Friston et al., 2014). Most notably, while ‘classic’ DCM inverts a generative model of the time-series of each modeled area, spDCM inverts a generative model of the cross-spectral density. The latter renders spDCM much more computationally tractable. This computational tractability comes at the cost of limiting modeling to time-invariant aspects of effective connectivity, which differs from ‘classic’ DCM that models both time-invariant and time-varying aspects of effective connectivity. However, ‘classic’ DCM becomes computationally impractical as the number of modeled areas grows. Therefore, spDCM is the more appropriate approach given the number of areas considered here. To complement spDCM, psycho-physiogical interaction (PPI) analyses were employed (described below) to capture time-varying aspects of effective connectivity. Hence, relative to previous work (Nee and D'Esposito, 2016; Nee and D'Esposito, 2017), the present study employed different methods that are computationally better-suited to answering questions at the network-level. An added benefit of its computational tractability is that the present approach can also scale up to answering questions about the interactions of the FPCN and other networks, which will facilitate future work.

Given that each individual has a specific topography in the PFC (Braga and Buckner, 2017), volumes of interest (VOIs) were defined based on each individual’s activation peaks. A 6 mm3 sphere was created around each individual’s activation peak that was close to the peak in the group contrast. To reduce noise in the VOIs, tiered thresholding was performed to eliminate unresponsive voxels. This threshold was started at p<0.001 (80.0% of VOIs), was lowered to p<0.05 if voxels did not survive (14.4% VOIs). If voxels still did not survive, the VOI was centered at the group peak and the threshold was lowered further to p<0.5 (5.1% of VOIs), and the threshold was eliminated if this was still insufficient (0.004% of VOIs). The model architecture utilized the candidate connectivity matrix estimated from the resting-state data described above.

spDCM’s required the estimation of 82 parameters using the model architecture based upon the candidate connectivity matrix. To provide sufficient data to estimate these parameters, pairs of runs were collapsed together using a modified version of spm_fmri_concatenate. The modifications allowed a flexible number of runs to be concatenated (default behavior is to concatenate all runs), and added a regressor to account for edge effects caused by run-wise (i.e. not concatenated) high-pass filtering. Other changes relative to the univariate modeling was that models of all participants included linear, squared, differential, and squared differential motion parameters, as well as a regressor to capture framewise displacement calculated across the six motion parameters (Power et al., 2012). The time-series’ for every VOI was extracted after regressing out all regressors related to confounds of non-interest (i.e. run means, motion, filter edge effects).

For each participant, two spDCM’s were estimated. The first modeled effective connectivity on time-series’ that excluded only confounds signals. The second modeled effective connectivity on time-series’ that additionally regressed out all task-related regressors included in the univariate modeling. Although spDCM is designed to estimate time-invariant effective connectivity, it is possible that task-related activity may nevertheless influence effective connectivity estimates (Cole et al., 2019). However, each of these spDCM’s produced similar results with no evidence of bias produced by including/excluding task-related regressors (Figure 6—figure supplement 1) consistent with the idea that spDCM estimated time-invariant effective connectivity as designed.

The following defaults were changed: the order of the AR model was set to 4 (this was the default for DCM12, but the default is 8 in DCM12.5). This was done after observing systematically poorer fits at the default levels in preliminary analysis. The maximum number of nodes to model was increased to 10 to accommodate the number of areas of interest. Finally, the maximum number of iterations for model fitting was increased to 1000 to ensure that all models converged.

spDCM was performed separately for each sample. This enabled the examination of the replicability of effective connectivity estimates and derivations thereof.

Psychophysiological interaction analysis

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To examine dynamic (time-varying) effective connectivity, psychophysiological interaction (PPI) analysis was performed. Here, a variant of the method detailed in Cole et al., 2013 was employed. Time-series’ from the same VOIs that were submitted to spDCM were modeled (in this case, the VOIs without the task regressed out since the task regressors are regressed out as part of PPI). For each connection in the probable connectivity matrix, the data were modeled as:

Ytarget=BconnYsource+BuniX+Bdep(bin(X)C.Ysource)

Here, Ytarget is the time-series of the target VOI, Ysource is the time-series of the source VOI, X is the univariate design matrix, bin(X) is a binarized version of the univariate design matrix wherein time-points that are above 0 are set to one and other time-points are set to 0, and C is the contrast matrix. This results in estimations of several contributions to the signal in the target VOI: Bconn which represents the time-invariant functional connectivity among the target and source, Buni which represents the univariate time-invariant task signals, and of main interest, Bdep which is the context-dependent changes in effective connectivity from the source to the target. This formulation is identical to Cole et al., 2013 except that contrasts are included within the model itself rather than being computed after parameter estimation. This change was performed because it reduces multi-collinearity, which is particularly problematic for PPI among highly correlated nodes. Preliminary analyses revealed that the more connected two regions were, the more negatively biased Bdep became using the method of Cole et al., 2013. This bias was eliminated by utilizing contrasts within the model.

Context-dependent connectivity (i.e. the PPI) is dictated by the contrasts defined in C. Here, five contrasts were defined which correspond to the four univariate contrasts of interest (Temporal Control, Contextual Control, Sensory-motor Control, Stimulus Domain) plus an additional interaction contrast that modeled Contextual Control x Stimulus Domain.

PPI analyses were performed separately for each sample. This enabled the examination of the replicability of the effective connectivity estimates and derivations thereof. PPI’s of Sensory-motor Control and Contextual Control x Stimulus Domain were unreliable across samples (Figure 7—figure supplement 1). Therefore, analyses were restricted to PPI’s of Temporal Control, Contextual Control, and Stimulus Domain.

Predicting higher level cognitive ability

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spDCM and PPI provided measures of static and dynamic effective connectivity, respectively. In particular, spDCM analyses revealed a role of contextual control-related areas in integrating cognitive control networks, and PPI analyses revealed greater integration across cognitive control networks during contextual control conditions. To examine the relevance of these measures to higher level cognition, static and dynamic effective connectivity were used to predict individual-differences in general higher-level cognitive ability.

General higher-level cognitive ability was assessed using the first principle component of the scores on the cognitive battery described above. To provide an index of static integration, for each network, between-network effective connectivity was contrasted against within-network effective connectivity. To isolate static integration of the contextual control network, the residualized static integration of the contextual control network was utilized after regressing out the static integration indices of the temporal control and sensory-motor control networks, as well as the root-mean square of framewise displacement (RMS FD) as a confound. Dynamic integration was calculated in a parallel manner to static integration. In this case, between-network effective connectivity was contrasted with within-network effective connectivity across all networks, but isolated to particular contrasts. For example, dynamic integration of contextual control indexed the degree to which there was greater between- relative to within-network communication for the contextual control contrast. Intuitively, whereas static integration of the contextual control network indicates the potential for contextual control areas to integrate networks, dynamic integration during contextual control indicates the actualization of this integration during the conditions that maximally activate contextual control areas. Similar to the static integration index, residualized dynamic integration during contextual control was utilized after regressing out the dynamic integration indices during temporal control and stimulus processing, along with RMS FD as a confound. To ensure independence among our samples, each of these indices (general higher level cognitive ability, static integration, dynamic integration) were calculated separately on sample 1 and sample 2.

Ridge regression was performed to predict general higher-level cognitive ability from static and dynamic integration. This was done in a two-fold manner, wherein each fold divided the dataset into training and test sets as a function of the samples (i.e. sample 1 and sample 2). For example, sample one was used to estimate weights using ridge regression, and then those weights were used to predict general higher-level cognitive ability in sample 2. Ridge regression was performed with at an arbitrarily chosen penalty parameter = 1, although significant prediction was achieved at penalties as high as 100 (which was the highest tested). The correlation between the observed and predicted general higher-level cognitive abilities was used to assess prediction performance. The observed correlation was compared to a permutation distribution formed by randomly permuting the rows of the prediction matrix 1000 times.

