• Anagh Pathak, 
• Demian Battaglia

x

Abstract

Citation: Pathak A, Battaglia D (2026) Arousal-driven critical roaming reproduces human functional connectivity dynamics. PLoS Biol 24(9): e3003916. https://doi.org/10.1371/journal.pbio.3003916

Academic Editor: Choong-Wan Woo, Sungkyunkwan University, REPUBLIC OF KOREA

Received: January 24, 2026; Accepted: July 8, 2026; Published: September 1, 2026

Copyright: © 2026 Pathak, Battaglia. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: The code used for all analyses and simulations is publicly available at https://doi.org/10.5281/zenodo.20798972. Data underlying the figures are provided in the Supporting information.

Funding: This research has been supported by the Fondation Vaincre Alzheimer to AP (project: Virtual brains to tailor sensory entrainment and boost memory in early Alzheimer; https://www.vaincrealzheimer.org/). We also acknowledge funding by the Agence Nationale de la Recherche, France through PEPR Digital Health (project Brain Health Trajectory, PEPR ANR-22-PESN-0012-BHT; https://pepr-santenum.fr/2023/11/08/bht/) to DB. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Abbreviations: AD, Alzheimer’s disease; AIC, Akaike Information Criteria; DWPs, dynamic working points; FCD, functional connectivity dynamics; FC, functional connectivity; GA, Genetic Algorithm; GSR, global signal regression; HCP, Human Connectome Project; MC, Meta-Connecitivity; MFM, mean-field model; OU, Ornstein–Uhlenbeck; SC, structural connectivity; sFC, static functional connectivity; SPD, symmetric positive definite; tMFM, autonomous mean-field models.

Introduction

Even during quiet wakefulness, the mind is rarely still—its ongoing mentation drifts and alights like a bird in flight [1]. The neural counterpart of this restless stream of consciousness is echoed in Functional Connectivity (FC)—the pattern of correlated activity across distributed brain regions measured with fMRI—which itself fluctuates dynamically over time [2]. Much like the complex trajectories of real bird flight [3], the temporal evolution of FC can be conceptualized as a random walk through a high-dimensional connectivity space, where each step reflects the reconfiguration of large-scale network interactions [4–6]. Empirical analyses have shown that the distribution of FC step lengths deviates substantially from a Gaussian form, exhibiting fat-tailed statistics that signal complexity [4]. These dynamics alternate between “knots” and “leaps”, i.e., epochs of transient FC stabilization and rapid reconfiguration, respectively [4]. Importantly, such temporal complexity in functional connectivity dynamics (FCD) correlates with individual differences in aging and cognition [4,5,7,8] and can serve as a neuromarker of cognitive decline in neurodegenerative diseases [9–13].

To understand the origin of these statistical features, one must consider the underlying dynamical system that generates them. A helpful intermediate-level description is provided by the metaphor of an attractor landscape, in which brain activity evolves like a particle moving across a manifold whose geometry constrains its trajectory [14]. Within this framework, the fat-tailed distribution of FCD step lengths can arise naturally from multi- or metastable dynamics–such as heteroclinic cycles producing slow drifts punctuated by rapid transitions, or noise-enabled switching among stable FC configurations [15–18]. Such behaviors can emerge from the autonomous collective dynamics of coupled, stochastic, nonlinear neural populations, which constitute a dominant modeling approach to explain the temporal structure of FCD [15,17]. In this paradigm, structured FCD reflects operation at a single, fixed Dynamical Working Point (DWP), hypothesized to lie near a critical point of the system’s dynamics [19–21].

A complementary and less explored mechanism involves changes in arousal. Here, we use arousal to denote a global brain state that shapes vigilance and behavioral responsiveness through diffuse neuromodulatory influences on cortical activity and input integration. Multiple systems contribute to arousal [22–24], including cholinergic and noradrenergic pathways that project broadly across the cortex and can rapidly reshape the attractor landscape of neural dynamics [25]. Computational models linking neuromodulatory effects to biophysical parameters show that activation of these systems can shift the brain between more integrative or segregative network states [26]. Such transitions–potentially sharp even in response to smooth fluctuations in neuromodulatory tone–are facilitated by critical boundaries separating distinct dynamical regimes, with neuromodulatory inputs acting as control signals that steer the system’s DWP through parameter space. The primary control knobs of this process—parameters such as cortical excitability or neural gain—represent plausible sites of neuromodulatory action, enabling the brain to expand or contract its repertoire of accessible network configurations in a task-contingent manner, traversing critical transition lines with qualitative changes in dynamics.

In time-resolved FC studies, arousal is often treated as a nuisance factor; yet, unlike motion or physiological noise, arousal fluctuations have a genuine neural origin [27]. Recent animal work shows that arousal can be captured by a low-dimensional variable—such as pupil diameter—that explains a substantial fraction of ongoing, large-scale neural activity [28,29]. While large swings in arousal accompany sleep–wake transitions, more subtle modulations also occur during quiet wakefulness, suggesting that continuous arousal fluctuations may act as a latent driver of spontaneous network reorganization [30,31]. Extending the attractor metaphor, brain activity would no longer unfold on a static landscape; rather, the landscape itself would be continually reshaped as the system’s DWP drifts under the influence of fluctuating arousal, altering its instantaneous distance from the critical transition lines that structure the system’s collective behavior [32–35].

