Large-scale brain dynamics are organized by a directional coordination hierarchy

Abstract

The cortical hierarchy is a central organizing feature of brain structure and function, yet whether it is continuously expressed in spontaneous neural activity remains unresolved. Here, we show that resting-state brain dynamics are organized along a directional coordination axis that recapitulates hierarchical information flow. Focusing on the directional dynamics of interregional coordination, we identify three recurrent coordination regimes: a feedback-dominated mode in which transmodal cortex leads sensory systems, a feedforward-dominated mode reflecting the reverse, and an integrative mode of balanced bidirectional exchange. These modes define a low-dimensional coordination landscape that replicates across four independent cohorts, establishing directional structure as a stable property of the adult brain. In schizophrenia, this landscape is selectively reorganized: feedback-dominated coordination becomes less persistent, integrative coordination becomes more persistent, and global dynamics shift toward faster convergence and reduced entropy, reflecting a loss of directional constraint and dynamical flexibility. These alterations track symptom severity, cognitive performance, and medication exposure. Mediation analyses suggest that medication-related reductions in integrative coordination are statistically routed through feedforward dynamics, consistent with dopaminergic modulation of recurrent cortical loops as a candidate mechanism. Together, these findings identify directional functional dynamics as a fundamental and clinically informative axis of large-scale brain organization.

1. INTRODUCTION.

The cortical hierarchy is one of the most fundamental organizational principles of the mammalian brain¹. Anatomical studies have established that the cerebral cortex is structured along a feedforward-feedback axis in which ascending projections propagate sensory signals from primary areas toward higher-order association cortex, while descending projections carry top-down predictions and contextual signals in the reverse direction^1,2. This hierarchical architecture includes functional computational frameworks such as predictive coding, which formalize it as the substrate through which the brain generates expectations, computes prediction errors, and continuously reconciles internal models with incoming sensory evidence^3,4. The cortical hierarchy is, in this sense, the organizational backbone of perception, cognition, and adaptive behavior.

Yet whether the cortical hierarchy is continuously expressed as a directional organization of spontaneous brain activity remains unresolved. The past decade of resting-state neuroimaging research has established that large-scale brain dynamics are not random. The brain at rest, as measured using blood-oxygenation-level-dependent (BOLD) fMRI, transitions through recurring functional configurations, or states, that exhibit structured temporal organization, reproducible spatial topology, and sensitivity to clinical and cognitive variables^5,6. These findings have transformed our understanding of intrinsic brain activity, revealing it as a rich dynamical system rather than mere noise^7,8. Prior work has revealed traces of hierarchical organization in spontaneous dynamics, including gradients of intrinsic timescales aligned with the cortical hierarchy^9,10 and propagating waves that traverse the hierarchical axis during rest¹¹. However, these approaches capture either static regional properties or average directional tendencies across time, and do not establish whether the cortical hierarchy is persistently expressed as a dynamical axis along which spontaneous brain activity flows across hierarchical regimes over time.

Most frameworks that characterize resting-state dynamics compound this limitation: they quantify the strength of synchrony or correlation between brain regions while discarding its direction, collapsing opposite lead-lag configurations onto a scalar value, and rendering the directional geometry of coordination invisible^12–19. Directed connectivity approaches such as Granger causality and dynamic causal modeling explicitly estimate causal influences between regions^20,21. However, those frameworks rely on strong model assumptions and are typically applied to pairwise or small network interactions, producing average directed estimates rather than characterizing the emergent whole-brain coordination dynamics that organize across time in relation to the cortical hierarchy.

Here we address this gap directly. By preserving the signed lead-lag geometry of interregional phase relationships that conventional approaches discard^{13,14,22–24}, we demonstrate that spontaneous brain activity is organized along a directional coordination hierarchy comprising three recurring regimes: a feedback-dominated mode in which transmodal association cortex systematically leads sensory systems, a feedforward-dominated mode reflecting the reverse hierarchical organization, and an integrative mode of balanced bidirectional exchange. These regimes define a low-dimensional coordination landscape that is robustly reproducible across four independent cohorts spanning diverse acquisition protocols, scanner sites, and populations of the adult brain, establishing directional coordination structure as a stable organizational property of large-scale brain dynamics rather than a dataset-specific artifact.

We then show that this landscape is selectively disrupted in schizophrenia, a disorder long theorized to involve the breakdown of the cortical hierarchy^15,25. Within this landscape, where basin depth captures the persistence of each coordination regime, the feedback basin becomes shallower while the integrative basin becomes deeper, reflecting an erosion of top-down directional constraint rather than a uniform collapse of coordination structure. Global dynamical properties, including spectral gap, mixing time, and entropy rate, shift in ways that signal a loss of dynamical flexibility and reduced temporal diversity of hierarchical trajectories. These alterations track positive symptom severity, cognitive performance, and antipsychotic medication exposure. Mediation analyses further reveal that pharmacological effects on integrative coordination are statistically fully mediated through feedforward dynamics, providing a directional coordination-level account of how dopaminergic modulation interfaces with large-scale brain dynamics.

Together, these findings reframe a fundamental question in systems neuroscience. The cortical hierarchy has been studied extensively as an anatomical and task-evoked phenomenon. We show that it is also a property of spontaneous brain dynamics, continuously expressed as a directional coordination axis that shapes how the brain traverses its state space at rest, and that disruption of this axis constitutes a defining dynamical signature of psychiatric illness. By treating direction as the signal rather than noise, we open a new dimension for understanding large-scale brain organization, one that bridges the gap between the brain’s hierarchical anatomy, its intrinsic dynamics, and its clinical pathology.

2. RESULTS

2.1. Directional phase information reveals a coordination structure missed by conventional measures

To characterize directional coordination in spontaneous brain activity, we developed a complex-valued phase synchrony (CVPS) framework that preserves the signed lead-lag geometry of interregional phase relationships. Conventional measures of resting-state coordination collapse opposite lead-lag configurations onto the same scalar value, rendering this directional geometry invisible. Simulations confirm that two phase-locked configurations differing only in lag sign (+60° versus −60°) are indistinguishable using cosine-based metrics (two-sample t-test, p = 0.74) but clearly separable when the full phase angle is preserved (Watson’s U², p ≅ 0; Fig. 1a). These distinctions are not merely technical. In empirical fMRI data, the cosine of relative phase (CRP) reflects only alignment strength, whereas the sine component captures systematic lead-lag relationships preserved by CVPS (Fig. 1b). At the edge level, CVPS reveals a robust control-schizophrenia difference in the precuneus-thalamus connection that is entirely missed by CRP (CVPS: p = 3.10 × 10; CRP: p = 0.78; Fig. 1c), demonstrating that meaningful group differences can reside purely in directional timing structure. Conversely, CRP detects a hippocampus-parietal difference that disappears when directional information is retained (CRP: p = 6.36 × 10³; CVPS: p = 0.18; Fig. 1d), indicating that cosine-only measures can also produce effects unsupported once phase directionality is considered. This directional sensitivity rests on accurate phase estimation under non-stationary BOLD-like conditions. We find that Gabor wavelet phase tracking yields significantly lower error than the more commonly used Hilbert-based estimation across signal-to-noise levels (Fig. 1e; paired test, p < 0.001). Together, these results show that brain functional relevance in coordination can carry directional information invisible to conventional measures, establishing direction as a core dimension of resting-state brain organization.

