You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


Introduction {#s1}
============

Context-appropriate behavior requires assessment of both present circumstances and future plans to determine the best course of action in the moment. Guiding behavior in accordance with internal representations rather than habitual stimulus-response tendencies requires cognitive control that depends on the lateral prefrontal cortex (LPFC; [@bib23]). Yet, how the functional properties and interactions among areas of the LPFC support cognitive control remains poorly understood.

Previously, we collected fMRI data on human participants to investigate how the LPFC supports cognitive control by examining intercommunication among LPFC areas across a variety of cognitive control demands ([Figure 1A,B](#fig1){ref-type="fig"}; [@bib26]). First, we used univariate analysis to determine the functional responses of different LPFC areas. This analysis revealed that caudal LPFC was responsive to attention to stimulus features (*Feature Control*), mid LPFC was responsive to contextual rules to be applied to the attended stimulus feature (*Contextual Control*), and rostral LPFC was responsive to retaining a past stimulus feature for a future rule (*Temporal Control*). Collectively, these results supported the hypothesis that progressively rostral LPFC areas perform progressively abstract processes ([@bib14]; [@bib19]; [@bib2]; [@bib3]). Second, we used dynamic causal modeling (DCM) to examine how intercommunication among LPFC areas supports cognitive control ([@bib13]). The estimated model ([Figure 1D](#fig1){ref-type="fig"}) demonstrated three principle properties: (1) caudal LPFC provides feature-specific inputs to the rest of the LPFC; (2) mid-rostral and caudal influences converge in mid LPFC during *Contextual Control*; and (3) the rostral-most LPFC remains largely segregated from the rest of the LPFC during *Temporal Control* (i.e. functional modulations do not extend to the rest of LPFC; [Figure 1D](#fig1){ref-type="fig"}, red arrows). Collectively, these results indicated that the mid LPFC is a nexus where multiple influences converge to guide context-appropriate action, providing a new framework upon which to understand how the functional interactions within the LPFC support cognitive control.

![Task, cTBS targets, and dynamic causal model.\
(**A**) The design orthogonally manipulated factors of *Stimulus Domain* (verbal, spatial) and two forms of cognitive control: *Contextual Control* (low -- *Control*, *Delay*; high -- *Restart*, *Dual*) and *Temporal Control* (low -- *Control*, *Restart*; high -- *Delay*, *Dual*). These factors were fully crossed in a 2 × 2 × 2 design. (**B**) The basic task required participants to judge whether a stimulus followed the previous stimulus in a sequence. The sequence in the verbal task was the order of the letters in the word 'tablet.' The sequence in the spatial task was a trace of the points of a star. The start of each sequence began with a decision regarding whether the currently viewed stimulus is the start of the sequence (e.g. 't' in the verbal task). Factors were blocked with each block containing a basic task phase, a sub-task phase, a return trial, and a second basic task phase (not depicted), for all but the *Control* blocks. *Control* blocks consisted only of the basic task phase extended to match the other conditions in duration. Colored frames indicated whether letters or locations were relevant for the block (verbal -- purple; spatial -- orange in this example; verbal condition depicted). The basic task was cued by square frames. Other frames cued the different sub-task conditions. In the *Delay* condition (circle frames), participants held in mind the place in the sequence across a distractor-filled delay. In the *Restart* condition (diamond frames), participants started a new sequence. In the *Dual* condition (cross frames), participants simultaneously started a new sequence, and maintained the place in the previous sequence. (**C**) Each sphere represents a stimulus target for an individual. Red -- rostral LPFC, green -- mid LPFC, blue -- caudal LPFC, black -- S1 (control site). (**D**) The dynamic causal model estimated previously ([@bib26]). Colored arrows denote modulations of effective connectivity during different cognitive control demands (orange -- attention to spatial features; purple -- attention to verbal features; green -- *Contextual Control*; red -- *Temporal Control*). Colors of the circles denote univariate sensitivities to *Feature Control* (blue), *Contextual Control* (green), and *Temporal Control* (red). Lightning bolts indicate targets for continuous theta-burst transcranial magnetic stimulation (cTBS). cTBS was predicted to affect behavior for which a given region was responsive, and also behaviors supported by downstream regions that require processing in upstream targets. cMFG, caudal middle frontal gyrus; FPl, lateral frontal pole; IFJ, inferior frontal junction; MFG, middle frontal gyrus; SFS, superior frontal sulcus; VLPFC, ventrolateral prefrontal cortex.](elife-28040-fig1){#fig1}

A central goal of neuroscience is to determine causal associations among stimuli, neural systems, and behavior as a gateway to specifying predictive models of behavior. Although DCM has been demonstrated to detail functional neural circuitry accurately ([@bib21]; [@bib10]; [@bib7]) modeling causal links among neural regions, it does not specify the causal relationship between neural interactions and behavior. Given the complexities of neural interactions, however, a model of directed influences is a critical intermediary to determine the link between brain and behavior ([@bib18]). That is, a model of directed influences affords predictions regarding how perturbations of specific brain regions affect other regions and ultimately behavior. Within this framework, one can identify parent and children nodes wherein perturbations of parents affect children, but not vice versa. This sort of framework is critical to establish neural hierarchies ([@bib4]; [@bib1]), and to navigate the complex pathways by which neural activity leads to behavior.

Here, we apply this logic by using continuous theta-burst transcranial magnetic stimulation (cTBS) to reduce cortical excitability reversibly ([@bib17]). We apply cTBS to either caudal (superior frontal sulcus; SFS), mid (ventrolateral prefrontal cortex; VLPFC), or rostral (lateral frontal pole; FPl) LPFC, as well as to a control site (primary somatosensory cortex; S1) in a within-subjects counterbalanced design ([Figure 1C](#fig1){ref-type="fig"}). Following the previously estimated DCM, we predicted that (1) cTBS to caudal LPFC would result in a *feature-specific* impairment acting generally across cognitive control demands. This follows from the model prediction that caudal LPFC provides feature inputs to the rest of the LPFC system. (2) cTBS to mid LPFC would result in a *feature-specific* impairment during *Contextual Control*. This follows from the model prediction that mid LPFC integrates feature information from caudal LPFC and task information from mid-rostral LPFC to perform *Contextual Control*. (3) cTBS to the rostral-most LPFC would result in a *feature-general* impairment during *Temporal Control*. This follows from the model prediction that the rostral-most LPFC is functionally segregated from other LPFC areas during *Temporal Control* and that this region is insensitive to feature information. These patterns of results would provide causal evidence linking the estimated neural dynamics to their presumed behavioral correlates.

Results {#s2}
=======

Replication of previous fMRI results {#s2-1}
------------------------------------

Prior to receiving cTBS, all participants underwent an fMRI session using the task described previously ([Figure 1A,B](#fig1){ref-type="fig"}; [@bib26]) in order to localize individual targets for cTBS ([Figure 1C](#fig1){ref-type="fig"}). The new sample offered an opportunity to replicate the previous findings. Each individual performed a single fMRI session in the present study compared to two sessions in the previous work, so the effects reported here are expected to have reduced power relative to those in the original study. Nevertheless, as depicted in [Figure 2](#fig2){ref-type="fig"} and its supplements, virtually all of the previously reported effects were replicated (replication statistics reported in the figure captions). As before, a progression of activation from caudal to rostral LPFC was observed for *Feature Control* to *Contextual Control* to *Temporal Control* ([Figure 2](#fig2){ref-type="fig"}). Sensitivity to stimulus features was present in caudal and mid, but not rostral LPFC consistent with more abstract processing in rostral LPFC ([Figure 2---figure supplement 1](#fig2s1){ref-type="fig"}). Caudal LPFC was related to present but not future behavior, rostral LPFC showed the inverse pattern, and mid LPFC showed sensitivity to both present and future behavior, collectively forming a temporal abstraction gradient ([Figure 2---figure supplement 2](#fig2s2){ref-type="fig"}). Finally, the effective connectivity parameters estimated by DCM were similar to those in the previous report. The major difference from the previously reported DCM results was that the pathways linking caudal to mid LPFC were not modulated by attention to stimulus features (i.e. *Stimulus Domain*). Instead, the stimulus inputs to caudal LPFC were increased several fold ([Figure 2---figure supplement 3](#fig2s3){ref-type="fig"}). Intuitively, these different findings reflect whether an attention-related gain is realized prior to (input parameter) or after (modulation of caudal to mid LPFC effective connectivity) feature information arrives at LPFC. Effectively, this leads to the same result -- feature information is propagated through the LPFC via input nodes in feature-specific caudal LPFC during attention to a given feature. Statistically, these different findings reflect an attentional gain that is sustained (modulation) versus transient (input). These differences do not affect the predictions of the model with regard to cTBS because either way, disruption of caudal LPFC is predicted to disrupt feature-specific inputs to the rest of the LPFC.