Predicting transcranial magnetic stimulation susceptibility

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As previously reported (Nee and D'Esposito, 2017), sample two was used to test the causal role of frontal areas to different forms of cognitive control. Each participant in sample two underwent an additional four sessions of the Comprehensive Control Task following continuous theta-burst stimulation (cTBS) to each of FPl, VLPFC, SFS, and S1 (control site). cTBS is patterned form of transcranial magnetic stimulation (TMS) thought to inhibit cortical tissue (Huang et al., 2005). Each TMS target was a node in a distinct PFC-PPC network and was predicted to produce distinct impairments in cognitive control. To examine whether static and dynamic integration of cognitive control networks is related to TMS susceptibility, the three observed TMS effects of interest were combined: the effect of FPl TMS on temporal control on error-rate, the effect of VLPFC TMS on the contextual control x stimulus-domain interaction on reaction time, and the effect of SFS TMS on stimulus-domain on error-rate (see Nee and D'Esposito, 2017 for additional details). For each effect, the frontal TMS effect was isolated by regressing out the corresponding effect following S1 TMS. Then, all TMS effects were combined using the first principle component.

Leave-1-out ridge regression was performed to predict the general cognitive control TMS effect from static and dynamic integration, wherein static and dynamic integration were computed identically to the above. The correlation between the observed and predicted general higher level cognitive abilities was used to assess prediction performance. The observed correlation was compared to a permutation distribution formed by randomly permuting the rows of the prediction matrix 1000 times.

Appendix 1

Supplemental results

Supplemental behavioral results

Behavioral data have been previously reported (Nee and D'Esposito, 2017; Nee and D'Esposito, 2016). Here, the focus is on two phases of the data: the sub-task phase wherein cognitive control demands are manipulated, and the return trials, wherein preparatory control processes readied during the sub-task phase are expressed.

Due to the complex design, it is useful to highlight particular data patterns that provide assurance that the task manipulations operate as desired. The interested reader is directed to Supplementary file 1 for complete factorial statistics.

First, effects of stimulus domain were examined. In sample 1, RTs on verbal and spatial tasks were well-matched during the sub-task (verbal: 644.32 ms; spatial: 642.4 ms; F(1,23) = 0.03, p=0.87) and return trials (verbal: 829.5 ms; spatial: 823.7 ms; F(1,23) = 0.12, p=0.74). Accuracies were also similar during sub-task (verbal: 92.8%; spatial: 93.9%; F(1,23) = 3.12, p=0.09), and return trials (verbal: 0.79%; spatial: 0.81%; F(1,23) = 3.01, p=0.10), though trending towards more errors on the verbal task. In sample 2, RT data provided some evidence that the verbal task was more difficult than the spatial task on sub-task trials (verbal: 792.9 ms; spatial: 757.8 ms; F(1,24) = 5.01, p=0.03), with a similar trend on return trials (verbal: 932.7 ms; spatial: 908.0 ms; F(1,24) = 3.80, p=0.06). Accuracies were not significantly different on sub-task (verbal: 94.5%; spatial: 95.4%; F(1,24) = 2.90, p=0.10) nor return trials (verbal: 84.5%; spatial: 84.6%; F(1,24) = 0.01, p=0.91). Combining the samples, there was no significant difference in verbal and spatial RTs during the sub-task (F(1,48) = 3.55, p=0.07) and return trials (F(1,48) = 2.32, p=0.13). There was a significant difference in verbal and spatial accuracies during the sub-task (F(1,48) = 6.09, p=0.02), but not return trials (F(1,48) = 1.62, p=0.21). Collectively, these data provide some scattered evidence that the verbal task was modestly more challenging than the spatial task, but overall, the stimulus domains were reasonably well-matched.

Second, it is desirable that the cognitive control manipulations produce clear and consistent effects on behavior. To illuminate these effects, I consider simple comparisons to the Baseline condition, although clear and consistent effects are observed using the full factorial framework and detailed in Supplemental Tables 1 and 2. Sensory-motor control involves selecting an appropriate action based upon the stimulus. Demands on these processes are minimized during the Planning sub-task phase, during which participants can reflexively respond without processing the verbal or spatial stimulus features. Correspondingly, RTs are expected to be speeded during the Planning sub-task phase. These expectations were met in both samples (sample 1: mean difference = −184.1 ms; Cohen’s d = 2.09; t(23) = −10.24, p=4.85e-10; sample 2: mean difference = −211.7 ms; Cohen’s d = 1.61; t(24) = −8.06, p=2.75e-8). Accuracies were also elevated in the Planning sub-task phase relative to Baseline indicating that RT speeding did not tradeoff from accuracy (sample 1: mean difference = 5.3%; Cohen’s d = 0.87; t(23) = 4.25, p=0.0003; sample 2: mean difference = 3.6%; Cohen’s d = 0.71; t(24) = 3.56, p=0.002).

Next, contextual control involves selecting the appropriate task set over-and-above sensory-motor control. This should incur an additional cost in RT reflected when comparing the Switching sub-task phase to the Baseline condition. These expectations were met in both samples (sample 1: mean difference = 60.8 ms; Cohen’s d = 1.08; t(23) = 5.31, p=2.17e-5; sample 2: 189.0 ms; Cohen’s d = 1.53; t(24) = 7.65, p=6.90e-8). Accuracy was either the same or slightly worse in the Switching condition, indicating that slowing was not a result of speed-accuracy tradeoff; sample 1: mean difference = 0.4%; Cohen’s d = 0.10; t(23) = 0.51, p=0.62; sample 2: mean difference = −1.8%; Cohen’s d = −0.43; t(24) = −2.16, p=0.04.

Finally, temporal control involves utilizing temporally extended representations to guide action. In the Planning condition, these representations are sustained during the sub-task phase, and utilized during the return trial. Hence, demands on temporal control are most clearly manifest in behavior on the return trial. In contrast to the above analyses that showed speeded RTs during the sub-task phase of the Planning condition relative to the Baseline condition, this same comparison on return trials showed slowed RTs for the Planning condition in both samples (sample 1: mean difference = 88.8 ms; Cohen’s d = 0.65; t(23) = 3.20, p=0.004; sample 2: mean difference = 71.9 ms; Cohen’s d = 0.59; t(24) = 2.96, p=0.007). Accuracies were also diminished (sample 1: mean difference = −13.1%; Cohen’s d = 0.93; t(23) = −4.54, p=0.0001; sample 2: mean difference = −6.5%; Cohen’s d = 0.63; t(24) = −3.16, p=0.004).

Collectively, the behavioral data produced the expected cognitive control-related patterns.

Supplemental imaging results

Although the analyses in the main text suggest that integration predicts a general susceptibility of cognitive control to TMS, it leaves open whether such effects are domain-general or domain-specific. The first principle component of the TMS effects loaded relatively equally on all TMS effects examined (0.67 on effect of FPl-TMS to temporal control; 0.49 on effect of SFS-TMS to spatial stimulus-domain; 0.56 on effect of VLPFC-TMS to verbal contextual control). The second principle component of TMS effects loaded positively on spatial effects, negatively on verbal effects, and negligibly on domain-general effects (−0.07 on effect of FPl-TMS to temporal control; 0.79 on effect of SFS-TMS to spatial stimulus-domain; −0.62 on effect of VLPFC-TMS to verbal contextual control) suggesting that the second principle component reflected domain-specific effects of TMS (i.e. spatial > verbal). Whereas static and dynamic integration were able to predict the first principle component of TMS effects as described in the main text, the second component reflecting domain-specific effects could not be predicted using analogous methods (r = 0.03, p>0.3). These data indicate that the predictive power of the integration measures are limited to domain-general cognitive control.

Data availability

All data and code needed to reproduce the figures in this report can be found at https://osf.io/938dx/.

The following data sets were generated
    1. Nee D
    (2020) Open Science Framework
    ID 938dx. PFC-PPC Integration.

References

  1. Report
    1. Brodmann K
    (1909)
    Vergleichende Lokalisationslehre Der Grosshirnrinde in Ihren Prinzipien Dargestellt Auf Grund Des Zellenbaues
    Barth.
  2. Book
    1. Sporns O
    (2010)
    Networks of the Brain
    MIT press.
  3. Book
    1. Yarkoni T
    2. Braver TS
    (2010) Cognitive neuroscience approaches to individual differences in working memory and executive control: Conceptual and methodological issues
    In: Gruszka A, Matthews G, Szymura B, editors. Handbook of Individual Differences in Cognition: Attention, Memory and Executive Control. Springer. pp. 87–107.
    https://doi.org/10.1007/978-1-4419-1210-7_6

Decision letter

  1. Timothy E Behrens
    Senior Editor; University of Oxford, United Kingdom
  2. Daeyeol Lee
    Reviewing Editor; Johns Hopkins University, United States
  3. Evan Gordon
    Reviewer; Veterans Health Administration, United States
  4. Moataz Assem
    Reviewer; MRC Cognition and Brain Sciences Unit, University of Cambridge, United Kingdom

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

The authors investigated how functional gradients of cognitive control might manifest in the fronto-parietal control network. The results suggest that the gradients in this network might reflect changes between internally-oriented vs. externally oriented control processes involved in planning for the future and specifying actions according to the present stimuli, respectively. An intermediary zone in this network might play an integrative function by providing the necessary contextual control.