Fig. 1: Directional phase estimation reveals information lost by conventional approaches.

(a) Directional ambiguity in cosine-based metrics. Two synthetic groups with mean phase offsets of +60° and −60° are indistinguishable using the cosine of phase difference (two-sample t, p = 0.74), but are clearly separable using full circular phase (Watson’s U², p = 0). (b) Population-level phase organization. Left: average complex-valued phase synchrony (CVPS) across the fBIRN cohort. Right: corresponding cosine (CRP) and sine (SRP) components of relative phase. The sine component, which encodes directional (lead–lag) relationships, is absent in CRP. (c) Empirical example (precuneus–thalamus): CRP shows no group difference (controls vs schizophrenia; p = 0.78), whereas CVPS reveals a significant separation (Watson’s test, p = 3.10 × 10⁻⁵). (d) Empirical example (hippocampus–superior parietal lobule): CRP indicates a difference (p = 6.36 × 10⁻³), but CVPS does not (p = 0.18), illustrating that cosine-only metrics can flag differences driven by magnitude while obscuring directional alignment. Together, these results establish that preserving directional phase information is critical for accurately characterizing interregional coordination. (e) Simulated non-stationary signal with slowly varying frequency (0.035–0.065 Hz; SNR = 10 dB). Left: time–frequency representation illustrating frequency modulation. Middle: phase tracking shows that the Gabor wavelet estimate closely follows the ground-truth trajectory, whereas the Hilbert transform deviates under nonstationarity. Right: RMSE across SNR levels (log scale) confirms improved accuracy of the Gabor approach (paired test; ***p<0.001). confirming that the Gabor wavelet tracks nonstationary phase more accurately than the Hilbert transform under BOLD-like conditions.

2.2. Spontaneous brain activity flows along a directional coordination hierarchy comprising three recurring regimes

Applying CVPS to whole-brain resting-state activity, we found that directional coordination was not randomly distributed across coordination space but was constrained to evolve along a structured axis with three identifiable and reproducible modes. These three dominant regimes emerged consistently across subjects: a feedback-dominated regime, a feedforward-dominated regime, and an integrative regime of balanced bidirectional exchange. Each regime was characterized by a distinct configuration of phase offsets across canonical functional systems (Fig. 2a–c), with coherent directional relationships specifying which systems lead and which lag. To quantify the dominant direction of coordination flow within each regime, we computed a directional hierarchy index (DHI), which summarizes the net lead-lag relationship between transmodal association cortex and sensory systems. Positive values indicate top-down flow, negative values indicate bottom-up flow, and values near zero indicate balanced bidirectional exchange.

Fig. 2: Directional coordination reveals structured large-scale brain states.

(a–c) Three dominant directional coordination states were identified from complex-valued phase synchrony (CVPS). Left: phase state matrices showing pairwise phase offsets across canonical functional domains (sensory, association, control, and subcortical systems). Right: cortical projections of relative driver scores (lead vs lag), with red indicating leading regions and blue indicating lagging regions. (a) Feedback state: association regions lead sensory systems (positive directional hierarchy index; DHI = +2.024, p = 4.0 × 10), consistent with topdown feedback organization. (b) Feedforward state: sensory regions lead association systems (negative DHI; DHI = −3.103, p ~ 0), reflecting bottom-up propagation. (c) Integrative state: distributed and balanced phase-leading across domains, with no dominant hierarchy (DHI ~ 0, n.s.), indicating coordinated integration rather than directed flow. These states define a low-dimensional directional coordination structure that captures recurring modes of information flow across large-scale brain systems. (d) Cross-dataset replication of directional coordination states. Pairwise complex correlation matrices quantify centroid similarity across independent cohorts (fBIRN, COBRE, HCP Aging S1–S4, HCP Adult) for each coordination state. Mean cross-dataset similarity was 0.91 for the feedforward and integrative states and 0.78 for the feedback state, demonstrating that all three directional coordination regimes are robustly reproducible across cohorts spanning different acquisition protocols, scanner sites, and populations. (e) State correspondence exceeds chance across all replication cohorts. For each external dataset, the optimal one-to-one state mapping to fBIRN was compared against all possible permutations. Z-scores range from 1.16 to 1.67 across cohorts, confirming that cross-dataset state alignment is systematically stronger than any alternative assignment and establishing the directional coordination hierarchy as a stable organizational property of large-scale brain dynamics.

The first identified regime is feedback-dominated: association regions systematically lead sensory systems (Fig. 2a). This pattern is reflected in a positive directional hierarchy index (DHI = +2.024, p = 4.0 × 10 ), indicating a top-down organization consistent with feedback processing. Spatially, this regime is characterized by leading activity in transmodal cortical areas and lagging responses in sensory regions, suggesting coordinated propagation from higher-order to lower-order systems. In contrast, the feedforward-dominated regime exhibits the opposite organization, with sensory regions leading association systems (Fig. 2b). This configuration yielded a strongly negative DHI (DHI = −3.103, p ≈ 0), indicating a bottom-up propagation pattern. Here, early sensory systems precede subsequent activity in higher-order regions, reflecting a reversal of the hierarchical flow observed in the feedback state.

Finally, we identified an integrative regime, characterized by distributed and balanced phase-leading across systems (Fig. 2c). In this regime, no single domain consistently leads, resulting in a relatively near-zero directional hierarchy index (DHI = 0.92, n.s.), indicating the absence of a dominant directional gradient. Rather than reflecting unidirectional propagation, this state is consistent with coordinated bidirectional exchange across domains, suggesting a regime of mutual interaction. This configuration is consistent with theoretical accounts of cortical processing as recurrent interaction between feedforward and feedback pathways, sustaining continuous bidirectional exchange of information⁴.