![Univariate replication.\
Top: previously reported univariate effects. Bottom: univariate effects in the present study. In both cases, *Temporal Control* elicited activation of rostral LPFC, *Contextual Control* of mid LPFC, and *Feature Control* of caudal LPFC, indicating a rostral-caudal gradient of cognitive control. All results thresholded at p\<0.001 at the voxel level with cluster extent providing family-wise error correction at p\<0.05.](elife-28040-fig2){#fig2}

As before, additional analyses on the effective connectivity parameters estimated by DCM were performed to examine hierarchical control and its relationship to higher-level cognitive ability, as indexed by a combination of short-term/working memory capacity and fluid intelligence (see [@bib26]) for complete details). Replicating the previous results, hierarchical strength, as measured by greater efferent relative to afferent fixed connectivity, peaked in mid-rostral LPFC and was low in FPl, the rostral-most area, suggesting that the rostral-most LPFC is not the apex of the hierarchy ([Figure 2---figure supplement 4](#fig2s4){ref-type="fig"}). Once again, individuals varied in the strength of bottom-up versus top-down modulations as a function of cognitive control with a tradeoff between the two reflected in a negative correlation between these parameters ([Figure 2---figure supplement 5A](#fig2s5){ref-type="fig"}). However, whereas we had previously reported that both individual differences in top-down modulations as a function of cognitive control ([Figure 2---figure supplement 5B](#fig2s5){ref-type="fig"}) and hierarchical strength in fixed connectivity ([Figure 2---figure supplement 5D](#fig2s5){ref-type="fig"}) were positively related to individual differences in trait-measured higher-level cognitive ability, this relationship was not evident in the present sample. A null effect might be expected given the reduced power in the present sample relative to the previous one, but the trends that were evident were opposite in sign to those observed previously. As reported in more detail below, the positive relationship between DCM parameters and trait-measured higher-level cognitive ability were also not replicated in the revised DCM. Given that nearly all of the other effects were replicated (over 50 independent tests performed), this particular lack of replication may indicate that our previous result was a false positive.

Behavioral results and effects of cTBS {#s2-2}
--------------------------------------

To examine the replication of the previously reported behavioral effects of cognitive control demands, separate 2 × 2 × 2 ANOVAs on error-rate (ER), and reaction times (RT) on correct trials were performed for data collected during the fMRI session during the sub-task phase. As before, these analyses revealed significant effects of cognitive control demands with main effects of *Temporal Control* (ER -- F(1,23) = 6.04, p\<0.05; RT -- F(1,23) = 11.34, p\<0.005), *Contextual Control* (ER -- F(1,23) = 60.30, p\<10^−7^; RT -- F(1,23) = 149.48, p\<10^−10^), and their interaction (ER -- F(1,23) = 6.92, p\<0.05; RT -- F(1,23) = 105.30, p\<10^−9^). While no main effect of *Stimulus Domain* was observed previously, in the present sample there was a main effect of *Stimulus Domain* in RT (F(1,23) = 4.28, p\<0.05) but not ER (F(1,23) = 2.33, p\>0.1). Participants performed more quickly on the spatial task relative to the verbal task. Performance on the spatial relative to verbal task improved with practice as is evidenced by an increase in the effect size during the cTBS sessions as reported below. Once again, there were no interactions between *Stimulus Domain* and cognitive control demands (ER and RT all p\>0.25), although this also changed with practice as detailed below.

Next, we examined effects of cTBS on behavior. cTBS targets were determined on the basis of individual activation peaks (see Materials and methods for full details). To test predictions that were based upon the previously estimated DCM ([@bib26]), one target was chosen from each of caudal, mid, and rostral LPFC. Of the caudal areas, SFS was the most accessible to stimulation. VLPFC in mid LPFC, and FPl in rostral PFC were subsequently chosen as targets that maximized between-target distance, which was anticipated to most readily yield dissociable patterns of stimulation. The full uncontrasted data are depicted in [Figure 3A--B](#fig3){ref-type="fig"}. Given that the hypotheses are borne out of interactions that can be difficult to visualize, we depict contrasts that address model predictions in [Figure 3C--F](#fig3){ref-type="fig"}. For each contrast of interest, linear mixed effects models were estimated including factors of *Target* (FPl, VLPFC, SFS, S1), *Time* (i.e. session number), and their interaction. Each model included random effects terms for *Subject*, and *Time* nested within *Subject* (i.e. individual differences in practice-related changes). As alluded to above, *Time* was included as a factor after changes in contrasts of interest were noted over sessions. Hereafter, we focus on the effects of *Target* as the factor of main interest. We also describe simpler ANOVAs in [Figure 3---figure supplement 1](#fig3s1){ref-type="fig"}.

![Behavioral effects following cTBS.\
Left: Uncontrasted data from (**A**) all trials averaged across the verbal and spatial tasks, respectively, and (**B**) sub-task trials averaged across the eight factors of the task design. Right: Contrasted data. In all bars, performance following cTBS to the control target (S1) has been subtracted out such that the y-axis indicates a behavioral impairment relative to control stimulation. Effects of *Time* have been regressed out (see [Figure 3---figure supplement 1](#fig3s1){ref-type="fig"} for data that do not control for effects of *Time*). The x-axis indicates the stimulation target (rostral -- rostral LPFC/FPl; mid -- mid LPFC/VLPFC; caudal -- caudal LPFC/SFS). (**C**) Impairments in *Spatial Stimulus Domain* relative to *Verbal Stimulus Domain* in error-rate (ER). (**D**) The interaction between *Stimulus Domain* x *Contextual Control* in reaction time (RT) contrasted such that relative verbal impairments are positive (i.e. greater verbal *Contextual Control* cost relative to spatial *Contextual Control* cost). (**E**) Impairments in the main effect of *Temporal Control* in ER. (**F**) Impairments in the main effect of *Contextual Control* in ER. \*p\<0.05; \*\*p\<0.005.](elife-28040-fig3){#fig3}

First, the model predicts that cTBS to caudal LPFC would result in a feature-specific impairment given that caudal LPFC provides feature inputs to the rest of the LPFC. In this case, we targeted the caudal superior frontal sulcus (SFS), roughly corresponding to the frontal eye-fields, which was modeled as the source of spatial feature inputs. We expected diminished spatial relative to verbal task performance to result from cTBS to SFS. To test this prediction, we examined how the effect of *Stimulus Domain* was modulated by cTBS *Target*. Linear mixed effects models were performed on the effect of *Stimulus Domain* (contrast of verbal and spatial performance). This analysis revealed a significant effect of *Target* in ER (F(3,23.17) = 4.46, p\<0.05), but not RT (F(3,37.98) = 1.363, p\>0.25). Follow-up tests comparing cTBS to SFS and S1 after controlling for *Time* revealed that cTBS to SFS resulted in significantly reduced spatial relative to verbal task performance in ER (t(22) = 2.15, p\<0.05; [Figure 3C](#fig3){ref-type="fig"}). While participants generally performed better on the spatial relative to verbal task after cTBS (FPl -- t(22) = 3.67, p\<0.005; VLPFC -- t(22) = 2.43, p\<0.05; S1 -- t(22) = 3.04, p\<0.01), this was not the case following cTBS to SFS (t(22) = 1.41, p\>0.15; ). Hence, cTBS to SFS resulted in a specific impairment in spatial task performance in line with model predictions.

Second, the model predicts that cTBS to mid LPFC would result in a feature-specific impairment in *Contextual Control* given that *Contextual Control* requires integration of bottom-up feature information (from caudal LPFC) and top-down task information (from mid-rostral LPFC). In this case, we targeted the ventrolateral prefrontal cortex (VLPFC), which was sensitive to *Contextual Control* for verbal information. Correspondingly, we expected diminished verbal relative to spatial *Contextual Control* performance to result from cTBS to VLPFC. To test this prediction, we examined whether the *Stimulus Domain* x *Contextual Control* interaction was modulated by cTBS *Target*. Linear mixed effects models revealed a significant effect in RT (F(3,24.14) = 6.97, p\<0.005), but not ER (F(3,39.73) = 1.28, p\>0.25). Follow-up tests comparing cTBS to VLPFC and S1 after controlling for *Time* revealed significantly increased RT costs associated with *Contextual Control* for the verbal relative to spatial task following cTBS to VLPFC (t(21) = 2.43, p\<0.05; [Figure 3D](#fig3){ref-type="fig"}). Similar differences were observed when comparing cTBS following VLPFC to FPl (t(21) = 3.19, p\<0.005) and SFS (t(21) = 3.31, p\<0.005). Thus, cTBS to VLPFC resulted in a feature-specific, control-specific impairment consistent with predictions of the model.

Finally, we examined the impact of cTBS on the rostral LPFC by targeting FPl. According to the model, effective connectivity from the FPl to mid LPFC is reduced during *Contextual Control*. In the previous report, we suggested that this negative modulation effectively nullifies positive associations between the FPl and mid LPFC in fixed connectivity, thereby serving to segregate the FPl from the rest of the LPFC. If so, cTBS to FPl would not be expected to have an effect on *Contextual Control* since cTBS is expected to perform a similar segregating function by way of reducing FPI cortical excitability. Another possibility is that the negative modulation reflects top-down inhibition from FPl to mid LPFC, which may serve to prioritize which contextual information is appropriate at which time. In this case, cTBS to FPl would be expected to affect *Contextual Control* since reducing FPI cortical excitability would, in turn, reduce the top-down bias it transmits. Either way, an effect on *Temporal Control* was anticipated given the region's sensitivity to *Temporal Control*. To test these predictions, we estimated linear mixed effects models separately for the effects of *Contextual Control* and *Temporal Control*. These analyses revealed no effect of *Target* on *Contextual Control* (ER -- F(3,23.22) = 2.52, p\>0.05; RT -- F(3,27.82) = 0.43, p\>0.7), but a significant effect of *Target* on *Temporal Control* in both ER (F(3,47.43) = 3.51, p\<0.05) and RT (F(3,35.79) = 3.02, p\<0.05). Follow-up tests comparing cTBS to FPl and S1 after controlling for *Time* revealed that FPl stimulation led to significantly increased *Temporal Control* costs in ER (t(21) = 2.41, p\<0.05), but not RT (t(21) = 0.57, p\>0.55). No such differences were observed on *Contextual Control* costs, which non-significantly trended in the opposite direction (i.e. reduced costs; ER -- t(21) = −0.44, p\>0.65; RT -- t(21) = −1.05, p\>0.3). Hence, these data indicate that the FPl is causally related to *Temporal Control* ([Figure 3E](#fig3){ref-type="fig"}), but do not provide evidence that cTBS to FPl affects *Contextual Control* ([Figure 3F](#fig3){ref-type="fig"}).