Decision letter after peer review:

Thank you for submitting your article "Integrative frontal-parietal dynamics supporting cognitive control" for consideration by eLife. Your article has been reviewed by Timothy Behrens as the Senior Editor, a Reviewing Editor, and three reviewers. The following individuals involved in review of your submission have agreed to reveal their identity: Evan Gordon (Reviewer #2); Moataz Assem (Reviewer #3).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

We would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). Specifically, when editors judge that a submitted work as a whole belongs in eLife but that some conclusions require a modest amount of additional new data, as they do with your paper, we are asking that the manuscript be revised to either limit claims to those supported by data in hand, or to explicitly state that the relevant conclusions require additional supporting data.

Our expectation is that the authors will eventually carry out the additional experiments and report on how they affect the relevant conclusions either in a preprint on bioRxiv or medRxiv, or if appropriate, as a Research Advance in eLife, either of which would be linked to the original paper.

Summary:

Nee presents a sophisticated set of new analyses on two previously published fMRI/TMS data sets to further examine the proposal of functional gradients of cognitive control in lateral prefrontal cortex (PFC) and posterior parietal cortex (PPC). The two prior papers have produced evidence for an integrative "apex" of control in the mid-lateral PFC. The current paper (a) provides a reconceptualization of these gradients as reflecting an externally to internally focused dimension (and offers some associated fMRI analyses), and (b) applies a series of connectivity and brain-behavior correlation analyses to test the integrative role of mid-lateral PFC and PPC regions. In particular, the author demonstrated that the Fronto-Parietal control network has a rostro-caudal organization, in which rostral regions are more engaged during sensory-motor control, caudal regions are more engaged during temporal control, and central regions are engaged during both; and further, activation of these regions predict behavior in a domain-specific fashion. He provides evidence that the central "Context Control" regions are the regions that are exerting primary influence over the other regions, both statically and especially dynamically, and that these static and dynamic influences are associated with both baseline cognitive abilities and with susceptibility to TMS effects. An understanding of the neuroanatomy of high-level control processes is a topic of great importance, and the basic approach (using a very complex and clever task) and analyses pursued by the author are compelling and sophisticated, and they ultimately produce a pretty coherent set of results.

Essential revisions:

1) The author should explain more clearly what aspects of the current paper are new. A devil's advocate (more precisely, a "novelty advocate") could argue that these functional gradients in PFC have been reported previously (in Nee and D'Esposito, 2016, 2017), and the same seems to be true for the PPC (Choi et al., 2018). Moreover, the proposal that the gradients that have previously been cast in terms of levels of abstraction (Badre) or temporal information integration (Koechlin) could also be thought of as reflecting an external-to-internal orientation of cognition is interesting but could be argued to just shift the semantics a little bit, without really widening the scope of phenomena explained. Similarly, some of the current "new" analyses could be argued to either reiterate previous results (Figure 2), re-package the previously reported results in slightly different ways (e.g., the MDS results in Figure 3), or represent foregone conclusions (the "present vs. future" results in Figure 4 seem to follow pretty inevitably from the way the task and brain regions' roles are being re-conceptualized, if I am not mistaken). That would leave only the connectivity-based analyses as providing new information, and even here it is not clear what is known already and what is novel (as DCM was already applied to the PFC data in the 2016 paper). Altogether, this created a murky impression as to what is old, what is new-ish (but fully expected within the re-conceptualized framework), and what is actually novel (in a nontrivial sense) in the results.

2) While the author frames the cortical subdivisions observed here as subcomponents of the Fronto-parietal control network, it is not entirely convincing that this is an accurate description of these areas. The "temporal control" areas, in localizing to angular gurus, far anterior middle frontal gyrus, and anterior temporal cortex, could arguably be better described as being within the Default network. The "Sensory-motor control" regions, in localizing to regions such as SPL and SFS, could be better described as being within the Dorsal Attention network. Certainly, the described differential functions of these regions fit well with known functions of these two networks. This could be adjudicated by a) showing medial surface views of Figure 2 (helpful especially for determining whether Default regions are involved), and b) computing an overlap metric of each set of regions (or activation map) with a publicly available network map, such as that described in (Yeo et al., 2011). If these regions do overlap better with non-FP networks, this doesn't necessarily invalidate any of the paper's findings, but it does change their interpretation somewhat: instead of reasoning that a central region of FP network regulates peripheral FP regions, we might conclude that FP regulates other networks, in a fashion similar to that outlined in (Gratton et al., 2018).

3) While the author has framed these results in the context of a macroscale gradient in frontal (and parietal) cortex, there is no strong evidence for this. Three sets of regions with different functions does not necessarily indicate a gradient; it could indicate three discrete networks. To make strong claims about finding a gradient, the author would need to test a continuous line of ROIs from one of the current seeds to the next, and show that brain function varies continuously with position. And ideally this would need to be done in individual subjects, to avoid the blurring that comes from averaging across subjects with variable spatial organization of FP (as detailed in Braga and Buckner, 2017). When such tests have previously been done (in resting-state data, at least), they indicate the existence of strong borders between discrete areas in lateral frontal cortex, not continuous gradients (see e.g. Wig et al., 2014, esp. Figure 7). It would not be completely necessary to perform such a test, because this concern doesn't invalidate any of the findings here. However, absent more comprehensive tests, the gradient interpretation might be simply only one of several frameworks that should be discussed. Towards that end, the author could make better contact with previous works that have subdivided the brain into discrete sub-networks (rather than framing it as a continuous gradient) (Abou Elseoud et al., 2011; Doucet et al., 2011; Meunier et al., 2009), and especially those that have characterized how FP subdivisions connect strongly with other networks. (Gordon et al., 2018) and particularly (Dixon et al., 2018) seem highly relevant here, and they fit very nicely with the present characterization of the central FP network providing separate top-down integrative control of internal and external stimuli.

4) The results in this manuscript leave open the question of how they can be reconciled with strong evidence that multitudes of tasks co-activate highly specific regions within the fronto-parietal cortices that largely overlap with regions of the intermediate zone (e.g. Shine et al., 2016; Fedorenko et al., 2013; Assem et al., 2020). Importantly, a recent study using hundreds of subjects and improved brain alignment methods (Assem et al., 2020) showed that even a simple 0-back task (similar to the baseline task used in this study) co-activates both caudal and rostral fronto-parietal regions. Is it possible the current task contrasts are missing out on regions with signals of comparable strengths? For example, in the sensory-motor contrast (Dual + baseline > Planning + switching), could the baseline task be also engaging broader frontal and parietal regions though more weakly than the other tasks? This would suggest that the intermediate zone has relative rather than absolute concrete/abstract gradient preferences.

5) An important methodological concern is that all the analysis used data with excessive unconstrained volumetric smoothing (8 mm) mixing signals from functionally distinct regions (see Coalson et al., 2018). Finding replicable results across two independent samples analyzed using the same non-optimal methods does not rule out the possibility of falling in the same pitfalls in both datasets. For example, while the manuscript claims to examine gradients within the fronto-parietal network, the temporal control contrast might be mainly highlighting DMN activations and connectivity dynamics. This also limits the interpretability of the connectivity indices and their relation to individual differences (Bijsterbosch et al., 2018, 2019). Ideally, the author is encouraged to repeat the task and connectivity analyses with minimal smoothing (2-4 mm). Further, why are all the analyses limited to the left hemisphere? If it is because the task effects are stronger on the left, this does not exclude decent effects on the right hemisphere which could provide a strong validation for the task and connectivity results.

6) To improve the interpretability of the effective connectivity results, it would be helpful to provide more details on the methodological and biological assumptions behind using positive and negative effective connectivity indices to suggest that they reflect excitation and inhibition, respectively, as well as the limitations related to fMRI effective connectivity analyses. Further, negative correlations between static connectivity and general cognitive abilities are in contrast with numerous reports showing that measures of resting-state functional connectivity across the fronto-parietal network positively correlate with general cognitive abilities (e.g. Dubois et al., 2018). Could the author comment on this difference?