These three regimes generalized across independent cohorts spanning different acquisition protocols, scanner sites, and populations, including the Center for Biomedical Research Excellence (COBRE)²⁶, four sessions of the Human Connectome Project Aging (HCP Aging)²⁷, and the Human Connectome Project Adult (HCP Adult)²⁸. Cross-dataset complex correlation between regime representations revealed mean cross-dataset similarity of 0.91 for both the feedforward and integrative regimes and 0.78 for the feedback regime (Fig. 2d). For each replication cohort, the one-to-one regime correspondence to our discovery dataset, the Function Biomedical Informatics Research Network (fBIRN)²⁹, consistently exceeded the permutation baseline, with z-scores ranging from 1.16 to 1.67 across datasets (Fig. 2e).

These results demonstrate that spontaneous brain activity is organized into a small number of recurring regimes fundamentally defined by directional structure, forming a low-dimensional representation of large-scale brain dynamics consisting of feedback, feedforward, and integrative modes of coordination. Critically, this organization is not a dataset-specific phenomenon but a stable and reproducible property of the adult brain, replicable across cohorts that differ in acquisition, site, and population.

2.3. Directional coordination defines a continuous persistence landscape disrupted in schizophrenia

Directional coordination is not only structured into discrete regimes but also organized along a continuous dynamical landscape that reflects their relative stability. To capture this, we constructed a persistence landscape integrating each regime’s intrinsic self-persistence with its long-run equilibrium weighting, derived from the Markovian structure of state transitions. Projection of the three coordination regimes into a low-dimensional simplex revealed a smooth topology with distinct basins corresponding to feedback, feedforward, and integrative modes (Fig. 3a). Basin depth indexed dynamical stability, with deeper regions corresponding to regimes with greater equilibrium weighting and stronger self-persistence. The landscape exhibited well-separated basins, indicating that large-scale brain coordination evolves within a constrained dynamical structure defined by a small number of stable regimes.

Fig. 3: Directional coordination organizes a persistence landscape disrupted in schizophrenia.

(a) State persistence landscape of directional coordination. Low-dimensional projection of coordination dynamics reveals a structured landscape with distinct regions corresponding to feedback, feedforward, and integrative modes. Surface height reflects persistence (state stability), with deeper basins indicating more stable and preferentially occupied coordination regimes. Controls are shown as a smooth manifold (plane), with schizophrenia overlaid as a mesh. The landscape exhibits separable basins associated with recurrent modes of large-scale coordination. (b) Group differences in persistence landscape (controls - schizophrenia). Controls show increased persistence in the feedback regime and reduced persistence in the integrative regime, whereas schizophrenia exhibits a shift toward deeper integrative basins (*** p < 0.001 ). These results indicate that directional coordination is organized along a continuous persistence landscape, with schizophrenia characterized by a redistribution of stability across coordination modes.

This structure was systematically altered in schizophrenia, manifesting as a redistribution of stability across regimes. Relative to controls, patients exhibited a pronounced deepening of the integrative basin alongside a flattening of the feedback basin (Fig. 3a–b). Quantitatively, controls showed significantly greater stability in the feedback regime, whereas schizophrenia was characterized by increased stability in the integrative regime (p < 0.001), with comparatively modest differences in the feedforward regime. These findings indicate a selective reorganization rather than a uniform disruption.

Together, these results show that directional coordination is not only partitioned into discrete regimes but also governed by an underlying dynamical structure that shapes their stability and accessibility. Schizophrenia is marked by a shift toward strong affinity towards integrative, bidirectional coordination at the expense of structured feedback-dominated dynamics, suggesting an altered balance between directionally structured and bidirectionally integrative modes of large-scale brain function.

2.4. Altered directional coordination dynamics in schizophrenia

Directional coordination dynamics exhibited systematic alterations in schizophrenia across multiple complementary metrics of state stability, occupancy, and transition structure (Fig. 4a–g). At the level of temporal persistence, patients showed a marked redistribution of dwell times, with reduced mean dwell time (MDT) in the feedback regime and increased dwell time in the integrative regime relative to controls (Fig. 4a). A similar pattern was observed for fraction rate (FR), indicating that schizophrenia is characterized by reduced engagement of feedback-dominated dynamics and increased overall occupancy of integrative coordination (Fig. 4b). These shifts were further reflected in the stationary distribution, with patients exhibiting a higher long-run probability of residing in the integrative regime and reduced weighting of feedback regimes (Fig. 4d).

Fig. 4: Directional coordination dynamics are altered in schizophrenia and relate to cognitive and clinical function.

(a–g) Group contrasts (controls vs schizophrenia) from GLMs controlling for age, sex, scanner site, and head motion (FDR-corrected). (a) Mean dwell time (MDT) by state. (b) Fraction rate (FR; overall occupancy) by state. (c) Transition probabilities. (d) Stationary distribution (long-run state proportions). (e) Spectral gap (rate of convergence to stationarity). (f) Mixing time (steps to within tolerance of stationarity). (g) Entropy rate (average unpredictability of the next state). Asterisks indicate FDR-corrected significance (* p < 0.05, ** p < 0.01, *** p < 0.001 ). FB = feedback, FF = feedforward, INT = integrative. (h) Within-group associations from GLMs (FDR-corrected) linking coordination dynamics (MDT, FR, transitions, stationary distribution, spectral gap, mixing time, entropy rate) to cognitive and clinical measures (CMINDS domains, CPZ dose, PANSS positive/negative), controlling for the same covariates (CPZ associations included symptom scores in covariates). Coefficients are sign-coded; asterisks indicate FDR-significant effects. Collectively, these results indicate a reorganization of coordination dynamics, with systematic shifts toward increased integrative engagement and altered transition structure in schizophrenia, and clear links to symptom severity, medication exposure, and cognitive performance.

Beyond state occupancy, the transition structure revealed a reorganization of how coordination evolves over time. Transition probabilities indicated altered flow between regimes in patients, with reduced transitions supporting feedback- and feedforward-dominated dynamics and increased transitions favoring integrative coordination (Fig. 4c). Consistent with this redistribution, global dynamical properties of the Markov system were also significantly altered. Schizophrenia was associated with an increased spectral gap and shorter mixing time, indicating faster convergence to the stationary distribution, alongside a reduced entropy rate, reflecting a shift toward more constrained and less diverse temporal trajectories (Fig. 4e–g).

This demonstrates that schizophrenia is characterized not simply by altered occupancy of specific coordination states, but by a broader reorganization of directional coordination dynamics spanning persistence, long-run equilibrium structure, and transition behavior. This pattern reflects a systematic shift away from structured feedback- and feedforward-dominated coordination toward increased stabilization of integrative, bidirectional dynamics, accompanied by reduced temporal flexibility and dynamical diversity.