Collectively, the analyses above suggest that caudal, mid, and rostral LPFC support separable cognitive control processes, the nature of which is predicted by a model of LPFC dynamics. To further corroborate these associations, we performed a 4 × 3 ANOVA with factors of *Target* and *Contrast* using the three contrasts reported above that were predicted to demonstrate dissociative effects (*Stimulus Domain*, *Stimulus Domain x Contextual Control*, *Temporal Control*). This analysis confirmed a significant interaction (F(6,126) = 4.51, p\<0.0005). A similar analysis extended to include the *Contextual Control* contrast was also significant (F(9,189) = 2.92, p\<0.005). Although we cannot conclude a triple dissociation because not all pairwise differences were significant for each measure, this result adds credence to the association of each region to its corresponding model-predicted effect.

Upon depicting the results of the analysis above, an unanticipated finding emerged: cTBS to SFS also had a negative effect on *Temporal Control*. To detail this effect further, we directly compared cTBS to SFS and S1 after controlling for *Time*. Similar to the pattern observed with cTBS to FPl, cTBS to SFS significantly increased *Temporal Control* costs in ER (t(21) = 3.24, p\<0.005), but not RT (t(21) = 0.41, p\>0.65), but had no effect on *Contextual Control* costs (ER -- t(21) = 0.18, p\>0.85; RT -- t(21) = 0.37, p\>0.7). This result was not predicted by the model and no such effects were observed comparing cTBS to VLPFC with S1 (all tests p\>0.1). However, it is important to note that using DCM requires two steps: first is a model comparison step wherein plausible models of neural dynamics are compared; and second are inferences on the parameters of the best model of the data. Given that SFS did not exhibit a positive univariate effect of *Temporal Control* in our original study, we did not include SFS modulations as a function of *Temporal Control* in our original model. However, taking the previously estimated model as a starting point, the SFS could potentially influence *Temporal Control* through interactions with the mid-rostral LPFC (MFG) or FPl. Thus, a behavioral impairment on *Temporal Control* following cTBS to SFS could be observed if SFS positively modulates MFG or FPl to facilitate *Temporal Control*.

Network dynamics revisited {#s2-3}
--------------------------

To examine whether the observed impact of SFS on *Temporal Control* could be due to a previously unappreciated modulation of SFS on rostral LPFC, we initially compared the model that we described previously ([Figure 1](#fig1){ref-type="fig"}; [Figure 2---figure supplement 3](#fig2s3){ref-type="fig"}) to models in which the SFS modulates processing in either the MFG or FPl during *Temporal Control*. This initial comparison revealed that models containing SFS-MFG connectivity and modulations were a substantially better match to the data (family model exceedance probability 0.9992). We then proceeded to explore the model space thoroughly assuming fixed connectivity between the SFS and MFG, and varying the pathways by which modulations of connectivity supported cognitive control.

Group-level Bayesian model comparison adjudicated between models of effective connectivity within the LPFC ([@bib30]) (see Materials and methods for full details of the procedure). Significant parameter estimates resulting from the revised best model (hereafter, the revised model) are depicted in [Figure 4](#fig4){ref-type="fig"} for the previously described data ([Figure 4---figure supplement 1A](#fig4s1){ref-type="fig"}), the present data ([Figure 4---figure supplement 1B](#fig4s1){ref-type="fig"}), and the data considered jointly ([Figure 4](#fig4){ref-type="fig"}). The major difference from the original model is that the feedback modulation from FPl to MFG as a function of *Temporal Control* has been replaced by a feedforward modulation from SFS to MFG. There is also evidence of a correspondingly negative feedback modulation from MFG to SFS. In this model, disruption of SFS by cTBS would be predicted to impair *Temporal Control* by disrupting feedforward influences from SFS to MFG. This modulation was not necessitated by the model comparison or estimation procedures. Models containing no feedforward modulation from SFS to MFG were directly compared to models containing this influence in several steps of the model space exploration. Furthermore, the model comparison procedure only posits what modulations might exist, not the sign or strength of the modulation. Hence, even within models containing the feedforward influence from SFS to MFG, the modulation could have been negative rather than positive (or even non-significant). That the best model of the data contained this positive modulation from SFS to MFG is therefore in striking agreement with the behavioral effects of cTBS, demonstrating the utility of combining models of regional dynamics with neural perturbations ([@bib18]).

![Revised LPFC dynamic causal model.\
Bayesian model selection indicated that the depicted model was the best model of the dynamics among the models tested. Arrows indicate direction of influence, numbers and line widths indicate the strength of influence, and dashed arrows indicated inhibitory influences. Parameter estimates have been averaged across the previous and present samples. (**A**) Fixed connectivity and inputs depicted in black. (**B**) Modulations of connectivity by *Contextual Control* (green), and *Temporal Control* (red) demands depicted in colors. All depicted parameters are significant after correction using false-discovery rate. cMFG, caudal middle frontal gyrus; FPl, lateral frontal pole; IFJ, inferior frontal junction; MFG, middle frontal gyrus; SFS, superior frontal sulcus; VLPFC, ventrolateral prefrontal cortex.](elife-28040-fig4){#fig4}

While the analyses above indicate that including a bidirectional modulation between SFS and MFG during *Temporal Control* provides the best fit of the data among the models tested, it remains possible that there may yet be other unexamined modulations that provide an even better fit. To examine the specificity of the proposed revised model, we explored whether adding bidirectional modulations during *Temporal Control* between each of the 4 other regions (IFJ, cMFG, VLPFC, and FPl) and MFG might further improve the model fit. These modulations were estimated in addition to, or in place of, the bidirectional modulation between SFS and MFG during *Temporal Control* for a total of eight additional models. These eight models were directly compared to the revised model described above using group-level Bayesian model comparison. In both the present (model exceedance probability = 0.52) and previous sample (model exceedance probability = 0.81), the revised model was clearly superior to these other potential models. Such data indicate that there is specificity to the interaction between SFS and MFG during *Temporal Control* and that simply adding additional modulations does not improve the model fit.

Finally, as in our original study, we examined measures of hierarchical strength and the relationship between model parameters and trait-measured higher-level cognitive ability. In the new model, effects of hierarchical strength remained highest in mid-rostral LPFC (both samples combined, positive peak of fitted vertex t(47) = 11.63, p\<10^−14^; mean position of vertex y = 21.7 in MNI space; [Figure 4---figure supplement 2](#fig4s2){ref-type="fig"}). However, no relationship was observed between model parameters and trait-measured higher-level cognitive ability (both samples combined, hierarchical strength -- r = −0.12, p\>0.4; top-down strength -- r = 0.18, p\>0.2; bottom-up strength r = 0.10, p\>0.4). While these data cast doubts on whether the model parameters can predict trait-measured cognitive ability, the good agreement between the effects of cTBS on behavior and the model predictions add validity to the model's relationship to behavioral manifestations of cognitive control.

Discussion {#s3}
==========

We used cTBS to test the causal relationship between a neural model of LPFC dynamics supporting cognitive control and behavioral manifestations of these control processes. In line with the model's predictions, cTBS to caudal LPFC disrupted stimulus feature processing, cTBS to mid LPFC disrupted the response to a stimulus feature based on prevailing contextual contingencies (*Contextual Control*), and cTBS to rostral-most LPFC disrupted the ability to balance ongoing and future demands (*Temporal Control*). Unexpectedly, cTBS to caudal LPFC also disrupted *Temporal Control*. This result could not be accommodated by our previously modeled connectivity dynamics ([@bib26]). However, a revised model that included a modulation from caudal LPFC to mid-rostral LPFC provided a better fit to the neural data and a ready explanation for the observed impairment. Collectively, these results demonstrate the mutually informative nature of models of neural dynamics and causal brain-behavior tests, and reveal how the LPFC supports cognitive control.

cTBS is presumed to reduce cortical excitability ([@bib17]), providing the ability to modulate behaviors for which neural activity of a stimulated region is critical. It is commonly assumed that applying cTBS to regions that show increased activity during a particular behavior will disrupt that behavior insofar as that area is necessary. With this logic in mind, it may be surprising to find that cTBS to caudal LPFC impacted *Temporal Control* as this area showed *decreased* rather than increased activity during *Temporal Control* (previous/present sample: F(1,23) = 14.62/6.77, p \< 0.05). cTBS presumably decreased activity in this region further, which is inconsistent with a simple mapping between univariate activity and behavior (i.e. further decreasing activity may have predicted a behavioral improvement). Moreover, the VLPFC showed increased activation during *Contextual Control* (previous/present sample: F(1,23) = 43.65/126.82, p \< 10^−5^), and verbal processing (previous/present sample: F(1,23) = 25.8/16.05, p \< 0.001), but not their interaction (previous/present sample: F(1,23) = 3.29/3.32, p \> 0.05). Yet, cTBS to this region specifically impaired the interaction among these processes. That behavioral impairments following cTBS do not necessarily track simple regional increases or decreases in activity underscores the need to inform predictions of neural perturbation by models of neural dynamics.