Also, the author interprets the negative between-network connectivity as reflecting functional segregation, and positive connectivity as reflecting integration. This is plausible but certainly not the only possible interpretation of such a pattern. For instance, increases in between-node connectivity with greater control demand are often interpreted as reflecting modulation/biasing of one region by the other, which seems conceptually distinct from "integration", at least the way the author conceptualizes integration (i.e., the mid-lateral PFC joining up information from posterior and anterior regions). I wonder whether there might be stronger tests of the claim that this node integrates information processed in the other nodes, perhaps by using an information-based analytic approach (like MVPA/RSA)?

7) It would be problematic at brain-behavior individual differences using a small sample size like the one used to probe connectivity-TMS effects due to their unreliability. If the author insists on keeping this section, it will be useful to examine any shared variance between general cognitive abilities and the observed TMS behavioral effects.

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "Integrative frontal-parietal dynamics supporting cognitive control" for further consideration by eLife. Your revised article has been evaluated by Timothy Behrens (Senior Editor) and a Reviewing Editor.

Summary:

The authors investigated how functional gradients of cognitive control might manifest in the fronto-parietal control network. The results suggest that the gradients in this network might reflect changes between internally-oriented vs. externally oriented control processes that are involved in planning for the future and specifying actions according to the present stimuli. An intermediary zone in this network might play an integrative function by providing the necessary contextual control.

The manuscript has been improved but there are some remaining issues that need to be addressed before acceptance, as outlined below:

1) In the Discussion section "Beyond the PFC: Towards a Network View of Cognitive Control" the author gives the impression that the majority of studies on cognitive control have solely focused on the PFC. This needs to be rebalanced to reflect that a distributed whole brain network view of cognitive control has long been argued (to name a few: Cole and Schnider, 2007; Power and Petersen, 2013; Fedorenko et al., 2013; Warren et al., 2014; Duncan et al., 2010 and 2020).

2) Some of the supplementary figures were missing (Figure 2—figure supplement 2, Figure 6—figure supplement 2, Figure 7—figure supplement 3), not sure if this was a problem with the submission system. There were also a few typos.

https://doi.org/10.7554/eLife.57244.sa1

Author response

Essential revisions:

1) The author should explain more clearly what aspects of the current paper are new. A devil's advocate (more precisely, a "novelty advocate") could argue that these functional gradients in PFC have been reported previously (in Nee and D'Esposito, 2016, 2017), and the same seems to be true for the PPC (Choi et al., 2018). Moreover, the proposal that the gradients that have previously been cast in terms of levels of abstraction (Badre) or temporal information integration (Koechlin) could also be thought of as reflecting an external-to-internal orientation of cognition is interesting but could be argued to just shift the semantics a little bit, without really widening the scope of phenomena explained. Similarly, some of the current "new" analyses could be argued to either reiterate previous results (Figure 2), re-package the previously reported results in slightly different ways (e.g., the MDS results in Figure 3), or represent foregone conclusions (the "present vs. future" results in Figure 4 seem to follow pretty inevitably from the way the task and brain regions' roles are being re-conceptualized, if I am not mistaken). That would leave only the connectivity-based analyses as providing new information, and even here it is not clear what is known already and what is novel (as DCM was already applied to the PFC data in the 2016 paper). Altogether, this created a murky impression as to what is old, what is new-ish (but fully expected within the re-conceptualized framework), and what is actually novel (in a nontrivial sense) in the results.

I acknowledge this perspective, especially given the way in which the manuscript was originally laid out. As I explain below, I have made edits to help guide the reader towards what I take as the main novelty of the manuscript (the connectivity-based analyses), indicate more clearly what might be considered more incremental based on prior work (functional analyses), and also explain that what sets this work apart is the combination of these two approaches which I take as greater than the sum of their parts. I unpack the reasoning behind this below:

Much of the novelty is in the connectivity-based analyses as has been pointed out (see more below). The intention of the analyses that precede the connectivity-based analyses are to provide a functional foundation from which the connectivity-based analyses can be interpreted. That is, showing that network A and network B interact in manner X has theoretical impact only insofar as one can determine, to a reasonable approximation, what functions networks A and B perform. In contemporary cognitive neuroscience, these functional underpinnings are oftentimes weakly and/or coarsely inferred. Consider, for example, that what I refer to as the “temporal control” network was interpreted in the previous round of reviews as the “default-mode” network (see Essential revision 2). Below I address this issue by computing overlaps with a widely used atlas, but I could argue that more direct evidence against such an interpretation can be levied by careful inspection of Figure 3 and Figure 4. In Figure 3, one can observe that areas within the temporal control network are more strongly activated in both the most demanding (dual) and least demanding (planning) conditions relative to the baseline condition. Such a pattern does not seem to accord with the (negative) monotonic demand-activation relationship typically observed in “default-mode” areas. Moreover, although a labored argument might be constructed to explain how “default”-related activations relate to future behavior (defined as reaction times in trials immediately following the sub-task period), the most straightforward explanation of this pattern is that these activations reflect preparation for the future (a control process), rather than some off-task internal mentation (a “default” process). Hence, the rich functional data offer detailed insights that significantly exceed what could be gained from a functionally unconstrained method such as resting-state, or a functionally coarse method such as quantitative reverse inference and/or a task battery. This precise characterization provides a firm functional foundation from which to interpret network interactions. Therefore, much of the manuscript is devoted to establishing that foundation, and I take it as an important innovation of the present manuscript.

In my view, properly establishing a functional foundation required some re-depicting of analyses previously described (PFC ROI analyses), demonstrating parallels in the PPC (replicating Choi et al., 2018), expanding upon the parallels in the PPC (demonstrating timescale/medium-specific brain-behavior relationships) and providing a theoretical perspective to synthesize the results (external/present-to-internal/future axis). It can be argued that the knowledge gained in this section of the manuscript is more incremental than novel, but without this foundation, I feared that the reader would be unable to interpret the network-based analyses. I do share the concern that perhaps the true novelty of the manuscript, which I take to be the network-based analyses, comes too late and a reader might be led to believe that the functional analyses are the focus. One possible solution to this issue would be to push some parts of Figure 2, Figure 3 and Figure 4 to supplemental material. I attempted this in a draft but was unsatisfied that the resulting manuscript was sufficiently self-contained, so I reverted such changes. Instead, I have made following edits: both at the end of the Introduction and towards the beginning of the Results section, I more clearly spell-out a road map of the analyses to follow. This includes highlighting the primacy of the network-based analyses, but also their dependence on establishing network-process relationships which follow closely from previous work. I have also interwoven these sentiments throughout the Discussion while further discussing the importance of the functional foundation which sets the present manuscript apart from other contemporary studies of network neuroscience.

From the Introduction:

“Here, two datasets that have demonstrated macroscale gradients of cognitive control in the PFC26,27 are examined to investigate dynamics in the broader FPCN. […] Collectively, these analyses elucidate the integrative organization of the FPCN whose insights may be useful to understand other transmodal networks.”

From the Results:

“The analyses that follow proceed in two parts. First, areas within the FPCN are functionally mapped and related to behavior by contrasting activation and performance across different task conditions. […] These dynamics are then related to individual differences in trait-level cognitive ability and amenability to neuromodulation to establish their importance more broadly.”

I note in passing that I am not sure that I understand the comment that the results in Figure 4 follow inevitably from the way the task and brain regions’ roles are conceptualized. I can see a multitude of ways in which reaction times and activations could have associated that would not follow the depicted patterns. Given that “task-positive” areas very often rise and fall with reaction time (i.e. present behavior), it seems that it could have easily been the case that present behavior explained the rise and fall of all areas. If this continues to be a concern, I would appreciate further discussion of the matter.