2.5. Directional coordination dynamics track cognitive performance, symptom severity, and medication exposure

Directional coordination dynamics tracked cognitive performance, symptom severity, and medication exposure (Fig. 4h), indicating that the observed dynamical reorganization is behaviorally, clinically, and pharmacologically relevant.

Cognitive performance exhibited distinct and group-specific relationships with coordination dynamics. In healthy controls, increased transitions from feedback to integrative regimes were associated with lower attention vigilance and composite cognitive scores, indicating that excessive departure from directed coordination may be detrimental to performance. Faster convergence to dynamical stability, reflected by higher spectral gap and shorter mixing time, was associated with improved verbal learning, suggesting that efficient stabilization of coordination supports specific cognitive functions. In schizophrenia, these relationships were disrupted. The same pattern of faster convergence (higher spectral gap and shorter mixing time) was instead associated with worse attention vigilance and composite cognitive scores. These findings indicate that the normative relationship between coordination dynamics and cognition is altered in schizophrenia, reflecting a reorganization of how dynamical stability and state transitions support cognitive function.

Directional coordination also revealed associations with clinical symptoms and pharmacological modulation in schizophrenia. Positive symptom severity was linked not to persistence within the integrative regime, but to transition structure. Greater transitions into the integrative regime were associated with lower positive symptoms, whereas transitions away from it toward the feedforward regime were associated with higher positive symptoms. This pattern suggests that access to integrative coordination may be relatively adaptive, while failure to sustain it, reflected in transitions toward feedforward-dominated dynamics, may index maladaptive hierarchical instability. Medication exposure further modulated coordination dynamics, with chlorpromazine (CPZ) dose showing significant associations with state persistence. Higher CPZ dose was linked to increased dwell time in the feedforward regime after controlling for symptom severity, indicating that pharmacological effects are reflected in the temporal organization of coordination dynamics.

Together, these results demonstrate that directional coordination dynamics are tightly linked to clinical and cognitive variability, capturing meaningful individual differences in symptom expression, cognitive performance, and treatment exposure. This establishes coordination dynamics as a functionally relevant axis of brain organization with direct relevance to neuropsychiatric dysfunction.

2.6. Antipsychotic effects on integrative coordination are mediated through feedforward dynamics

Pharmacological effects on directional coordination were expressed through a specific dynamical pathway. Mediation analysis revealed a significant indirect pathway linking CPZ-equivalent dose to reduced integrative regime engagement through feedforward dynamics (Fig. 5a). CPZ dose was associated with increased feedforward engagement (path a, p = 8.33 × 10⁻³), which in turn predicted reduced integrative engagement (path b, p = 2.48 × 10⁻⁶ for FR; p = 8.75 × 10⁻³ for MDT). The indirect effect was significant for both FR and MDT, whereas the direct effect was not significant, consistent with full mediation within the tested statistical model. In contrast, no significant mediation was observed for feedback regime engagement (Fig. 5b), indicating that CPZ effects are selectively expressed along a feedforward-to-integrative pathway. This selectivity suggests that CPZ-related modulation of directional coordination is preferentially expressed along the feedforward-to-integrative pathway, rather than through feedback dynamics, pointing to dopaminergic modulation of recurrent cortical loops as a candidate mechanism.

Fig. 5: Coordination dynamics mediate associations between medication and state engagement.

(a) Mediation analysis linking CPZ-equivalent dose to integrative state engagement through feedforward-state dynamics. CPZ dose was significantly associated with feedforward-state metrics (path a), which in turn were significantly associated with reduced integrative engagement (path b). The indirect effect (path ab) was significant for both fraction rate (FR) and mean dwell time (MDT), while the direct effect (path c) was not significant, indicating a fully mediated association within the tested statistical model. These results demonstrate that pharmacological effects on integrative coordination are expressed indirectly through modulation of feedforwardstate dynamics. (b) Mediation analysis linking CPZ-equivalent dose to feedback state engagement revealed no significant mediation, as the indirect effect (path ab) was not significant. This indicates that CPZ-related effects are specifically routed through feedforward dynamics and selectively impact integrative engagement rather than feedback coordination. Together, these findings suggest that CPZ selectively reduces integrative engagement indirectly by increasing engagement in the feedforward directional regime.

3. DISCUSSION

We establish that spontaneous brain activity is not merely organized into recurring functional states^5,6, but is constrained to evolve along a directional coordination axis that reflects systematic patterns of hierarchical information flow across cortical systems. Using complex-valued phase synchrony, which preserves the signed lead-lag geometry of interregional phase relationships discarded by conventional approaches^12–14, we identify three directional coordination modes: a feedback-dominated regime in which transmodal association cortex systematically leads sensory systems, a feedforward-dominated regime reflecting the opposite hierarchical organization, and an integrative regime of balanced bidirectional exchange. These modes define a low-dimensional coordination landscape that is stable and consistent across independent cohorts spanning diverse acquisition protocols, scanner sites, and populations, replicating across fBIRN²⁹, COBRE²⁶, HCP Aging²⁷, and HCP Adult²⁸ datasets, establishing it as a robust organizational property of the adult brain.

Anatomical and computational studies have long established that the cortex is organized into a feedforward-feedback hierarchy in which ascending connections propagate signals from sensory areas toward higher-order association areas, while descending connections carry top-down projections back, forming the structural basis of hierarchical cortical processing². Computational accounts of predictive coding have formalized this anatomy into a functional framework in which feedforward pathways carry precision-weighted prediction errors upward and feedback pathways carry top-down predictions downward to constrain lower-level representations^3,4. The feedback-dominated regime we identify, in which transmodal association cortex leads sensory systems (Fig. 2a: DHI = +2.024, p = 4.0 × 10⁻⁵), directly reflects this top-down propagation pattern, while the feedforward-dominated regime, in which the directional flow reverses with sensory cortex leading association areas (Fig. 2b: DHI = −3.103, p ≈ 0), reflects the ascending transmission of bottom-up signals. Critically, these modes emerge spontaneously at rest, in the absence of external task demands. This observation extends the predictive coding framework beyond its traditional domain as a theory of task-evoked perceptual processing toward a description of the brain’s intrinsic dynamical organization^30,31. This suggests that the cortical hierarchy is not merely recruited in response to sensory inputs but constitutes a persistent structural axis along which spontaneous neural activity is continuously organized.