Causal methods provide strong tests of hierarchical relationships. The logic of this approach can be understood by visualizing hierarchy as a pyramid --- perturbation of the lowest levels of the hierarchy affect all levels above, whereas perturbation of the top level of the hierarchy does not disrupt the lower levels. The underlying neural mechanism of this hierarchical organization can be understood by the flow of information within hierarchical networks. Lesion data have been used to examine the organization of the LPFC and its hierarchical dependencies. [@bib4] found that damage to caudal LPFC impaired the ability to base responses on color-feature associations (Feature Task, lower-level deficit). This function is similar to *Feature Control* examined here, with both studies demonstrating a critical role of caudal LPFC. By contrast, [@bib4] found that damage to mid LPFC impaired the ability to base responses on color-feature dimension associations (Dimension Task, higher-level deficit). This function has semblance to *Contextual Control* studied here in that both cases require the use of a higher-order context to determine which feature--feature associations govern the appropriate response. Since Badre et al. did not examine different stimulus domains, it is impossible to tell whether the observed deficit was also stimulus-selective, as was observed here. Critically, [@bib4] demonstrated both hierarchical dependence and selectivity in the reported deficits. Damage to a lower-order controller led to non-parametric deficits at higher levels, but not vice versa (e.g. damage to caudal LPFC impaired the Dimension Task *uniformly* across demands, but damage to the mid LPFC did not impair the Feature Task at all). Furthermore, parametrically varying demands on a given control function revealed parametrically varying deficits when the region involved in that control function was damaged (e.g. damage to caudal LPFC caused *parametrically varying* deficits for the Feature Task, but deficits in the Dimension Task were uniform). This pattern of results is similar to those observed here -- cTBS to caudal LPFC was selective at the level of function (i.e. impaired spatial *Feature Control*), and general at higher levels (i.e. was present during, but did not interact with other control demands). Similarly, cTBS to mid LPFC was selective to the level of function (i.e. impaired verbal *Contextual Control*), but did not influence lower levels (i.e. did not impair verbal *Feature Control* more generally). Hence, the pattern of deficits are consistent across these studies, suggesting that similar neural dynamics are engaged by the studied tasks.

[@bib1] also reported hierarchical dependencies along the rostral-caudal axis using tasks spanning three levels of control: color-response mapping (Sensory Control, low), color-task-response mapping (Contextual Control, mid), episode-color-task-response mapping (Episodic Control, high). In correspondence to the results here, damage to caudal LPFC impaired Sensory Control, damage to mid LPFC impaired Contextual Control, and damage to rostral LPFC impaired Episodic Control. Furthermore, [@bib1] reported hierarchical dependencies among these deficits such that higher-level deficits followed lower-level deficits, but not vice versa. Unlike [@bib4], cognitive control demands at each level were not parametrically varied, nor were factorial contrasts used to isolate different control processes. This is potentially problematic in that the tasks used to examine higher levels of control (e.g. Episodic Control) naturally contained the lower levels of control (e.g. Sensory Control). Hence, a patient with an impairment in Sensory Control could show poor performance in the Episodic Control task due to the Sensory Control impairment impacting Episodic Control (hierarchical deficit), or simply due the Sensory Control aspects of the Episodic Control task (non-hierarchical deficit). Hence, it is difficult to establish correspondences between the reported patterns of deficits and those described here. Nevertheless, the pattern of deficits observed by [@bib1] are consistent with a rostral-to-caudal cascade of activity whereby progressively rostral areas influence caudal areas as the level of cognitive control demands increases ([@bib19]; [@bib20]). A top-down cascade is ostensibly at odds with the dynamics reported here, which demonstrate a convergence of influences towards the mid LPFC. However, these data may be reconciled by considering the caudal LPFC in more detail. In [@bib19], the caudal LPFC is assigned an output role, establishing the appropriate motor response. By contrast, here, the caudal LPFC is assigned an input role, establishing stimulus features for other cognitive control processes. It is likely that caudal LPFC is comprised of both input- and output-related regions, with roles depending upon contrasts used to isolate the caudal LPFC. Furthermore, neural dynamics probably depend upon the role of the investigated region (i.e. output - receives modulations from PFC, input - sends modulations to PFC). Future work investigating both input- and output-related regions simultaneously would help to better illuminate the neural dynamics of cognitive control.

TMS studies have been less convincing with regard to demonstrating hierarchical dependencies among PFC areas. [@bib6] applied TMS to rostral and caudal LPFC, previously identified with Episodic and Response Control, respectively ([@bib5]). TMS to rostral LPFC selectively impaired Episodic Control, but TMS to caudal LPFC produced no measurable impairments. The former result is in agreement with [@bib1], whereas the latter result is seemingly at odds with the results of [@bib1] wherein lesions to caudal LPFC impaired performance on all tasks. A notable difference among these studies is that the caudal LPFC area identified by [@bib1] was localized dorsally, at or near the SFS, whereas the caudal LPFC area targeted in [@bib6] was localized ventrally, at or near the IFJ. If Episodic Control corresponds to *Temporal Control* studied here, an effect of SFS but not IFJ TMS on Episodic Control would be consistent with our data and revised model. Finally, [@bib29] applied cTBS to caudal, mid, and rostral LPFC during a perceptual decision-making task. Consistent to the results reported here, cTBS to caudal LPFC impaired spatial attention. cTBS to mid LPFC (correspondingly most closely with MFG here) impaired trading off between fast and accurate responding, a domain-general form of *Contextual Control* that our model would predict to depend upon MFG. Finally, cTBS to rostral LPFC improved meta-cognitive accuracy. This latter result has no clear correspondence in the present task. Regardless, independent effects were observed following cTBS to each PFC area, which showed no discernable hierarchical pattern. However, the lack of hierarchical dependence in this case is probably due to the task wherein each demand could be performed largely independently. We would conjecture that process interdependence is key for examining hierarchical interactions. In such cases, predictions of the effects of focal disruption would be facilitated by models of neural dynamics.

Other TMS studies have examined behaviors relevant to those studied here without directly linking them to models of neural dynamics and hierarchy. [@bib25] found that TMS to dorsal caudal LPFC (at or near SFS) selectively impaired spatial, but not verbal working memory, whereas TMS to ventral caudal LPFC (at or near IFJ) selectively impaired verbal but not spatial working memory. Such results are consistent with our model wherein SFS maintains spatial stimulus features, whereas IFJ maintains verbal stimulus features, which would support spatial and verbal working memory, respectively. Other studies targeting areas at or near the area we have referred to as 'VLPFC' have reported TMS-related reductions in semantic association ([@bib9]; [@bib16]; [@bib32]), long-term memory ([@bib22]; [@bib8]), and binding multiple features in working memory ([@bib24]). It is unclear whether a common function underlies all of these cases, but each involves associating identity-based (i.e. ventral stream) representations in a contextual manner. Finally, TMS to the FPl impacts the integration of temporally distal representations into ongoing cognition ([@bib11]), and ordering tasks in a sequence in the absence of overt cues ([@bib12]). These cases are reminiscent of the *Temporal Control* studied here that relies on FPl. Collectively, these data show broad consistencies in effects. Our study further embeds these effects within a model of neural dynamics.

Our original report challenged prevailing accounts positing that the rostral-most LPFC (i.e. FPl) is the apex of the LPFC hierarchy. By definition, a higher place in a hierarchy entails greater influence over that which is lower and vice versa ([@bib3]). Previously, we found that the mid-rostral PFC (i.e. MFG) showed the presumed signature of a hierarchical apex -- greater outward than inward influence in fixed connectivity. This connectivity pattern was also observed in the present dataset, and in the revised model in both datasets. Furthermore, we previously observed that modulations of connectivity dynamics indicated that, during cognitive control, activity converges towards mid LPFC. This result was also observed in the revised model, although some of the pathways along which information flows through the network have been altered. Nevertheless, it is clear that activity diverges (fixed connectivity) and converges (connectivity modulations) to/from the middle of the LPFC in the modeled neural dynamics. Collectively, these data corroborate the hypothesis that we posited previously, that the mid LPFC is a critical nexus for cognitive control. Other work has demonstrated that areas of functional convergence, referred to as dynamic hubs, are particularly important for behavior ([@bib27]). While the described work has described hubs within the PFC, hubs that connect networks more globally throughout the brain are also particularly important with damage to such regions producing profound global brain reorganization ([@bib15]) and behavioral impairments ([@bib31]). Collectively, such data suggest that importance for brain function and behavior depend critically on where information converges, rather than where it arises.

While the significant effects observed in the present study were by-and-large predicted by a model of LPFC dynamics, the effects were generally limited by task accuracies that were near ceiling (average performance across the task \~95%). As error trials are typically considered separately in fMRI data, we included extensive practice to ensure that participants could perform the task with maximizing power for the fMRI data in mind. Nevertheless, we did not anticipate that many of the behavioral modulations resulting from cTBS would be borne out in errors. A more suitable procedure may have been to titrate the task to individual performance levels, potentially by requiring adaptively speeded responses to keep performance from ceiling. Given these ceiling effects, it is difficult to interpret null effects in the cTBS data, even though null effects are also important for validating the model. It is also difficult to model the behavioral data (e.g. drift-diffusion modeling) to make inferences regarding the effects of cTBS on different aspects of the decision process (e.g. drift rate, bias). Future explorations using these methods would do well to keep these considerations in mind.