As for the novelty of the effective connectivity analyses employed in the present manuscript, there are a few things that are worth emphasizing. Previously, we performed “classic” dynamic causal modeling (DCM) as a generative modeling approach to the time-series of six areas of the PFC. This approach answered questions regarding which areas, if any, might be considered the apex of the putative PFC hierarchy as operationalized by asymmetry of influence. This manuscript considers the broader question of how areas within the FPCN interact to support cognitive control. This question bridges literatures that have been narrowly focused on the organization of the PFC to literatures that have considered the network organization of cortex more globally but without fine-grained functional specificity. Classic DCM is computationally quite demanding and quickly becomes computationally infeasible when more than a handful of areas are considered. Hence, to move towards network-level descriptions, a different approach is needed. Here, I performed spectral DCM as generative modeling approach to the frequency cross-spectra of the FPCN. Despite shared nomenclature, classic and spectral DCM differ substantially in both algorithm and scope (c.f. Friston et al., 2014). Given the stationarity of the spectral DCM approach, it was then complemented by psycho-physiological interaction (PPI) analyses to detail non-stationary aspects of effective connectivity, which is another method algorithmically distinct from the previous work. Thus, the connectivity-based analyses are new analyses that follow in the spirit of recent trends to apply new, but often related analytic approaches to existing datasets (e.g. HCP, Midnight Scan Club) in order to answer novel questions. Collectively, these approaches revealed unique insights into integrative FPCN dynamics underpinning cognitive control that could not be explored by our previous approach, and provide a macroscale picture that could not be properly appreciated within our previous approach. I have added text to the Materials and methods to highlight these points more clearly.

From the Materials and methods:

“Time-invariant effective connectivity was estimated using spectral dynamic causal modeling (spDCM) implemented in SPM12 and DCM12.5. spDCM inverts a biophysically plausible generative model of the fMRI cross-spectral density32–34. […] An added benefit of its computational tractability is that the present approach can also scale up to answering questions about the interactions of the FPCN and other networks, which will facilitate future work.”

Finally, I would like to close with the broader point that novelty often comes from a unique combination of factors rather than any one factor alone. Classic, task-based approaches can offer strong functional inference, but such studies can often suffer from being narrow either in the processes examined, brain areas detailed, or both. Contemporary, network-based approaches consider networks in their entirety, but can be difficult to integrate into cognitive and neuroscientific theory without a firm functional foundation. I see the present study as a bridge that incorporates the best of both of these approaches that I hope serves as a paradigmatic way forward to provide mechanistic insights that are grounded in fine-grained function. Collectively then, I hope you will agree that the combination of the functional foundation, which has been expanded here relative to previous works, and new connectivity-based analyses offers sufficient novelty when considered jointly.

2) While the author frames the cortical subdivisions observed here as subcomponents of the Fronto-parietal control network, it is not entirely convincing that this is an accurate description of these areas. The "temporal control" areas, in localizing to angular gurus, far anterior middle frontal gyrus, and anterior temporal cortex, could arguably be better described as being within the Default network. The "Sensory-motor control" regions, in localizing to regions such as SPL and SFS, could be better described as being within the Dorsal Attention network. Certainly, the described differential functions of these regions fit well with known functions of these two networks. This could be adjudicated by a) showing medial surface views of Figure 2 (helpful especially for determining whether Default regions are involved), and b) computing an overlap metric of each set of regions (or activation map) with a publicly available network map, such as that described in (Yeo et al., 2011). If these regions do overlap better with non-FP networks, this doesn't necessarily invalidate any of the paper's findings, but it does change their interpretation somewhat: instead of reasoning that a central region of FP network regulates peripheral FP regions, we might conclude that FP regulates other networks, in a fashion similar to that outlined in (Gratton et al., 2018).

I agree with the editors/reviewers that making more direct contact with publicly available network maps would be useful to both better situate the networks observed here, and also offer functional insights into well-established networks whose precise functions remain unclear. I have computed the overlap between the networks mapped by the task contrasts and the Yeo et al., 2011 atlas as recommended. Below I depict the overlap of the networks mapped by the task with relevant networks described by Yeo et al., 2011 in their 17-network parcellation. Note that the “FPN”, nomenclature is in keeping with Dixon et al., 2018 and Murphy et al., 2020, which differs from Yeo’s nomenclature. This analysis indicates that the temporal control network (red) aligns most clearly with “FPN A”. This network has been recently hypothesized to be a bridge between the FPCN and DMN (Dixon et al., 2018; Murphy et al., 2020) which accords well with the idea of it being on the internal end of the FPCN axis. The sensory-motor control (blue) networks aligns most closely with “FPN B” and also showing some semblance to the “DAN”. This accords well with the sensory-control network being on the external end of the FPCN axis, and the recent hypothesis that “FPN B” is a bridge between FPCN and DAN (Dixon et al., 2018; Murphy et al., 2020). Finally, the contextual control network aligns most closely with “FPN B”, but also overlaps with “FPN A” suggesting the integration of these two networks for contextual control. Collectively, these data re-affirm the idea that the task contrasts map networks involved in cognitive control as designed. Moreover, I believe that these data serve to “ground” these connectivity-based networks more concretely in function, adding insights into the roles of these networks that cannot be established by connectivity-patterns alone. I have added a depiction of these overlaps to Figure 2 and added text to the Materials and methods, Results and Discussion accordingly.

From Materials and methods:

“For each activation contrast, the overlap with the Yeo et al.11 17-network parcellation was examined. For each of the 17 networks, the percentage of significant voxels for a given activation contrast that overlapped with the network was tabulated.”

From Results:

“Previous work has suggested that the FPCN can be fractionated into sub-networks10–13. In particular, it has been proposed that an FPCN network A acts as an intermediary between the FPCN and internally-oriented “default-mode” network (DMN). […] Furthermore, these observations offer more precise functional descriptions of previously fractionated sub-networks.”

From Discussion:

“The position of the FPCN with respect to macroscale gradients of cortex is intermediary between canonical circuits involved in modality-specific processing, and the default-mode network involved in internal mentation21,44[…] Collectively, these data serve to functionally ground the sub-networks that have been identified through co-activations.”

3) While the author has framed these results in the context of a macroscale gradient in frontal (and parietal) cortex, there is no strong evidence for this. Three sets of regions with different functions does not necessarily indicate a gradient; it could indicate three discrete networks. To make strong claims about finding a gradient, the author would need to test a continuous line of ROIs from one of the current seeds to the next, and show that brain function varies continuously with position. And ideally this would need to be done in individual subjects, to avoid the blurring that comes from averaging across subjects with variable spatial organization of FP (as detailed in Braga and Buckner, 2017). When such tests have previously been done (in resting-state data, at least), they indicate the existence of strong borders between discrete areas in lateral frontal cortex, not continuous gradients (see e.g. Wig et al., 2014, especially Figure 7). It would not be completely necessary to perform such a test, because this concern doesn't invalidate any of the findings here. However, absent more comprehensive tests, the gradient interpretation might be simply only one of several frameworks that should be discussed. Towards that end, the author could make better contact with previous works that have subdivided the brain into discrete sub-networks (rather than framing it as a continuous gradient) (Abou Elseoud et al., 2011; Doucet et al., 2011; Meunier et al., 2009), and especially those that have characterized how FP subdivisions connect strongly with other networks. (Gordon et al., 2018) and particularly (Dixon et al., 2018) seem highly relevant here, and they fit very nicely with the present characterization of the central FP network providing separate top-down integrative control of internal and external stimuli.

The editors/reviewers raise an interesting question regarding the resolution of so-called “macroscale gradients.” I have added text to be clear about what I mean by “gradient” so that it is not mistaken for the idea of being “continuous” at some fine spatial scale. By “gradient”, I take the weak position that there are spatial axes of functional change along the cortex. The spatial resolution of those axes may be areal or something finer (e.g. columnar). The data as analyzed are consistent with an areal scale, but remain silent regarding whether or not finer scales exist. Given that any form of averaging/interpolation can cause discrete functions to appear continuous, I do not think that analyses on the present dataset would be convincing regarding finer scales when considering the voxel sizes acquired, preprocessing performed, and SNR of the data absent averaging/interpolation. So, I believe that an appropriate answer to this concern would require a dataset more specifically designed to address such questions. I have added a footnote in the Introduction to clarify what is meant by “gradient” in the present manuscript. I have also added text to the Discussion regarding the limitations of the present dataset to uncover the resolution of the “gradient.” Finally, I have included discussion of the suggested references along with a recent preprint that examined gradients in the non-human primate at a spatial scale finer than can be obtained with fMRI and found support for the areal level of resolution. The present data are not inconsistent with these findings.