The integrative mode, characterized by a non-significant directional hierarchy (Fig. 2c) and balanced phase-leading across systems, represents a qualitatively distinct regime of recurrent bidirectional exchange in which feedforward and feedback interactions coexist without one systematically dominating the other, consistent with theoretical accounts of how the brain sustains flexible integration of information across distributed systems through simultaneous top-down and bottom-up communication³². Notably, the integrative regime was the most frequently occupied across all subjects, accounting for the largest share of resting-state dwell time. This dominance is expected in the context of resting-state fMRI, without external sensory demands or goal-directed constraints to impose a directional hierarchy. The brain thus defaults to this balanced mode of mutual exchange, consistent with the foundational observation that unconstrained rest is characterized by organized, internally directed activity rather than passive waiting^7,8. The predominance of the integrative regime at rest therefore reflects not a failure to establish directional coordination, but the brain’s natural operating condition when released from the constraints that would otherwise bias it toward feedforward or feedback dominance.

Schizophrenia has long been characterized as a disorder of hierarchical dysconnectivity, in which aberrant modulation of synaptic efficacy disrupts the precision-weighting of prediction errors propagated through the cortical hierarchy, destabilizing the top-down feedback signals that normally constrain lower-level sensory representations^15,25. Consistent with the disconnection hypothesis, empirical neuroimaging studies have demonstrated that schizophrenia is marked by transient states of disrupted functional integration and altered dwell-time distributions across coordination states¹⁶. Furthermore, converging evidence from dynamic functional connectivity analyses has confirmed that such temporal redistribution of brain state occupancy is a reliable feature of the disorder^5,6. The coordination landscape reorganization we observe provides a dynamical systems-level characterization of precisely this failure (Fig. 3). The selective flattening of the feedback basin and deepening of the integrative basin in schizophrenia (Fig. 3b: p < 0.001) does not reflect a uniform collapse of coordination structure. Instead, it indicates a specific loss of directional constraint. Patients spend less time in the feedback-dominated regime, where the transmodal cortex systematically leads sensory systems, and more time in the integrative regime, where no directional gradient dominates. This is not simply a passive redistribution of dwell time across states, given that the feedforward basin is comparatively preserved. Critically, the deepening of the integrative basin is not merely a passive consequence of feedback erosion but reflects an independent pathological stabilization of bidirectional coordination, consistent with prior evidence that schizophrenia is associated with a collapse of the hierarchical distance between sensory and association systems and a reduction in the diversity of directed functional interactions^33,34. Furthermore, the feedback erosion indicates that the disruption targets top-down hierarchical propagation specifically. The mechanistic implication is direct: if feedback-dominated dynamics reflect the brain’s capacity to impose top-down predictions on lower-level representations, then the erosion of this regime in schizophrenia constitutes a breakdown in hierarchical control, consistent with proposals that psychotic symptoms arise when top-down predictions lose their capacity to contextualize and suppress aberrant bottom-up signals^35–38.

This reorganization of the coordination structure is further reflected in the global dynamical properties of the system. Schizophrenia was associated with an increased spectral gap and shorter mixing time (Fig. 4e–f), indicating that patients’ coordination dynamics converge to their stationary distribution faster than those of healthy controls.

In Markov chain theory, the spectral gap quantifies the rate at which a system relaxes from any initial configuration toward its long-run equilibrium, with larger values indicating faster convergence and, critically, reduced ability to sustain transient excursions away from that equilibrium^39,40. A larger spectral gap and consequently shorter mixing time, therefore, does not reflect greater efficiency but rather a reduction in the system’s capacity to explore its dynamical repertoire, consistent with prior evidence that schizophrenia is characterized by markedly reduced dynamism of time-varying brain connectivity, with patients switching less often between coordination states and exploring a more restricted region of the available state space^41,42. This premature convergence is the dynamical signature of a system that has lost its dynamical flexibility: rather than persisting in structured, directionally organized regimes long enough to support hierarchical information transmission, the coordination dynamics collapse rapidly toward the integrative attractor, bypassing the feedback and feedforward regimes that constitute the functional architecture of the cortical hierarchy. The reduced entropy rate compounds this picture (Fig. 4g). Entropy rate measures the average uncertainty or unpredictability of a system’s trajectory over time, with higher values reflecting greater diversity of temporal sequences and lower values reflecting more stereotyped, constrained dynamics^39,40. The observation that patients exhibit a lower entropy rate than controls means that their coordination trajectories are not only convergent but informationally impoverished: the sequences of states they traverse are more predictable, less varied, and carry less information about the brain’s moment-to-moment hierarchical organization. Taken together, the increased spectral gap, shorter mixing time, and reduced entropy rate constitute a coherent dynamical signature of a system that has lost the temporal flexibility required to sustain structured hierarchical coordination, collapsing instead into a low-diversity, rapidly equilibrating regime dominated by undifferentiated integration. This pattern extends and deepens what has been observed in prior dynamic connectivity studies of schizophrenia^16,41,42 by showing that the loss of dynamical diversity in this disorder is not merely a connectivity phenomenon but a failure at the level of directional coordination structure itself.

Directional coordination dynamics showed meaningful associations with cognitive performance, clinical symptoms, and pharmacological exposure, demonstrating that the reorganization observed at the level of coordination structure has direct behavioral and clinical relevance. In healthy controls, the relationship between coordination dynamics and cognition followed a normative pattern: increased transitions from feedback toward integrative regimes were associated with lower attention vigilance and composite cognitive scores, indicating that excessive departure from directed hierarchical coordination is detrimental to performance. This is consistent with evidence that the quality of directed information flow at rest predicts cognitive ability in healthy adults⁴³. Faster convergence to dynamical stability, indexed by higher spectral gap and shorter mixing time, was associated with improved verbal learning in controls, suggesting that efficient stabilization of coordination supports the cognitive processes underlying new learning. In schizophrenia, these relationships were inverted. Faster convergence to stability was instead associated with worse attention vigilance and composite cognitive performance, indicating that the normative coupling between coordination dynamics and cognition is not merely weakened but qualitatively reorganized in the disorder. This is consistent with a growing body of evidence demonstrating that schizophrenia is characterized by reduced dynamical flexibility of large-scale brain networks, and that this reduction in the brain’s capacity to reconfigure across states underlies cognitive impairments in the disorder^44,45. At the level of clinical symptoms, positive symptom severity was linked to transition structure. Greater transitions into the integrative regime were associated with lower positive symptoms, while increased transitions toward the feedforward regime were associated with higher positive symptoms. This pattern suggests that the capacity to access and sustain integrative coordination may be relatively adaptive, whereas failure to maintain it, reflected in transitions toward feedforward-dominated dynamics, indexes a form of maladaptive hierarchical instability. This is also reflected in proposals that positive symptoms arise from failures of top-down prediction to contextualize ascending signals, such that increased feedforward engagement without the counterbalancing influence of integrative exchange amplifies the conditions for aberrant salience and failed prediction error signaling^35,36. Finally, a higher CPZ-equivalent dose was associated with increased dwell time in the feedforward regime after controlling for symptom severity, establishing that pharmacological modulation is directly reflected in the temporal organization of directional coordination dynamics. Together, these results demonstrate that the directional coordination axis identified here is not merely a descriptive feature of large-scale brain dynamics but a functionally and clinically relevant dimension of brain organization that tracks cognitive variability, symptom expression, and treatment exposure across the schizophrenia continuum.

