Prior to receiving cTBS, all participants underwent an fMRI session using the task described previously (Figure 1A,B; Nee and D'Esposito, 2016) in order to localize individual targets for cTBS (Figure 1C). 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 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). 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). 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). 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). 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.

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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 Nee and D'Esposito, 2016) 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). 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). 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) and hierarchical strength in fixed connectivity (Figure 2—figure supplement 5D) 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.

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 (Nee and D'Esposito, 2016), 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. 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. 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.

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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). 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). 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), but do not provide evidence that cTBS to FPl affects Contextual Control (Figure 3F).

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.

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; Figure 2—figure supplement 3) 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 (Stephan et al., 2009) (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 for the previously described data (Figure 4—figure supplement 1A), the present data (Figure 4—figure supplement 1B), and the data considered jointly (Figure 4). 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 (Jazayeri and Afraz, 2017).

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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). 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.

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 (Rahnev et al., 2016), 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.

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 (Nee and D'Esposito, 2016). 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 (Huang et al., 2005). 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.

Analysis of the fMRI data used methods that were virtually identical to those described previously (Nee and D'Esposito, 2016). 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 (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 Huang et al. (2005). 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 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), 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.).

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). 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.

DCM was originally performed as previously described (Nee and D'Esposito, 2016). 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 (Penny et al., 2010). 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 (Nee and D'Esposito, 2016). 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 (Stephan et al., 2009) 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), 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 Nee and D'Esposito, 2016 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 Nee and D'Esposito, 2016 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.

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

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.

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.

© 2017, Nee et al.

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