From the Introduction:

“A “gradient” refers to a change in a property along an axis. With respect to cortex, a functional gradient means that functions vary in a roughly monotonic fashion with cortical distance along a spatial axis. The resolution of the gradient, or in other words, the steps along the axes, may be discrete and areal, or approach continuity. The present study remains silent regarding the resolution of these gradients, and takes the weak position that functions change along cortical axes at some unknown rate/resolution.”

From the Discussion:

“One question that remains open is the spatial resolution of macroscale cortical gradients. […] Because of the processing and spatial resolution of the data here, the present dataset is unable to speak to finer gradations that may exist below the areal level, and is not inconsistent with the idea that the resolution of macroscale gradients is the areal level.”

4) The results in this manuscript leave open the question of how they can be reconciled with strong evidence that multitudes of tasks co-activate highly specific regions within the fronto-parietal cortices that largely overlap with regions of the intermediate zone (e.g. Shine et al., 2016; Fedorenko et al., 2013; Assem et al., 2020). Importantly, a recent study using hundreds of subjects and improved brain alignment methods (Assem et al., 2020) showed that even a simple 0-back task (similar to the baseline task used in this study) co-activates both caudal and rostral fronto-parietal regions. Is it possible the current task contrasts are missing out on regions with signals of comparable strengths? For example, in the sensory-motor contrast (Dual + baseline > Planning + switching), could the baseline task be also engaging broader frontal and parietal regions though more weakly than the other tasks? This would suggest that the intermediate zone has relative rather than absolute concrete/abstract gradient preferences.

I believe that this is a point about the specificity observed in the data with regard to areal-process associations/dissociations relative to other studies. If I am mistaken in that interpretation, I would welcome further clarification and discussion.

It is not clear to me that the observation of activation across the FPCN when contrasting 0-back with fixation (i.e. Assem et al., 2020) has strict bearing upon the patterns observed here, and I am not sure that sample sizes and processing methods are operational in this regard. Rather, it is notable that BOLD fMRI is a unitless measure that affords only relative claims. Given the limitations of BOLD, well-matched comparisons are key for dissociating the roles of functionally related areas. For example, one can observe activation in the FFA when comparing scrambled faces to fixation. One could potentially interpret such a result as an indication that the FFA is not preferentially involved in face processing, but rather is involved in visual processing more generally. Yet, adding faces as a third comparison would reveal that the FFA responds more strongly to faces than to scrambled faces, suggesting a role in visual processing, as well as a more selective role in face processing (c.f. Kanwisher et al., 1997 among countless other works). This underscores the importance of well-controlled comparisons to dissociate functional roles of related areas (along with the need for causal methods to validate correlational patterns). Therefore, that some or all of the areas detailed here are activated for 0-back relative to fixation does not undermine more specialized control functions of some of the areas therein, just as observation FFA activation during non-face tasks does not undermine its role in face processing. Hence, I see no necessary inconsistency with the cited studies and the data reported here.

This issue speaks to contentions between accounts that regard the FPCN as functionally homogenous (or nearly so) whose organization is unclear, and accounts that regard the FPCN as functionally heterogeneous and organized along particular dimensions. I have spoken to this debate elsewhere (e.g. Badre and Nee, 2018) and I am not sure that this manuscript is the appropriate outlet to repeat/expand upon such arguments. Although the present data certainly fall on one-side of this debate, and a particularly interested reader could closely inspect the radar plots in Figure 3 to determine how much each area responds to the baseline condition alone, it is not the focus of the present study and I worry that discussing the matter would only further divert focus from the essence of the study (as per Essential revision 1). Therefore, I have opted to set this debate aside for the moment, but I would be willing to add to the Discussion if the editors feel it is essential.

5) An important methodological concern is that all the analysis used data with excessive unconstrained volumetric smoothing (8 mm) mixing signals from functionally distinct regions (see Coalson et al., 2018). Finding replicable results across two independent samples analyzed using the same non-optimal methods does not rule out the possibility of falling in the same pitfalls in both datasets. For example, while the manuscript claims to examine gradients within the fronto-parietal network, the temporal control contrast might be mainly highlighting DMN activations and connectivity dynamics. This also limits the interpretability of the connectivity indices and their relation to individual differences (Bijsterbosch et al., 2018, 2019). Ideally, the author is encouraged to repeat the task and connectivity analyses with minimal smoothing (2-4 mm). Further, why are all the analyses limited to the left hemisphere? If it is because the task effects are stronger on the left, this does not exclude decent effects on the right hemisphere which could provide a strong validation for the task and connectivity results.

After additional discussion with the editors and reviewer, I have repeated the analyses using 4 mm volumetric smoothing. In particular, follow-up discussion revealed concern that the integrative role of mid-positioned areas may have arisen from signal mixing caused by an excessively large smoothing kernel. We have agreed that 4 mm volumetric smoothing would sufficiently dampen such potential confounds and all analyses have been repeated with this processing choice.

As now reported, the observed results do not appear to be artifacts of a large smoothing kernel. Activation gradients (Figure 2—figure supplement 1), activation profiles (Figure 3—figure supplement 1), brain-behavior relationships (Figure 4—figure supplement 1), lobular source-target relationships (Figure 5—figure supplement 1), static network interactions (Figure 6—figure supplement 2), and dynamic network interactions (Figure 7—figure supplement 3) remain unchanged. Integration dynamics also continue to explain individual differences in susceptibility to TMS (Figure 9—figure supplement 1). The lone analysis that did not replicate in full was the relationship of integration dynamics to individual differences in cognitive ability. Previously, I had observed a weak negative relationship between cognitive ability and static integration (r = -0.22), and a weak positive relationship between cognitive ability and dynamic integration (r = 0.23). These integration dynamics could be jointly used to significantly predict cognitive ability (r = 0.32). In the re-analysis, the weak positive relationship between cognitive ability and dynamic integration remained intact (r = 0.26), but I no longer observed a relationship between cognitive ability and static integration (r = – 0.04). As a result, the joint use of these variables no longer predicted cognitive ability (r = 0.03).

I am unaware of a straightforward mapping of smoothing kernel choice to the change in this result, especially in light of the many results that did replicate. I performed a variety of validation checks which were unremarkable. The only matter of note was a significant reduction in the explained variance of signals summarizing each individual/area. To unpack this: each area for each individual was summarized into a single time-series using the first eigenvariate of the time-series’ of the voxels comprising the area. With reduced smoothing, the first eigenvariate explained significantly less variance of each area’s time-series, which is unsurprising given that smoothing would be expected to reduce each area’s heterogeneity. One possibility is that this reduction in explained variance inflated noise in network estimates. I am not convinced of this possibility – I checked the test-retest reliability of the spectral DCM parameters (from which static integration is computed) for sample 1 (which performed 2 sessions) and they were similar with 8 mm and 4 mm smoothing (>0.6 on average in both cases). The group-level replicability of spectral DCM parameters remained excellent with 4 mm smoothing (>0.95). This suggests that a simple explanation regarding increased noise with less smoothing is insufficient.

Given the above, I am left with two interpretations that I do not think can be readily resolved at the moment. First, it is possible that with reduced smoothing, the resultant signals used to summarize each individual/area were less representative of an individual’s/area’s population activity, thereby reducing the ability to explain individual trait-variability. That is, even if stability remained unchanged, the computed measures themselves may no longer be adequately capturing the individual variability that is relevant for behavior. Behavior arises from population-level dynamics such that considering more of the relevant population-level signals should facilitate better explanations of behavior. Hence, while less smoothing makes the signals more focal, which is good for dissociating nearby areas, it may be that pooling across nearby areas makes the signals more representative of the population-level dynamics that explain behavior. Towards this possibility, prediction of individual susceptibility to TMS was reduced in magnitude, though still significant, with less smoothing. It is possible that this reduction reflects regression towards the mean. That is, it is often the case that effect sizes that are conditioned on significance are smaller when investigated with alternative analysis strategies/samples. Mitigating this concern, entirely new analyses using activation features to predict cognitive ability also showed poorer prediction accuracy with less smoothing. These analyses are unlikely to reflect regression to the mean since these analyses were performed simultaneous on both preprocessing pipelines.