The mediation analysis identifying a feedforward-specific pathway through which CPZ dose reduces integrative engagement provides a mechanistic window into how antipsychotic pharmacology shapes directional coordination dynamics (Fig. 5a). Chlorpromazine exerts its primary antipsychotic effect through postsynaptic blockade of dopamine D2 receptors, with additional affinity for D1 receptors that distinguishes it from higher-potency typical antipsychotics^46,47. Dopaminergic signaling, particularly via D1 receptors, is known to facilitate sustained recurrent activity in prefrontal cortical networks by deepening the basins of attraction of high-activity states and stabilizing persistent neural representations against interference and noise^48,49. This recurrent, self-sustaining cortical activity is the neural substrate of the integrative coordination regime we identify, in which feedforward and feedback exchanges coexist in balanced bidirectional exchange without directional dominance. One interpretation is that medication-related shifts in directional coordination may reflect altered engagement of recurrent cortical loops, consistent with known dopaminergic effects on prefrontal circuit stability. The specificity of the mediation pathway is mechanistically informative: the CPZ effect on integrative engagement is fully mediated through feedforward dynamics and not through feedback dynamics (Fig. 5a–b). This selectivity indicates that antipsychotic D2 blockade does not simply suppress coordination broadly but disrupts the feedforward-to-integrative transition specifically, consistent with proposals that dopamine modulates the balance between input-driven feedforward processing and internally sustained recurrent activity in prefrontal circuits⁴⁹. The finding that CPZ effects are expressed through this specific dynamical pathway, rather than through a global reduction in coordination engagement, provides a directional coordination-level account of how antipsychotic pharmacology interfaces with large-scale brain dynamics, and points toward coordination structure as a candidate substrate for pharmacological response variability in schizophrenia.

The present findings establish directional coordination structure as a stable, reproducible, and clinically relevant dimension of large-scale brain dynamics, with results converging across independent cohorts and multiple levels of analysis. Several directions remain open for future investigation. The current framework characterizes directional coordination at the timescale of hemodynamic responses, which reflects the slow envelope of neural dynamics rather than the millisecond-precision signaling that underlies hierarchical cortical transmission⁵⁰. Future work combining CVPS with electrophysiological methods such as EEG or MEG would allow the coordination hierarchy to be examined at finer temporal scales and linked to oscillatory signatures of feedforward and feedback processing, including gamma-band feedforward and alpha/beta-band feedback dynamics⁵¹. The cross-sectional design, while sufficient to characterize the structure and clinical correlates of the coordination landscape, does not resolve whether the feedback erosion and integrative stabilization observed in schizophrenia precede symptom onset or reflect stable trait-level features of the disorder. Longitudinal designs tracking coordination dynamics from clinical high-risk states through first episode and chronic illness would substantially deepen the mechanistic account offered here. Whether analogous reorganizations of the coordination landscape characterize other conditions involving altered hierarchical dynamics, including bipolar disorder, autism spectrum disorder, and major depression, represents a natural extension of the present work.

Large-scale brain dynamics have long been characterized through the lens of what states the brain occupies and how often. The present work proposes a complementary and deeper question: not merely which states recur, but in which direction the brain moves between them, and what that directionality reveals about the hierarchical organization of neural information flow. By preserving the signed geometry of interregional phase relationships that conventional measures discard, we uncover a low-dimensional coordination axis along which spontaneous brain activity is continuously organized, one that is robust and reproducible across independent cohorts, acquisition protocols, and populations, establishing it as a stable property of the adult brain rather than an artifact of any single dataset or acquisition approach. This axis is a reflection of the cortical hierarchy itself, manifesting as three distinct dynamical regimes whose relative occupancy, transition structure, and dynamic convergence properties convey information about cognitive capacity, symptom expression, pharmacological exposure, and the breakdown of hierarchical control in schizophrenia. The implication is that the brain’s moment-to-moment trajectory through coordination space, and not simply its connectivity profile, constitutes a fundamental dimension of neural organization. Prior frameworks have treated direction as noise to be averaged away. We treat it as the signal. In doing so, we open a new axis for understanding how the healthy adult brain sustains hierarchical information transmission, how psychiatric illness disrupts it, and how pharmacological intervention reshapes it, suggesting that the directional structure of large-scale coordination is as informative for understanding brain function and dysfunction as the states themselves.

4. METHODS

4.1. Complex-valued phase synchrony for directional coordination

To quantify directional coordination between brain regions, we develop the complex-valued phase synchrony, which estimates instantaneous phase using a time–frequency localized complex Gabor wavelet. This approach preserves both magnitude and signed lead–lag relationships, enabling analysis of directional coordination dynamics. The CVPS can be understood within the dynamic co-modulation (DyCoM) framework, which expresses time-varying interactions through a small set of fundamental signal processing operations⁵². Here, we propose a phase-based instantiation in which the DyCoM representation operator is defined by a Gabor wavelet transform, and the DyCoM interaction/energy operator is captured through complex phase differences, without any instantiation of the DyCoM temporal or normalization operators.

Let x(t) be the BOLD time-series at one region, sampled at the repetition time (TR) Δt. The Instantaneous phase φ(t) is estimated by convolving x(t) with a complex Gabor wavelet that is both frequency and time localized:

$$g(t)=e^{\left(j2\pi f_{0}t\right)}{e}^{\left(-\frac{t^2}{2{\sigma }_t^2}\right)},{\sigma }_t=\frac{1}{2\pi f_{bw}},$$ (1)

where f₀ is the center frequency, and f_bw is the half-bandwidth (Hz).