Another limitation of the present work is the temporally tonic nature of cTBS neural modulations. This method precludes inference of precisely when a given region is necessary for behavior. A more time-resolved approach using single pulses or short bursts of TMS (e.g. [@bib12]) could further elucidate the temporal necessity of each region to cognitive control. Hierarchical dependencies could potentially be revealed by relative orderings of necessity for behavior (e.g. a parent node would be necessary earlier in the trial epoch than a child node). Such methods would be a useful avenue for future investigation.

Materials and methods {#s4}
=====================

Many of the materials and methods used in this work are identical to those described in our previous report ([@bib26]). We present abbreviated details here, highlighting differences as well as the cTBS procedures.

Participants {#s4-1}
------------

We report results from 24 (15 female) right-handed native English speakers (mean age 20.5 years, range 18--27). 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. A sample size of 24 participants was acquired to match to our previous study, which was well-powered to examine fMRI effects. We also considered the efficacy of cTBS. A previous study involving a subset of the authors used a similar cTBS design with a smaller sample size of 17 ([@bib29]), suggesting that our target sample would probably be adequate. In addition, a sample size of 24 offered the ability to counter-balance the order of cTBS stimulation targets perfectly. All 24 participants are included for the fMRI analyses. In one participant, the control site (S1) was mistargeted, resulting in stimulation of an area that was active for the task (superior parietal lobule). The cTBS data from this participant are excluded. Another participant appeared to misunderstand the instructions for the *Restart* condition, demonstrating below-chance accuracy on return trials. This participant was excluded for all cTBS analyses that included cognitive control demands, but was included in the analysis of *Stimulus Domain* with trials from the *Restart* condition excluded. Inclusion of these data was deemed appropriate over outright exclusion, given that the analysis of *Stimulus Domain* was orthogonal to the cognitive control demands, and given the costs in data acquisition. These exclusions resulted in 23 participants for cTBS analyses focused solely on *Stimulus Domain*, and 22 participants for the remainder of the cTBS analyses.

Three participants performed the fMRI session but were excluded from cTBS sessions. For two participants, functional mapping revealed right-lateralized language processing despite self-reported right-handedness. Another participant was excluded due to an incidental finding. Three participants did not complete all of the cTBS sessions and were therefore excluded from analyses. Two of these participants experienced transient discomfort during stimulation of the rostral LPFC target, which mandated the abortion of that session and subsequent sessions. One participant withdrew from the study after the first cTBS session. These data were excluded from all analyses. In addition, due to a technical error, the final two runs of data were not collected for one session for one participant.

Procedure {#s4-2}
---------

The task design was a factorial 2 × 2 × 2, with factors of *Stimulus Domain* (verbal, spatial), *Contextual Control* (high, low), and *Temporal Control* (high, low). The procedure was nearly identical to that described in our previous report and details can be found there ([@bib26]). Here we report differences in the procedure.

Whereas previously, participants performed two fMRI sessions, only a single fMRI session was performed here. The number of trials of the basic task at the beginning of each block was reduced from 2--5 trials to 2--3 trials, which helped to improve trial yield for trials-of-interest in the cTBS sessions. Otherwise, the fMRI session was identical to the previously described procedure.

Timing details were mistakenly omitted in our previous report. For fMRI sessions, stimuli were presented for 500 ms followed by a variable inter-trial interval (ITI) of 2600--3400 ms. 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 at the end of the block. Blocks were spaced by a variable 2600--3400 ms interval. Self-paced breaks were administered in-between runs. For cTBS sessions, the ITI was reduced to 1500--1900 ms, and the interval between blocks was reduced to 1100--1900 ms in order to improve trial yield. Breaks between runs were fixed at 30 s. With these timing reductions, 8 runs were administered, resulting in 16 blocks for each cell of the design. It has been reported that reduced cortical excitability following cTBS begins approximately 5 min post-stimulation and lasts until approximately 60 min post-stimulation ([@bib17]). Our timing procedures closely matched this window. A practice run of the task that was half the duration of the experimental runs immediately followed cTBS. As a result, experimental runs began approximately 5 min post-stimulation. A preliminary cursory inspection of run effects (indexed by run within session) revealed no appreciable patterns, so effects of run were not further explored.

Participants performed six sessions scheduled as follows: participants first completed a behavioral session wherein they were introduced to the task and given extensive practice as previously described. Assays of higher-level cognitive ability were also collected as previously described. The fMRI session followed on a separate day, within 10 days of the behavioral session (one participant was scanned 17 days after the behavioral session due to a scheduling issue). The first cTBS session followed within 10 days of the fMRI session (12 days for one participant with a scheduling issue). All cTBS sessions were spaced by one week, with each session beginning at the same time of day for a given individual. The order of stimulation targets was fully counterbalanced and randomized across participants.

fMRI analysis {#s4-3}
-------------

Analysis of the fMRI data used methods that were virtually identical to those described previously ([@bib26]). Regions-of-interest (ROI) analyses were centered on the peak coordinates of our previous report. The one exception to this was for the caudal middle frontal gyrus (cMFG), which was centered on peak activation for *Contextual Control* in the present sample (−26 14 52) to accommodate individual variability in slice prescription that left out the previous peak (−34 10 60) in some participants. ROIs were used to explore abstraction effects both by analysis of *Stimulus Domain* and by correlations with behavior, as previously described.

Transcranial magnetic stimulation procedures {#s4-4}
--------------------------------------------

Transcranial magnetic stimulation (TMS) was delivered using a MagStim Super Rapid2 stimulator equipped with a figure-eight double air film coil with a 70 mm diameter. Electromyography (EMG) was recorded using electrodes placed on the first dorsal interosseus (FDI) muscle on the right-hand using a Delsys Bagnoli system (Delsys Inc.). Individual active motor threshold (AMT) was determined immediately before each session of cTBS. First, a 'hunting procedure' was used to determine the scalp location in the left hemisphere producing the maximal contralateral hand twitch at the minimal stimulation intensity. Next, the participant maintained voluntary contraction of the FDI muscle at \~20% of maximum contraction. AMT was determined as the minimal stimulation intensity needed to produce a motor-evoked potential in 5 out of 10 pulses. Across sessions and participants, the average AMT was 48% of the stimulator output.

cTBS was delivered in a standard manner as described by [@bib17]. Bursts of three pulses at 50 Hz were delivered every 5 Hz for a total of 600 pulses over 40 s. Stimulation intensity was delivered at 80% of the individual's AMT. During all TMS procedures, participants were continually monitored and verbally queried for signs of pain, dizziness, or other adverse effects. Just prior to the start of cTBS, a single test pulse was delivered to the target site at the same intensity of cTBS. The test pulse was used to help the participant determine whether stimulation of the target would be painful. As reported above, two participants found stimulation of rostral LPFC painful during this test and were excluded from further participation. No adverse effects were reported in the sample used for analysis.

cTBS targets {#s4-5}
------------

cTBS targets were defined on the basis of individual activation maxima (LPFC) or anatomy (S1). We restricted targets to the left hemisphere. LPFC targets were chosen to dissociably stimulate caudal, mid, and rostral LPFC. As reported previously, both dorsal and ventral peaks exist along the rostral-caudal axis of the LPFC. The choice of which target to stimulate for each rostral/caudal sector was motivated by the desire to maximize the distance between targets. Furthermore, given that the ventral caudal LPFC area (i.e inferior frontal junction; IFJ) was distanced from the scalp surface (mean MNI peak −38 6 26 previously), the dorsal caudal LPFC was selected as a more suitable target. This led to the targeting of the ventral mid LPFC and FPl rostrally.

The caudal LPFC target was chosen as the maximal activation for the *Stimulus Domain* contrast, whose sign was dictated by the contrast of *Spatial Stimulus Domain* \> *Verbal Stimulus Domain* (mean MNI location: −23.9--0.6 55.6). Previously, it was found that the mid LPFC shows univariate sensitivity to both *Stimulus Domain* and *Contextual Control*, but not to their interaction. As can be observed in the whole-brain univariate maps (e.g. [Figure 2](#fig2){ref-type="fig"}), the *Contextual Control* contrast elicits activation along much of the rostral-caudal axis of the LPFC, potentially rendering identification of the appropriate stimulation target difficult on an individual basis. We thus chose to use the *Stimulus Domain* contrast to define the mid LPFC target as this contrast produced more confined activations that were anticipated to reduce variability in target location across participants. In this case, areas were defined as those showing greater activity for the *Verbal Stimulus Domain* \> *Spatial Stimulus Domain*. The ventral mid LPFC area previously described extended from the inferior frontal sulcus (IFS) into the inferior frontal gyrus ventrally and into the middle frontal gyrus dorsally. To maintain consistency, we chose targets restricted to the inferior frontal gyrus. As a result, we now describe the ventral mid LPFC area as the ventrolateral prefrontal cortex (VLPFC) as this term more accurately describes the targeted site. For the first six participants, the maximal activation on the lateral surface of the inferior frontal gyrus was chosen as the stimulation target. At this point, it was determined that this choice of target definition was producing targets that were consistently caudal to the ventral mid LPFC area previously described (mean MNI y-coordinate of the first six participants = 14.0 compared to 20 previously). The procedure was therefore adjusted to target the rostral-most local maxima within pars triangularis and pars opercularis. This resulted in targets that were more clearly situated in mid LPFC (mean MNI location: −51.3 17.5 17.5).