I think a systematic investigation of this matter could be performed with a careful and complete parcellation of the FPCN that takes advantage of the tasks’ detailed functional profiling. Consider the possibility that all areas within the FPCN contribute to cognitive ability, but only a subset are summarized for analyses, as is the case here. In such a case, more smoothing may allow more of the relevant areas/signals to be represented in the analysis. An alternative approach would be to analyze all areas of the FPCN. If this could be done, then representation becomes a non-issue, and less smoothing would help to preserve distinctions among areas that may be useful for understanding individual variability. This will necessarily be a more difficult analysis – it will be non-trivial to appropriate align all relevant functional areas across participants especially in light of heterogeneity in the FPCN (e.g. Braga and Bucker, 2017; Gordon et al., 2017; Gratton et al., 2018). The rich task data here, along with connectivity profiling, may help to facilitate such alignments. However, appropriate investigation into this matter is likely to be a study in its own right, and is left as a future direction.

The second possibility is that the original result was a false positive and/or this non-replication indicates instability of effect size estimates at the present sample size (i.e. insufficient power). Given the sample size, the originally observed prediction effect was just within reasonable power reach (i.e. ~80% power). The failure to replicate this effect could mean that the true effect size is smaller than originally observed, if present at all. A smaller such effect would not be detectable in the present dataset, and the observation of such an effect could be considered spurious. I do not believe that the present dataset can satisfactorily speak to this possibility, and replication with a larger sample would be necessary. For the moment, collection of such a dataset is not feasible, and it is not clear how to perform analogous analyses in large open datasets.

Given these issues, I have added discussion of these matters and the warning that this analysis should be interpreted with caution. I also wrestled with the idea of removing the analysis from the manuscript entirely, but I thought it better to document and discuss appropriately rather than to “file-drawer” the analysis.

From the Results:

“The same analyses were repeated with reduced smoothing. Although dynamic integration was again positively associated with cognitive ability, with reduced smoothing, no relationship was observed among cognitive ability and static integration. As a result, integration measures could not be used to predict cognitive ability (r = 0.03; p = 0.44; Figure 8—figure supplement 2). On the other hand, activation based measures remained significantly predictive (r = 0.31, p = 0.04; Figure 8—figure supplement 3) and significantly improved prediction when added to models containing integration measures alone (r = 0.32, p = 0.03; nested model comparison using ordinary regression: F(4,42) 3.05, p = 0.04). I return to the implications of the non-replication with reduced smoothing in the Discussion.”

From the Discussion:

“Third, multiple steps have been taken to ensure the replicability of the findings here including replicating results across independent samples, and repeating the analyses with different preprocessing choices. […] Whether the lack of replication of FPCN integration measures predicting cognitive ability with reduced smoothing indicates that the original result/analysis was a false positive/had insufficient power or whether this is a reflection of a true result varying as a function of preprocessing choices requires future investigation. For the time-being, this result should be taken with some measure of caution.”

Although I have focused a large amount of this response on the one result that did not satisfactorily replicate with the change in smoothing kernel, I would like to reiterate that all other analyses did, in fact, replicate. I believe this should quell notions that the results are, by-and-large, an artifact of a somewhat arbitrary preprocessing choice.

Finally, with regard to hemisphere, it is common for tasks in the abstraction/hierarchy literature to be more prominently left lateralized. I have commented on this in the past when meta-analytically gathering activation foci from related works (c.f. Nee et al., 2014; Badre and Nee, 2018). Although strong bilateral activations were observed in the present study (maps are available on OSF as indicated in the manuscript https://osf.io/938dx/, as well as in NeuroVault https://neurovault.org/collections/6054/), the stimulus domain factor only showed differentiation in the left hemisphere (i.e. no area showed a preference for the verbal conditions in the right hemisphere). Therefore, the choice was made previously, and carried through here, to focus on the left hemisphere. This leaves open characterization of hemispheric differences, which I hope to follow-up on, but are outside the scope of the present manuscript. I have included additional discussion detailing limitations of the present work given the focus on the left hemisphere alone.

From the Discussion:

“Fourth, the analyses presented here have focused exclusively on the left hemisphere. This is in keeping with prior work with these data26,27 and is consistent with the preponderance of work in the domain of abstraction and hierarchical control showing more marked recruitment of the left hemisphere4,38,78–84. The reason for this left lateralization is unclear, but may relate to the presumed development of internalized control structures via interactions with the language system85,86. However, some control processes, such as those responsible for the inhibition of motor responses tend to be more right lateralized87,88. Future work would do well to compare and contrast network integration of the left and right FPCN.”

6) To improve the interpretability of the effective connectivity results, it would be helpful to provide more details on the methodological and biological assumptions behind using positive and negative effective connectivity indices to suggest that they reflect excitation and inhibition, respectively, as well as the limitations related to fMRI effective connectivity analyses. Further, negative correlations between static connectivity and general cognitive abilities are in contrast with numerous reports showing that measures of resting-state functional connectivity across the fronto-parietal network positively correlate with general cognitive abilities (e.g. Dubois et al., 2018). Could the author comment on this difference?

Also, the author interprets the negative between-network connectivity as reflecting functional segregation, and positive connectivity as reflecting integration. This is plausible but certainly not the only possible interpretation of such a pattern. For instance, increases in between-node connectivity with greater control demand are often interpreted as reflecting modulation/biasing of one region by the other, which seems conceptually distinct from "integration", at least the way the author conceptualizes integration (i.e., the mid-lateral PFC joining up information from posterior and anterior regions). I wonder whether there might be stronger tests of the claim that this node integrates information processed in the other nodes, perhaps by using an information-based analytic approach (like MVPA/RSA)?

I have added additional discussion regarding the assumptions of the utilized effective connectivity approaches, and how those assumptions impact interpretation of the results. As is always the case with fMRI, the neurophysiological underpinnings remain somewhat unclear, and conclusions need to be measured accordingly.

From the Discussion:

“Several limitations should be considered to properly contextualize the findings reported here. […] Hence, these observations should be taken as a starting point from which more complex and biologically plausible networks can be expanded.”

With regard to the relationship between static connectivity and cognitive ability, I am grateful for the reference provided, which I have added to the manuscript. There is a broader discussion to be had regarding how to reconcile (A) that modular brain organizations are related to better cognition, (B) that strong within-network connectivity is related to better cognition, and (C) that classically defined networks are composed of sub-networks. This leads to the question of whether modularity at the sub-network level is beneficial or harmful to cognition, which appears to be an open question. I suggest that static integration reflects less modularity at the sub-network level, and commensurately poorer cognitive ability, but this warrants follow-up with a graph theoretic approach, ideally on a larger dataset. I have added text to the discussion regarding this interesting future direction.

From the Discussion:

“Previous work has indicated the presence of an integrative core of regions important for multiple tasks14–17,25,53–56. […] Our data situate the areas associated with such integration in an intermediary zone of the FPCN.

In contrast to the integrative dynamics of intermediary areas, sensory-motor proximal and distal areas acted in a segregative fashion. Segregation is likely to be important to select relevant information while suppressing irrelevant information. Consistent with the data here, Shine57 posited that rostral areas of the PFC are involved in segregation while mid-lateral areas are involved in integration. He theorized that segregation is mediated by cholinergic modulations while integration is mediated by noradrenergic modulations. Further research into the influences of distinct PFC-PPC networks on neuromodulatory mechanisms would be fruitful to elucidate such effects.

The data demonstrated both static and dynamic forms of integration. Areas involved in contextual control tended to excite other control networks, providing a potential substrate for integration through binding. Moreover, demands on contextual control increased inter-network communication producing a dynamic form of integration. Both static and dynamic integration were related to individual differences in higher-level cognitive ability. Interestingly, the different forms of integration tended to be associated with opposite effects. On the one hand, increased static integration was associated with decreased higher-level cognitive ability. It has been posited that an appropriate balance of segregation and integration into distinct networks or modules is important to optimize brain efficiency58. In particular, it has been observed that more segregation between networks, and integration within networks (i.e. modularity) at rest is associated with memory capacity59. Therefore, integration across networks in a stationary manner may be sub-optimal for cognition. On the other hand, increased dynamic integration was associated with increased higher-level cognitive ability. These data are consistent with previous studies that have shown that integrative reconfigurations of brain networks from rest to task are related to improved performance on complex tasks60–62. These data suggest that the brain’s ability to integrate “on-demand” is beneficial to cognitive processing.”