To reduce computation while retaining 99.7% of the Gaussian energy, the kernel is truncated to $\in \left[-3{\sigma }_t,+3{\sigma }_t\right]$⁵³, sampled on the TR grid (t = kΔt, k ∈ ℤ). The analytic signal is

$$z\left(t\right)=\left(x\mathrm{*}g\right)\left(t\right)=\sum _{k}x\left(k\mathrm{\Delta }t\right)g(t-k\mathrm{\Delta }t)\mathrm{\Delta }t$$ (2)

with g(t) normalized to unit energy to avoid edge bias. The instantaneous phase and amplitude follow as:

$$\phi \left(t\right)=\mathrm{a}\mathrm{r}\mathrm{g}\left[z\right(t\left)\right],A\left(t\right)=\left|z\right(t\left)\right|$$ (3)

Although the wavelet itself is frequency-localized, we chose a central frequency f₀ = 0.05Hz and half-bandwidth f_bw = 0.02Hz to match the conventional [0.03 – 0.07]Hz range used in phase synchrony studies, thereby isolating physiologically meaningful BOLD fluctuations while allowing direct methodological comparison^12,13,54,55. Relative to a Hilbert band-pass pipeline, the adaptive Gabor kernel affords sharper time–frequency localization for the non-stationary BOLD spectrum while preserving the full complex phase necessary for subsequent synchrony analysis⁵⁶.

For two time series x(t) and y(t), we define the asymmetric complex phase synchrony signal as:

$$\begin{gathered} \mathrm{\Delta }{\phi }_{x\to y}(t)=e^{j\left({\phi }_x\left(t\right)-{\phi }_y(t)\right)}, \\ \mathrm{\Delta }{\phi }_{y\to x}(t)=e^{j\left({\phi }_y\left(t\right)-{\phi }_x\left(t\right)\right)} \end{gathered}$$ (4)

which retains both synchrony strength and signed lead–lag information. Unlike conventional approaches that define coordination states by synchrony magnitude and discard phase directionality, CVPS embeds lead-lag geometry directly into the state definition, preserving the full circular structure of phase relationships. This enables the construction of a persistence landscape that reveals the hierarchical attractor organization of coordination dynamics rather than simply cataloguing state occupancy.

4.2. Simulation studies

4.2.1. Validating phase estimation accuracy under non-stationary BOLD conditions

To evaluate phase estimation under non-stationary conditions, we simulated frequency-modulated signals with BOLD-like spectral characteristics and noise levels (1000 samples, 600 s). Instantaneous phase was estimated using both Hilbert-based and Gabor wavelet approaches, and accuracy was quantified relative to the known ground-truth phase trajectory using root mean square error (full details in Supplementary material).

4.2.2. Assessing the necessity of full phase geometry for directional characterization

To assess the importance of preserving directional phase information, we generated phase-coupled sinusoidal signals with controlled phase offsets (+60° and −60°) and added variability. Synchrony was quantified using both cosine-based measures and complex phase representations, and group differences were evaluated using standard and circular statistical tests.

We further illustrate that preserving the full angle of phase synchrony is relevant in the fMRI data; we analyze two pairs of brain networks extracted using the NeuroMark independent component analysis (ICA) pipeline. The mean CVPS is computed across the temporal sequence for each brain region and subject.

4.3. fMRI data & processing

We analyzed resting-state fMRI from the Phase III of Function Biomedical Informatics Research Network (fBIRN) consortium²⁹. Data were acquired with a repetition time of 2 s and comprised 160 healthy controls (37.0 ± 10.9 yr, 45 F/115 M) and 151 individuals with schizophrenia (38.8 ± 11.6 yr, 36 F/115 M). Volumes underwent standard preprocessing—discarding the initial 10 volumes, slice-timing correction, rigid-body realignment, MNI spatial normalization, and 6 mm full-width at half maximum Gaussian smoothing⁵⁷. Spatially independent components were then extracted by implementing the NeuroMark pipeline, a fully automated spatially constrained ICA on the preprocessed fMRI data⁵⁸. Using the neuromark_fMRI_1.0 template (available in GIFT at http://trendscenter.org/software/gift and also at http://trendscenter.org/data), we extracted 53 intrinsic connectivity networks (ICNs) for each subject. These ICNs are grouped into brain functional domains, including subcortical, auditory, sensorimotor, visual, cognitive control, default mode, and cerebellum. The resulting ICN time courses were z-scored to unit mean and variance and subsequently submitted to the complex Gabor-wavelet phase-synchrony analysis. This study was conducted retrospectively using data collected from human participants in compliance with all relevant ethical standards.

To assess the reproducibility of the identified directional coordination regimes, we additionally analyzed resting-state fMRI from three independent replication cohorts: the Center for Biomedical Research Excellence dataset, the Human Connectome Project Aging dataset, and the Human Connectome Project Adult dataset. These cohorts span a broad range of ages, scanner sites, and acquisition protocols, providing a stringent test of generalizability across diverse populations and imaging conditions. For all replication cohorts, the same NeuroMark framework with the neuromark_fMRI_1.0 template was applied to extract 53 ICNs, ensuring directly comparable network parcellations across datasets. CVPS was then computed identically to the primary fBIRN analysis. Full demographic and acquisition details for each replication cohort are provided in the Supplementary Information.

4.4. Identifying recurring directional coordination regimes

Temporal coordination dynamics were modeled as a sequence of discrete regimes through which brain activity evolves over time, consistent with prior work representing time-resolved fMRI dynamics as transitions between a finite set of states¹⁶. Each complex edge value $\mathrm{\Delta }{\phi }_{x\to y}=a+jb$ was represented as a two-dimensional real vector [a, b], yielding a 2E-dimensional feature vector per time point. To reduce redundancy, one direction per pair was retained, as the opposite direction is given by sign inversion. These embeddings preserve circular phase geometry: Euclidean and city block distances in the [cos φ, sin φ] representations are monotonic functions of angular separation, and the arithmetic mean of embedded points corresponds to the circular mean (Supplementary Information). Discrete regimes were then identified using k-means clustering with Euclidean and city block distances.

Clustering was performed using 20 random initializations and a maximum of 10,000 iterations to ensure convergence. The optimal number of clusters was determined as three using the elbow criterion. Cluster centroids were mapped back to the complex domain to yield representative coordination patterns for each regime. Results were consistent across the Euclidean and city-block distances, and the city-block distance was used due to improved numerical stability in high-dimensional space⁵⁹. Additional details are provided in the Supplementary Information.