The rostral LPFC target was chosen to be in the vicinity of the FPl previously described (mean MNI location: −34.1 56.9 0.7). In most cases, the rostral LPFC target was identified as the maximal activation for the conjunction of *Temporal Control* and *Contextual Control*. However, if the activation peak was deemed too close to the orbits to stimulate without pain, a more dorsal local maxima was used. In five cases, a target could not be identified through the conjunction contrast. In these cases, either the main effect of *Temporal Control*, main effect of *Contextual Control*, or the simple contrast of Dual \> Control was used with the main-effect contrasts taking precedence. This procedure resulted in a target that, on average, was equivalently engaged during *Temporal Control* and *Contextual Control* (average t-statistic for *Temporal Control* -- 4.15, average t-statistic for *Contextual Control* -- 4.38). Finally, the control site (S1) was chosen as the dorsal-most portion of the post-central gyrus defined anatomically. cTBS targets were guided by a frameless stereotactic localization system (Brainsight; Rogue Research, Inc.).

cTBS analysis {#s4-6}
-------------

Behavioral modulations following cTBS were analyzed using linear mixed effects modeling in SPSS version 23 and repeated measures ANOVAs. For the analysis of *Stimulus Domain*, all trials were considered in order to maximize power. This was because the demand to select a stimulus feature (either verbal or spatial) was present in all trials of the task with the potential exception of the sub-task phase of *Delay* trials (notably, removing Delay trials from the analyses does not change the results). Other analyses were restricted to trials from the sub-task phase wherein the other cognitive control demands were manipulated (e.g. *Temporal Control* was not present before and after the sub-task phase). Reaction times (RTs) were computed from correct trials only. RTs greater than 2.5 standard deviations of the condition mean were discarded as outliers, as were trials with RTs less than 200 ms or greater than 2000 ms. \~ 3.5% of the trials were removed as outliers. Including these outliers in the analyses weakens, but does not fundamentally alter, the pattern of results. For analyses on accuracy/error-rate, condition-wise measurements of % correct were arc-sine transformed to normalize the distributions. Accuracies at ceiling (i.e. 100% correct) were corrected prior to transformation with the formula (*n*--0.5)/*n*, where *n* is the number of trials in the condition. Statistics were performed on these transformed data. To present error-rates, transformed accuracies were subtracted from the corrected transformed ceiling. Error-rates are presented rather than accuracies to facilitate interpretation alongside RTs, such that greater numbers consistently reflect worse performance.

All linear mixed effects models include a factor of *Time* to account for practice-related changes over sessions. These models also included random effects terms of *Subject*, and *Time* nested within *Subject* (i.e. *Time* \| *Subject*). No assumptions were made of the covariance structure of the random effects terms, which was modeled using restricted maximum-likelihood estimation. Because of the rank of the data, models could only include either *Time* \| *Subject* or *Target* \| *Subject*. Although both effects may be present, the inclusion of *Time* \| *Subject* offered superior model log likelihoods of the covariance structure than did the inclusion of *Target* \| *Subject*, so *Time* \| *Subject* was modeled. In order to simplify the covariance structure, the modeled data were contrasts of interests: *Stimulus Domain* = spatial task -- verbal task; *Stimulus Domain x Contextual Control* = \[(verbal Dual + verbal Restart) -- (verbal Delay + verbal Control)\] -- \[(spatial Dual + spatial Restart) -- (spatial Delay + spatial Control)\]; *Contextual Control* = (Dual + Restart) -- (Delay + Control); *Temporal Control* = (Dual + Delay) -- (Restart +Control). Given the assumptions and choices inherent in linear mixed effects modeling, we also present standard full factorial repeated measure ANOVAs (which exclude the factor of *Time*) to provide statistical analyses with fewer assumptions ([Figure 3---figure supplement 1](#fig3s1){ref-type="fig"}). Upon finding significant linear mixed model effects of *Target*, t-tests directly comparing Targets were performed after controlling for the effects of *Time*. These analyses were performed on the residuals after regressing out both *Time* and *Time* \| *Subject*.

To test for contrast x Target interactions, the contrasts of the main effect of *Stimulus Domain* in ER, *Stimulus Domain* x *Contextual Control* in RT, and *Temporal Control* in ER were computed (after controlling for *Time* as above) and z-scored across individuals. To make the signs consistent, contrasts containing *Stimulus Domain* were computed such that positive values indicated worse performance on the verbal relative to the spatial task. These were entered into a 3 × 4 repeated measures ANOVA. A follow-up 4 × 4 ANOVA added the contrast of *Contextual Control* in ER.

Dynamic causal modeling {#s4-7}
-----------------------

DCM was originally performed as previously described ([@bib26]). The presence/absence of connectivity pathways and modulations was matched to our previous report and the model was estimated in the present sample. Inferences on the parameter estimates were performed in a manner identical to that described previously.

Given the unanticipated effect of cTBS to caudal LPFC on *Temporal Control*, additional DCM analyses were performed on the present sample. First, the original model was compared to two other families of models: 1) fixed connectivity between the SFS and FPl along with modulations (either feedforward, feedback, or bi-directional) as a function of *Temporal Control*, and 2) fixed connectivity between the SFS and MFG along with modulations (either feedforward, feedback, or bi-directional) as a function of *Temporal Control*. Bayesian model selection was first performed family-wise ([@bib28]). In this comparison, families including connectivity between SFS and MFG were overwhelmingly favored (model exceedance probability = 0.9992). Given this result, all subsequent model comparisons included fixed connectivity between the SFS and MFG, with modulations as a function of *Temporal Control* (feedforward, feedback, bi-directional, or absent) varying across models. We used an iterative procedure as previously described to explore the model space while maintaining computational feasibility ([@bib26]). Here, the model space was identical to that described before with the addition of the possibility of modulations between the SFS and MFG as a function of *Temporal Control*. In this case, the iterative procedure did not converge, instead hitting an infinite loop. In total, 913 models were explored. Simultaneous comparison of these models using Bayesian model selection ([@bib30]) did not identify a single best model in terms of an exceptional model exceedance probability. A scree plot of the models ordered by their exceedance probabilities identified potential step-wise differences for the top 18 and top 27 models. It is possible that the failure to identify a clearly superior model was due to the large number of models explored that overlapped in many features. Hence, Bayesian model selection was performed on a reduced model space taking the top 27 models. Once again, no single model was clearly favored, but the top 19 models (all model exceedance probability \~0.04) were ordered similarly to before and were once again consistently favored over the other models (model exceedance probabilities \~0.02). Nevertheless, these model exceedance probabilities were no different than uniform (1/27 = 0.037).

In order to better adjudicate between the models of LPFC dynamics, the best 19 models identified above were compared within the previous sample. Given that the previous sample contained twice the fMRI data per subject, this offered the ability to produce more stable model parameter estimates with better potential to delineate among the models. The original model was also included for comparison to verify that the addition of SFS to MFG connectivity was prudent, making a total of 20 models for comparison. In this case, far more convincing evidence was found for the top model (model exceedance probability = 0.2526, compare to a uniform of 0.05). Other models with better-than-uniform model exceedance probabilities shared the main features that were found to be significant in the data reported in the main text (feedforward modulation from SFS to MFG for *Temporal Control*, feedback modulation from FPl to MFG and MFG to cMFG/VLPFC for *Contextual Control*), bolstering the credibility of these effects. Parameter estimates for the best model were examined for the previous dataset and the present dataset, and compared for consistency. Noting good agreement among the parameter estimates ([Figure 4---figure supplement 1](#fig4s1){ref-type="fig"}), the two datasets were combined for subsequent inference. Random effects inference on the parameters of the winning model then proceeded in a manner identical to our previous report.

To summarize:

i) The winning DCM from [@bib26] was estimated on the present dataset.

ii) New DCM's were estimated on the present dataset to examine whether the observed effect of cTBS on SFS on *Temporal Control* could be accommodated by a revised model.

iii) The top 19 models from (ii) were difficult to adjudicate among, and were subsequently compared to each other and the winning DCM from [@bib26] in the previous dataset.

iv) Parameter estimates from the best model in (iii) were examined in both the present and previous datasets and pooled for inference.

Funding Information
===================

This paper was supported by the following grants:

-   http://dx.doi.org/10.13039/100000065National Institute of Neurological Disorders and Stroke F32 NS0802069 to Derek Evan Nee.

-   http://dx.doi.org/10.13039/100000065National Institute of Neurological Disorders and Stroke P01 NS040813 to Mark D\'Esposito.

-   http://dx.doi.org/10.13039/100000025National Institute of Mental Health R01 MH063901 to Mark D\'Esposito.

This research was supported by National Institute of Neurological Disorders and Stroke Grants F32 NS0802069 (DN) and P01 NS040813 (MD), and by National Institute of Mental Health Grant R01 MH063901 (MD). The authors thank Dobromir Rahnev for helpful advice with the TMS procedure, and Max Wang, Lara Krisst, Grace Lee, Joanne Lin, and Chelsea Harmon for help with data collection.

Additional information {#s5}
======================

No competing interests declared.

Conceptualization, Data curation, Software, Formal analysis, Funding acquisition, Investigation, Visualization, Methodology, Writing---original draft, Project administration, Writing---review and editing.