Finally, the editors/reviewers raise an intriguing idea that an information-based approach might be able to adjudicate among mechanisms providing top-down biasing on the one hand and integration on the other. I think this is a pressing question that has recently been elegantly discussed by Badre and colleagues (https://psyarxiv.com/asdq6/). The appropriately conceived analysis/dataset to address this question would have widespread impact for the study of cognitive control and brain function. I tend to think that addressing this question is a study in its own right that would in the very least require a different analysis pipeline (e.g. no smoothing or spatial normalization to preserve insofar as possible the multi-variate signals), but would likely also require an innovative analytic approach, and a dataset more specifically designed to address the question (e.g. Badre and colleagues suggest repetition suppression designs might be necessary given limitations of multi-variate signals in the PFC as measured by fMRI). Therefore, although I would very much like to pursue an answer to this question, I feel as though it is outside the scope of the present manuscript. In lieu of addressing this question directly, I have added discussion of these matters. First, I recognize a modulation-based interpretation, offer why I favor an integration view, but also admit that new data/analysis will be needed to resolve this matter:

From the Discussion:

“Although I have suggested an integrative role of areas positioned in the middle of the FPCN, other accounts are plausible. […] Resolving this matter would likely require additional data that can identify the distinct representations of different areas of the FPCN and how those representations are modified by network dynamics.”

7) It would be problematic at brain-behavior individual differences using a small sample size like the one used to probe connectivity-TMS effects due to their unreliability. If the author insists on keeping this section, it will be useful to examine any shared variance between general cognitive abilities and the observed TMS behavioral effects.

I agree that a larger sample size would be preferable for exploring the relationship between connectivity and TMS. That said, I hope the editors/reviewers will indulge me a philosophical point so as to speak to recent trends that I think are unfairly trivializing smaller n studies: the utility of small, carefully collected samples should not be dismissed as evidenced by classic work on lesion patients, extensive insights gleaned from the neurophysiology of pairs of monkeys, and the many recent impactful findings garnered from the Midnight Scan Club dataset. While it would be desirable to perform individual difference analyses of TMS-connectivity relationships on datasets the size of HCP or ABCD, no such dataset exists. Given the non-triviality and cost of functionally defining multiple TMS targets at the individual level, and then assessing TMS effects in multiple follow-up sessions, one would probably want good cause prior to pursuing large n investments of such designs. Consider that large datasets such as HCP would never have been collected had it not been for studies with sample sizes on the order of the one explored here paving the way with both promises and pitfalls. Hence, analyses such as these are essential for showing sufficient promise to warrant the investment needed to collect larger samples with those larger samples then providing more definitive conclusions. In other words, we need small data before we can get big data, which I feel is an important point for proponents of big data to recognize and support. On the other hand, conclusions based on small data should be appropriately measured.

With that said, I am in full agreement that the sample sizes limit strong conclusions. That the observed relationships continued to be significant even after re-processing the data speaks to the idea that there is some reliable relationship here. However, replication with an independent, larger sample is certainly needed. I have added discussion regarding the tentative nature of the observed results given these issues.

From the Discussion:

“Second, conclusions regarding the relationships among individual differences in FPCN network integration and cognitive ability/susceptibility to neuromodulation should be tempered by the sample sizes studied. […] However, replication with larger samples is needed to draw firm conclusions regarding the relationships among FPCN network integration, cognitive ability, and susceptibility to neuromodulation.”

I have also examined and detailed other related variables as recommended. First, there was a non-significant negative correlation between cognitive ability and TMS susceptibility (r = -0.33). To examine whether integration measures predicted TMS susceptibility over-and-above cognitive ability, cognitive ability was regressed out of measures of static and dynamic integration. The resultant predictors still significantly predicted TMS susceptibility in the data as originally processed (r = 0.46, p = 0.02), and in the data with reduced smoothing (r = 0.41, p = 0.04). Second, as detailed below, activations could be used to predict cognitive ability. Interestingly, activations alone could not be used to predict TMS susceptibility (correlations among predicted and observed TMS effects all <0). Finally, integration measures predicted TMS susceptibility after regressing out both cognitive ability and activations in the data as originally processed (r = 0.47, p = 0.02), and in the data with reduced smoothing (r = 0.37, p = 0.045). [Note, below I use a model comparison approach rather than controlling for variables as I do here. I control for variables here because the small sample size precludes adding too many predictors, thereby making a model comparison approach inappropriate, as far as I can tell.] Although sample sizes preclude strong conclusions, these data indicate the utility of connectivity-based measures to predict TMS effects. I have added these details to the manuscript.

From the Results:

“Next, additional relationships among TMS susceptibility, cognitive ability, and activation were examined. […] Hence, these data suggest that network integration is useful for predicting susceptibility to neuromodulation over-and-above cognitive ability and control-related activations.”

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

1) In the Discussion section "Beyond the PFC: Towards a Network View of Cognitive Control" the author gives the impression that the majority of studies on cognitive control have solely focused on the PFC. This needs to be rebalanced to reflect that a distributed whole brain network view of cognitive control has long been argued (to name a few: Cole and Schnider, 2007; Power and Petersen, 2013; Fedorenko et al., 2013; Warren et al., 2014; Duncan et al., 2010 and 2020).

I apologize for misrepresenting the literature. It was my intention to address the literature on hierarchical cognitive control that has been disproportionately dominated by examinations of the lateral PFC. I have edited this section accordingly, adding in the recommend references along with others, while being careful to more clearly indicate the more specific focus that I am attempting to expand with this study:

From the Discussion

“A substantial body of work has focused on the functional organization of the lateral PFC and interactions therein that support cognitive control. Despite long-standing recognition that cognitive control is supported by areas distributed across the frontal and parietal lobes9,11,15,17,38–42, much work, particularly in the domain of hierarchical cognitive control, has centered narrowly on how processing varies along the rostral-caudal axis of the PFC4,22,23,26,27,43,44. Although a number of insights have been gained by focusing on the PFC, such a narrow focus ignores the broader networks in which the PFC participates. Choi28 recently demonstrated that the same rostral-caudal organization for control observed in the PFC is reflected in the PPC consistent with the idea that the PFC and PPC are comprised of ordered networks for control. The data here replicate those findings while also linking PFC-PPC activations with behavior along distinct timescales. Hence, it appears to the case that many functions that have been attributed to the PFC are also present in the PPC. This necessitates expanding the study of cognitive control beyond the PFC to network and brain-wide levels.”

2) Some of the supplementary figures were missing (Figure 2—figure supplement 2, Figure 6—figure supplement 2, Figure 7—figure supplement 3), not sure if this was a problem with the submission system. There were also a few typos.

My apologies for these oversights. I have edited the typos and uploaded the missing figures.

https://doi.org/10.7554/eLife.57244.sa2

Article and author information

Author details

  1. Derek Evan Nee

    Department of Psychology, Florida State University, Tallahassee, United States
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Funding acquisition, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing
    For correspondence
    derek.evan.nee@gmail.com
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-7858-6871

Funding

National Institute of Neurological Disorders and Stroke (F32 NS0802069)

  • Derek Evan Nee

National Institute of Mental Health (R01 MH121509)

  • Derek Evan Nee

Florida State University (COFRS 0000034175)

  • Derek Evan Nee

National Institute of Neurological Disorders and Stroke (P01 NS040813)

  • Derek Evan Nee

National Institute of Mental Health (R01 MH063901)

  • Derek Evan Nee

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

This research was supported by National Institute of Neurological Disorders and Stroke Grants F32 NS0802069 (DN) and P01 NS040813 (Mark D’Esposito), National Institute of Mental Health Grants R01 MH063901 (Mark D’Esposito) and R01 MH121509 (DN), and Florida State University COFRS Award 0000034175 (DN). The author thanks Regina Lapate, Mac Shine, and Anila D’Mello for helpful discussions of this work.

Ethics

Human subjects: Informed consent was obtained in accordance with the Committee for Protection of Human Subjects at the University of California, Berkeley (2010-04-1314, 2010-02-781).

Senior Editor

  1. Timothy E Behrens, University of Oxford, United Kingdom

Reviewing Editor

  1. Daeyeol Lee, Johns Hopkins University, United States

Reviewers

  1. Evan Gordon, Veterans Health Administration, United States
  2. Moataz Assem, MRC Cognition and Brain Sciences Unit, University of Cambridge, United Kingdom

Publication history

  1. Received: March 30, 2020
  2. Accepted: March 1, 2021
  3. Accepted Manuscript published: March 2, 2021 (version 1)
  4. Version of Record published: March 16, 2021 (version 2)

Copyright

© 2021, Nee

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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Further reading

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