4.5. Quantifying hierarchical directional flow within coordination regimes

To interpret the directional coordination regimes identified by clustering, we quantified the dominant direction of coordination flow across brain systems. Each cluster centroid was represented as a complex-valued edge vector $Z=R{e}^{j\mathrm{\Delta }\phi }$, where Δφ denotes phase (directionality) and R denotes magnitude (reliability). For a given regime, we identified edges that most strongly distinguished that regime from others. Specifically, for each edge e, we computed a discriminative score defined as the circular phase difference between the target regime and all other regimes, weighted by the minimum magnitude across regimes:

$$\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}\left(e\right)=\mathrm{\Delta }\phi \left(e\right)\cdot \mathrm{m}\mathrm{i}\mathrm{n}\left(R_{\text{target}}\left(e\right),R_{\text{others}}\left(e\right)\right),$$

where $\mathrm{\Delta }\phi \left(e\right)$ is the minimum circular difference between phase angles. This prioritizes edges that exhibit both strong directional separation and reliable phase structure.

We further quantified node-level directional influence by aggregating signed edge contributions. For each edge connecting nodes i and j, the direction of influence was determined by the sign of $\mathrm{s}\mathrm{i}\mathrm{n}\left(\mathrm{\Delta }{\phi }_e\right)$, reflecting lead–lag relationships. Node-level driver scores were then computed by summing weighted directional contributions across edges, yielding a measure of each region’s net directional influence within the regime. To assess large-scale organization, nodes were grouped into sensory (visual, sensory motor, auditory) and transmodal (cognitive control, default mode) systems. We then tested whether directional coordination preferentially flowed between these systems by comparing mean driver scores using permutation testing (50,000 permutations). Statistical significance was assessed by comparing the observed difference between systems to a null distribution generated by random label permutations.

4.6. Characterizing coordination dynamics using Markov chain properties

Temporal evolution of directional coordination was modeled as a stochastic process over discrete coordination regimes. For each subject, the sequence of regime assignments defines a trajectory on a finite state space, which we model as a first-order Markov process. State persistence was quantified using mean dwell time, defined as the average duration spent in a regime once entered. State occupancy, or fraction rate, measures the proportion of time spent in each regime. Transition structure was characterized by estimating subject-specific transition probability matrices from observed regime sequences⁶⁰.

From these, we derived the stationary distribution, representing the long-run equilibrium distribution over coordination regimes. To further quantify dynamical properties, we computed the spectral gap (one minus the second-largest eigenvalue of the transition matrix), which indexes the rate of convergence to equilibrium, with larger values indicating faster relaxation. The mixing time was defined as the number of steps required for the evolving state distribution to approach the stationary distribution within a tolerance of 10⁻¹⁰. The entropy rate quantifies the uncertainty of regime transitions, with lower values indicating more structured, predictable dynamics. For interpretability, the entropy rate is reported as a percentage of the maximum for a three-state system. Together, these measures provide a compact characterization of persistence, transition structure, and dynamical stability of directional coordination regimes. Formal derivations are provided by Wiafe et al⁶¹.

4.7. Constructing a persistence landscape of directional coordination dynamics

To visualize the global organization of directional coordination dynamics, we constructed a low-dimensional coordination landscape that integrates regime occupancy and persistence. For each regime, stability was defined as the product of its stationary probability and self-transition probability, capturing both how frequently the regime is visited and how persistently it is maintained. These stability values were normalized to preserve relative structure across regimes. Regimes were embedded in a two-dimensional simplex, providing a minimal geometric representation of the three-state coordination system. A continuous landscape was then generated by placing isotropic Gaussian kernels at each regime location, with amplitudes proportional to their stability, and summing their contributions to form a smooth surface. The resulting landscape was inverted such that deeper basins correspond to more stable regimes, yielding an intuitive energy-like representation of coordination dynamics. To enable direct comparison across groups, both landscapes were scaled using a common reference defined by the global minimum across conditions, ensuring that differences in basin depth reflect relative regime stability. This construction provides a compact geometric representation of how coordination regimes are organized, highlighting differences in stability and dominance across conditions.

4.8. Statistical framework for clinical and cognitive association

Group differences between healthy controls and individuals with schizophrenia were assessed using generalized linear models (GLMs), with age, sex, scanning site, and head motion parameters, such as mean frame displacement, included as covariates. Analyses were performed on coordination metrics, including MDT, FR, transition probabilities, stationary distribution, spectral gap, mixing time, and entropy rate. Multiple comparisons were controlled using the Benjamini–Hochberg false discovery rate (FDR) procedure.

Within the fBIRN dataset, GLMs were used to assess associations between coordination metrics and cognitive performance as measured by the Computerized Multiphasic Interactive Neurocognitive System (CMINDS), including domains of processing speed, attention/vigilance, working memory, verbal learning, visual learning, and reasoning/problem solving. To account for potential group differences, analyses were conducted separately within each group. For transition probabilities, FDR correction was applied across all tested transitions. Associations with symptom severity were evaluated using Positive and Negative Syndrome Scale (PANSS) scores. To isolate medication-related effects, analyses involving chlorpromazine dose included PANSS positive and negative scores as additional covariates, ensuring that observed medication associations were not driven by symptom severity.

4.9. Mediation analysis of pharmacological effects on coordination dynamics

To assess whether pharmacological effects on clinical outcomes are expressed through modulation of directional coordination dynamics, we performed mediation analyses within the schizophrenia group. All continuous variables, including chlorpromazine dose, coordination metrics, and head motion, were z-scored prior to analysis. All models included age, sex, scanning site, head motion, and PANSS positive and negative scores as covariates.

We tested whether CPZ-related changes in coordination were mediated through engagement with the feedforward coordination regime, quantified using its MDT. Mediation was evaluated using a standard regression-based framework, with paths estimated via generalized linear models. Indirect effects were computed as the product of the predictor-to-mediator (a) and mediator-to-outcome (b) paths, and statistical significance was assessed using bootstrap resampling (10,000 draws), with 95% confidence intervals. Multiple comparisons across tested mediation pathways were controlled using the Benjamini–Hochberg false discovery rate procedure.

Two families of mediation models were evaluated. First, to assess whether pharmacological modulation of coordination reduces engagement of higher-order integration, outcomes included the fraction rate and mean dwell time of the integrative regime. Second, to assess whether pharmacological effects are associated with shifts toward lower-level coordination modes, outcomes included the fraction rate and mean dwell time of the feedback regime. In both cases, significant indirect effects indicate that medication-related changes in coordination are expressed through altered engagement of directional coordination regimes.

7. DATA & CODE AVAILABILITY STATEMENT.

The data was not collected by us and was provided in a deidentified manner. The Institutional Review Board (IRB) will not allow sharing of data or individual derivatives, as a data reuse agreement was not signed by the subjects during the original acquisition.