Conceptualization, Supervision, Funding acquisition, Writing---review and editing.

Human subjects: Informed consent was obtained in accordance with the Committee for Protection of Human Subjects at the University of California, Berkeley under protocol number 2010-02-781.

Additional files {#s6}
================

10.7554/eLife.28040.014

Major datasets {#s7}
--------------

The following dataset was generated:

Derek Evan NeeMark D\'Esposito2017Causal Evidence for Lateral Prefrontal Cortex Dynamics Supporting Cognitive Control<https://oneshare.cdlib.org/stash/dataset/doi:10.15146/R3Q37R>Publicly available on Oneshare

10.7554/eLife.28040.018

Decision letter

Davachi

Lila

Reviewing Editor

New York University

United States

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

Thank you for submitting your article \"Causal Evidence for Lateral Prefrontal Cortex Dynamics Supporting Cognitive Control\" for consideration by *eLife*. Your article has been reviewed by two peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Timothy Behrens as the Senior Editor. The following individual involved in review of your submission has agreed to reveal his identity: Charan Ranganath (Reviewer \#2).

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

The reviewers both commend the authors for providing a nice replication of your previous fMRI work dissociating LPFC regions with further manipulation of those circuits using stimulation methods and testing the predictions from their dynamic causal modeling results.

However, they agreed that there were several issues that need to be addressed to clarify the strength of the findings and better understand what the implications are for broadening our understanding of PFC function.

1\) While you state that the findings in ER were unexpected, there is little explanation for why some effects would be observed in RT and some in ER? Given the emphasis on modeling and model testing, it would be nice to see an attempt at a testable account for this difference among the nodes. Relatedly, please present the full results for both RT and ER in the main figure (instead of in the supplemental).

2\) From a statistical perspective, the behavioral effects of TMS, as framed in the paper, are relatively weak. This may be due to the choice of analysis approaches. The 2x2x4 ANOVA approach is nice in the sense that it makes few assumptions, but it is not powerful for detecting the predicted stimulation target-related interactions because of the nonsphericity correction. Please think outside of the box on this issue -- all ANOVAs are effectively fitting particular models to the data, but they are just non-optimal models for a study like this. One alternative approach would be to run an omnibus F-test to first show that there is something going on, and then to break it down by fitting a model of the exact pattern of results predicted by the authors\' model for each stimulation approach. This model can be tested against reduced or alternative models. That\'s just a suggestion, however, the point is that the current approach of reporting nonsignificant interactions and then running planned comparisons seems to undermine the whole ANOVA approach in the first place.

3\) You nicely show that if the model is updated, better model fits are obtained based on including further potential connectivity and modulators. Is this true for any of the other nodes in the network? Particularly the IFJ? If SFS and IFJ has a similar function but in different modalities, then it might follow that their influence on the network might be similar? This space should be explored. It also raises the question of other nodes having unanticipated connections. While testing all possibilities is clearly not feasible, showing that other potential connections (e.g. FPl to SFS) do or do not produce changes in model fit could help clarify the proposed functioning of the network.

4\) Please discuss how the current results should alter our view of PFC function. It was noted by a reviewer that \"the authors describe various findings in the literature and conclude that, \"Collectively, these results indicate that whether or not hierarchical dependencies exist depends critically upon task-elicited regional interdependencies.\" It is a concern that this statement *completely nullifies* the significance of the study -- if the presence or absence of a hierarchy is completely task dependent. Please reconcile this with the statement you make that the \"data provide causal evidence for LPFC dynamics supporting cognitive control\".

5\) Please address the issue of practice more thoroughly. Does it have any effect on the modeling and relationship to cognitive capacity results -- especially given that there were differences? A cursory examination of within-session practice effects was made but not elaborated upon. Given that the participants are participating in many, spaced sessions, the effect of session should be examined both in isolation and as a covariate. There is the potential for effects to interact with practice.

6\) Please justify the use of a one-tailed test for the comparison between SFS and S1. Was there an a-priori reason for doing so? If not, this should not be included as a significant result. In terms of the analysis of the cTBS results, please clarify why for all but Stimulus Domain analyses a subset of trials were analyzed. Also, with some of the TMS effects in RT, why remove long RT\'s? Was there a systematic kind of trial that was removed with this process? Does including those RTs alter the results in any way?

7\) Was the entire DCM run on the new sample only or on the combined data from the current sample and the previous *eLife* publication? It looks like some combination of the two, which is odd especially because the initial replication DCM was performed separately on the new dataset (right?). Some clarification is warranted.

10.7554/eLife.28040.019

Author response

> The reviewers both commend the authors for providing a nice replication of your previous fMRI work dissociating LPFC regions with further manipulation of those circuits using stimulation methods and testing the predictions from their dynamic causal modeling results.
>
> However, they agreed that there were several issues that need to be addressed to clarify the strength of the findings and better understand what the implications are for broadening our understanding of PFC function.
>
> 1\) While you state that the findings in ER were unexpected, there is little explanation for why some effects would be observed in RT and some in ER? Given the emphasis on modeling and model testing, it would be nice to see an attempt at a testable account for this difference among the nodes. Relatedly, please present the full results for both RT and ER in the main figure (instead of in the supplemental).

Our expectation that effects of TMS would be observed primarily in RT was driven by a simple conception of an accumulator decision process wherein cTBS to a given region would slow the rate of evidence accumulation by way of inhibiting neuronal activity (e.g. the inverse of what has been observed via microstimulation in Hanks et al., 2006, Nat Neurosci). Whether effects that are borne out in ER rather than RT are telling regarding the decision process is unclear to us. RT and ER tend to tradeoff and subjects can strategically shift between the two (e.g. Fitts et al., 1966, JEP), and we have previously demonstrated that such shifts are under PFC control (Rahnev et al., 2016, PNAS). While deeper exploration of the locus of the effect (i.e. ER vs. RT) and potential interactions with speed-accuracy tradeoffs strategies would be interesting, the low number of errors by condition renders it difficult to model the decision process (e.g. drift diffusion modeling). While we have made some attempts to do so, we could not achieve satisfactory model fits. Given that we cannot gain theoretical traction on the matter, we refrain from speculating why some effects are observed in ER and others in RT. Instead, we discuss the limitations that the low ERs place on the interpretation of these data in the Discussion.

"While the significant effects observed in the present study were by-and-large predicted by a model of LPFC dynamics, the effects were generally limited by task accuracies that were near ceiling (average performance across the task \~95%). \[...\] Future explorations using these methods would do well to keep these considerations in mind."

As recommended, the full RT and ER results are now reported in [Figure 3A-B](#fig3){ref-type="fig"}.

> 2\) From a statistical perspective, the behavioral effects of TMS, as framed in the paper, are relatively weak. This may be due to the choice of analysis approaches. The 2x2x4 ANOVA approach is nice in the sense that it makes few assumptions, but it is not powerful for detecting the predicted stimulation target-related interactions because of the nonsphericity correction. Please think outside of the box on this issue -- all ANOVAs are effectively fitting particular models to the data, but they are just non-optimal models for a study like this. One alternative approach would be to run an omnibus F-test to first show that there is something going on, and then to break it down by fitting a model of the exact pattern of results predicted by the authors\' model for each stimulation approach. This model can be tested against reduced or alternative models. That\'s just a suggestion, however, the point is that the current approach of reporting nonsignificant interactions and then running planned comparisons seems to undermine the whole ANOVA approach in the first place.

A fair point is made that it is somewhat awkward to state the absence of a significant interaction, but follow up with significant planned contrasts. While we appreciate the sentiment of "thinking outside the box" with regard to examining hypothesized effects in a potentially more sensitive manner, we are also cautious about exercising degrees of freedom in analysis so as to avoid overfitting the data. Nevertheless, we believe that a middle ground has been achieved:

In addressing the issue of practice, we have had to adjust the modeling framework. The resultant models have yielded results that strengthen the previously reported patterns. In particular, we now report the results of linear mixed effects models that add time as a covariate in order to account for practice effects over cTBS sessions. As the reviewers keyed in on, many of the cognitive control effects varied with time and accounting for this variance reduced the error of the contrasts of interest. In order to simplify modeling the co-variance structure of the data, the linear mixed effects models are estimated on contrasts of the behavior effects, thereby providing a more streamlined and targeted approach, as recommended. In the present manuscript, significant effects of Target are now observed in either ER or RT for all of the hypothesized interactions. In addition to amending the Results with the aforementioned statistical tests, [Figure 3](#fig3){ref-type="fig"} has been revised to depict the contrasts of interests after controlling for effects of time.

As the reviewers note, ANOVAs are nice in that they have few assumptions and the ANOVAs reported previously were the originally planned analyses. For the sake of transparency and reproducibility, the revised manuscript retains all of these analyses in [Figure 3---figure supplement 1](#fig3s1){ref-type="fig"} (with slight modification to account for an error detailed in our third response to comment \#6). We hope that this presentation strikes a balance between hypothesis driven analysis that controls for confounding factors, and assumption-free analysis.

See Results subsection "Behavioral Results and Effects of cTBS"; [Figure 3C-F](#fig3){ref-type="fig"}.

> 3\) You nicely show that if the model is updated, better model fits are obtained based on including further potential connectivity and modulators. Is this true for any of the other nodes in the network? Particularly the IFJ? If SFS and IFJ has a similar function but in different modalities, then it might follow that their influence on the network might be similar? This space should be explored. It also raises the question of other nodes having unanticipated connections. While testing all possibilities is clearly not feasible, showing that other potential connections (e.g. FPl to SFS) do or do not produce changes in model fit could help clarify the proposed functioning of the network.

The reviewers raise a good point about specificity. If adding a bidirectional Temporal Control modulation between SFS and MFG improves the model, it is possible that a similar addition from other nodes (e.g. IFJ to SFS, FPl to SFS) might do the same. In the least, a similar modulation from IFJ would give the model symmetry. To explore this matter, we estimated 8 new models in the current (TMS) sample, and replicated the same analysis in the previous (fMRI only) sample. These models added bidirectional Temporal Control modulations between MFG and each of IFJ, VLPFC, cMFG, or FPl. These modulations were added in addition to, or in place of the bidirectional modulation between SFS and MFG previously described. In both the TMS sample and the fMRI only sample, adding these modulations did not improve the model fit as evidenced by the previously reported model having a clearly superior model exceedance probability in the 9 model comparison (TMS sample exceedance probability = 0.5192, fMRI only sample exceedance probability = 0.8076, compare to a uniform of 0.1111). While exploring the full space of unanticipated connections is computationally infeasible, this result is consistent with specificity with regard to the reported SFS to MFG connection.

From the Results:

"While the analyses above indicate that including a bidirectional modulation between SFS and MFG during *Temporal Control* provides the best fit of the data among the models tested, it remains possible that there may yet be other unexamined modulations that provide an even better fit. \[...\] Such data indicate that there is specificity to the interaction between SFS and MFG during *Temporal Control* and that simply adding additional modulations does not improve the model fit."

> 4\) Please discuss how the current results should alter our view of PFC function. It was noted by a reviewer that \"the authors describe various findings in the literature and conclude that, \"Collectively, these results indicate that whether or not hierarchical dependencies exist depends critically upon task-elicited regional interdependencies.\" It is a concern that this statement completely nullifies the significance of the study -- if the presence or absence of a hierarchy is completely task dependent. Please reconcile this with the statement you make that the \"data provide causal evidence for LPFC dynamics supporting cognitive control\".

The reviewers raise good points. We had previously attempted to keep the Discussion short, attempting to leave the theoretical heavy-lifting in our previous report and making this piece more about A) a test of the theory, and B) a method that can be used to test these and related theories. However, hierarchical cognitive control is a complex literature that may be done a disservice by cursory treatments.

The Discussion has been revised substantially in order to better elucidate the role of PFC in cognitive control. In particular, we make a stronger effort to denote the correspondences between the present data and the literature, as well as explain the discrepancies. We have also fleshed out the main idea about PFC function that we wished to convey in this domain -- that perhaps importance should shift from identifying the "top" to identifying hubs where information coalesces.

A last point that we'd like to respond to: we continue to maintain that the presence or absence of hierarchy is task dependent, and we disagree with the statement that this position nullifies the significance of the study. It is our position that the PFC can act hierarchically only insofar as the task demands it. By way of analogy, consider baseball -- the manager can exert hierarchical control over the players (e.g. determining who plays, where, and even how). Once the game is in motion, the game often dictates how much hierarchical control the manager should exert. For example, if the team is winning and the players are performing well, the manager does relatively little. In this case, control is left to the players (e.g. the pitcher and catcher determine the pitches, the shortstop orchestrates infield defensive shifts, etc.). However, if the game is tight, the manager is likely to exert more control (e.g. making pitching/batting substitutions, calling for bunts or intentional walks, etc.). It is our position that a similar situation plays out in the PFC. If a task does not call for hierarchical control, it will likely not engage hierarchical dynamics. In this case, even if a region's role includes exerting hierarchical control, such influences will not be revealed if the task is ill-suited to reveal it. This does not nullify the significance of that region in general, but only for that task. To expect that a PFC region will perform the same function for all tasks is perhaps expecting too much simplicity from an area that is defined by its very adaptability.

See the Discussion.

> 5\) Please address the issue of practice more thoroughly. Does it have any effect on the modeling and relationship to cognitive capacity results -- especially given that there were differences? A cursory examination of within-session practice effects was made but not elaborated upon. Given that the participants are participating in many, spaced sessions, the effect of session should be examined both in isolation and as a covariate. There is the potential for effects to interact with practice.

Please see our response to comment \#2.

> 6\) Please justify the use of a one-tailed test for the comparison between SFS and S1. Was there an a-priori reason for doing so? If not, this should not be included as a significant result.

As detailed, we predicted that cTBS to SFS would impair spatial processing. The appropriate test for this is to compare spatial processing with a well-matched control (i.e. verbal processing), and SFS to a well-matched control (i.e. S1). Hence, the test that was performed was a planned analysis that was a priori expected to produce the observed result. Thus, we deemed a one-tailed test appropriate. However, after taking effects of time into account (see response 2/3 above), all significant results are significant at two-tailed levels.

> In terms of the analysis of the cTBS results, please clarify why for all but Stimulus Domain analyses a subset of trials were analyzed.

For all analyses, all relevant trials were included. For the tests of Stimulus Domain, this includes all trials since on all trials, participants focus attention on either the spatial or object (letter) feature. For tests that examine Contextual Control and/or Temporal Control and/or their interactions, the relevant trials are the sub-task phase during which time those control processes are manipulated. These matters have been clarified in the text.

From the Materials and methods:

"For the analysis of *Stimulus Domain*, all trials were considered in order to maximize power. \[...\] Other analyses were restricted to trials from the sub-task phase wherein the other cognitive control demands were manipulated (e.g. *Temporal Control* was not present before and after the sub-task phase)."

> Also, with some of the TMS effects in RT, why remove long RT\'s? Was there a systematic kind of trial that was removed with this process? Does including those RTs alter the results in any way?

While outlier removal is a common practice in analysis of behavioral data, it is important to ensure that it does not bias the results in some way. To ensure that outlier removal did not systematically remove any one type of trial, outliers were identified condition-wise either by Stimulus Domain (when considering all trials), or by the crossing of Stimulus Domain x Contextual Control x Temporal Control (when considering sub-task trials). This manner of outlier correction ignores the effect of Target. However, it is possible that long RTs may systematically result from one Target or another. This did not appear to be the case as outliers were evenly distributed across Targets (all trials: FPl -- 3.6%, VLPFC -- 3.6%, SFS -- 3.5%, S1 -- 3.3%; sub-task trials: FPl -- 3.5%, VLPFC -- 4.0%, SFS -- 3.5%, S1 -- 3.8%). In 3 of the 4 planned comparisons, inclusion of these trials tends to reduce interactions with Target, be they significant or non-significant \[Target x Stimulus Domain (all trials): p = 0.269 (Corrected RT) -\> 0.479 (Uncorrected RT); Target x Stimulus Domain x Contextual Control (sub-task trials): p = 0.002 (Corrected RT) -\> 0.081 (Uncorrected RT); Target x Temporal Control (sub-task trials): p = 0.021 (Corrected RT) -\> 0.061 (Uncorrected RT); Target x Contextual Control (sub-task trials): p = 0.733 (Corrected RT) -\> 0.255 (Uncorrected RT)\]. This is to be expected if these outlier RTs add noise to the analysis.

One note: in doing this analysis, it was discovered that error trials were not removed from the RT distributions for factorial analysis of the TMS data due to a coding mistake. Error trials were correctly removed for the fMRI data and for the computation of outlier RTs (i.e. outlier RTs were calculated on correct trials only). Given the small number of error trials, this mistake had a minimal impact on the RT analyses. The manuscript now correctly reports data drawn from correct RT distributions, which have also been cleaned of outliers. This detail accounts for minor discrepancies between the original submission and the data reported in [Figure 3](#fig3){ref-type="fig"} and [Figure 3---figure supplement 1](#fig3s1){ref-type="fig"}.

> 7\) Was the entire DCM run on the new sample only or on the combined data from the current sample and the previous eLife publication? It looks like some combination of the two, which is odd especially because the initial replication DCM was performed separately on the new dataset (right?). Some clarification is warranted.

We regret that these details were not clear. The manuscript has been amended to clarify. To summarize:

i\) We estimated the winning DCM from Nee and D'Esposito, 2016 on the present sample as a way of replication.

ii\) We estimated new DCM's on the current sample to examine whether the effect of cTBS of SFS affecting Temporal Control could be accommodated by a revised DCM. The initial intention was to arrive at a best model in the current sample, and then validate this choice in the previous sample by comparing the best *n* models, where *n* would be dictated by a fall-off in model exceedance probabilities.

iii\) However, step ii did not fully converge and resulted in 19 (of 913 estimated) equally plausible DCM's. To adjudicate among these models, we returned to the previous sample which had twice the data, and could potentially offer better power to determine the best model.

iv\) The 19 DCM's mentioned in step iii were compared in the previous sample. The winning DCM from Nee and D'Esposito, 2016 was also included in this comparison. The comparison resulted in a clear winning DCM.

v\) Parameter estimates for the winning DCM from step iv is depicted with the samples combined (i.e. averaging across all participants) in [Figure 4](#fig4){ref-type="fig"}, and separately for each sample in [Figure 4---figure supplement 1](#fig4s1){ref-type="fig"}.

From the Materials and methods:

"To summarize:

i\) The winning DCM from Nee and D'Esposito, 2016 was estimated on the present dataset. \[...\] iv) Parameter estimates from the best model in iii. Were examined in both the present and previous datasets and pooled for inference."