Here, we adopt a whole-brain computational modeling approach to assess whether dynamic complexity at a DWP near criticality is sufficient to generate structured and fluid FCD, or whether temporal fluctuations of the DWP are also required to account for the empirically observed organization of FCD. Specifically, we simultaneously fit multiple quantitative features of human resting-state fMRI FCD using two alternative families of connectome-based whole-brain models: first, autonomous dynamical systems in which activity unfolds on a fixed landscape; and second, nonautonomous (explicitly time-dependent), arousal-driven models in which the dynamical landscape itself changes over time through stochastic fluctuations in model parameters, mimicking arousal-related modulation.

We focus in particular on how well each model reproduces the fat tails of the empirical FCD fluidity and speed distributions, rather than just their mean values. Although both model classes capture general features of FCD, only the time-varying (nonautonomous) models naturally generate the very slow-speed events and the “viscous” reconfiguration patterns observed in empirical data—phenomena reflected in frustrated link-to-link interactions along FCD trajectories [11,12,36]. This is notable because precisely these reductions in dynamical fluidity—robust across multiple approaches yet poorly captured by previous modeling frameworks—have been proposed as markers of cognitive decline in aging, demanding task states, and neurodegenerative disease [4–6,11–13].

Our findings therefore suggest that intrinsic FCD is sculpted by ongoing fluctuations in neuromodulatory tone associated with arousal. They also refine earlier theories proposing that the brain sits near a single critical boundary. Instead, our fitted simulations indicate that the DWP roams across a broad inter-critical zone—spanning a large expanse along the ignition threshold [37]—giving rise to nonmonotonic changes in FCD fluidity as arousal varies.

Results

Unlike previous approaches that segment FCD into discrete transitions between quasi-stable FC states [38], we describe FCD as a smooth, continuous flow through a space of continually morphing connectivity configurations [4]. Conventional analyses of static FC emphasize the spatial structure of connectivity networks while discarding most temporal information. An alternative perspective collapses each FC matrix into a single point in the high-dimensional space of all possible FC configurations—connectivity space. The erratic motion of this point through time can then be viewed as a stochastic trajectory or random walk across the manifold of possible network states. Most prior modeling studies have focused on reproducing the distribution of FCD values, while neglecting the sequential dependencies that define the temporal organization of FC reconfigurations [39,40]. Randomly shuffling the FCD streams, for instance, preserves the overall distribution but destroys its temporal structure—thus erasing the random-walk nature of the process [4]. To capture this essential aspect of FCD, we extend model fitting beyond the FCD distribution itself to include its step-length distribution, quantified as FCD speed (Fig 1). This metric characterizes how rapidly the system traverses connectivity space and the tails of this distribution encode rare but dynamically important transitions (corresponding to FCD “knots” and “leaps” [4]).

In the attempt to reproduce a rich FCD structure in silico, we first focus on a type of mean-field model (MFM) that has been extensively applied to characterize large-scale brain dynamics and reproduce key features of FC [15,40–42]. The model contains several parameters that can plausibly serve as control knobs for arousal, including cortical excitability and neural gain (which together set responsiveness and the relationship between synaptic input and population firing rate), the amplitude of stochastic noise, and the strength of local recurrent coupling within each neural population. Owing to a diversity of model parameters and nonlinear architecture, the MFM provides multiple avenues through which neuromodulatory input can transform system dynamics, making it a suitable platform for probing how arousal reshapes large-scale functional organization. In the following, we refer to the autonomous formulation as the MFM and to its time-dependent extension as tMFM, where t denotes the explicit temporal modulation introduced by arousal. Further, we label each tMFM variant according to the specific parameter endowed with temporal dependence: for the global scaler of inter-regional coupling (G, coupling gain), for background noise amplitude (), for the gain parameter of regional sigmoidal response functions (a), and for the intra-regional recurrent connectivity strength (w).

Discussion

Spontaneous brain activity is richly structured in time, yet the dynamical principles governing these fluctuations have remained elusive. Here we show that slow, global modulations of cortical excitability—an interpretable proxy for neuromodulatory arousal—provide a parsimonious explanation for the heavy-tailed, intermittently reorganizing structure of FCD. By directly contrasting conventional MFM with explicitly nonautonomous, arousal-driven variants, we demonstrate that many hallmark features of ongoing FC—fat-tailed step-length distributions, alternating epochs of persistence and rapid reconfiguration (Fig 2), and additional out-of-sample signatures such as SC–FC coupling, fit to static FC and MC (Fig 5)—emerge only when the model’s DWP is allowed to drift over time. In the autonomous case, reconfigurations require the system to hover near intrinsic bifurcations; the nonautonomous model naturally traverses these transitions, greatly expanding the repertoire of accessible large-scale network states (Fig 6).

A key conceptual advance enabling this result is our explicit focus on the sequential organization of FCD. Building on previous work quantifying FC variability, we introduce FCD Speed as a measure of the stepwise progression of the system through FC space [4,5,11]. Unlike statistics that summarize FCD variability alone [52,53], FCD Speed captures the stochastic, random-walk–like structure of FC trajectories and their occasional large “leaps” [4]. These heavy-tailed excursions turn out to be crucial: improvements in model performance arise almost entirely from the tails of the FCD and FCD-Speed distributions, not their means, which both model families already reproduce well (Fig 3). This highlights that meaningful dynamical events—those that reshape whole-brain FC—are rare, abrupt, and deeply informative about underlying mechanisms.

The presence of such intermittent, large-scale reconfiguration events naturally raises the question of where the brain operates relative to critical boundaries. Criticality has long been proposed as an organizing principle of neural dynamics, yet its functional role remains debated. Emerging evidence suggests that the brain does not maintain a fixed proximity to a critical point; rather, it approaches or retreats from criticality depending on behavioral and cognitive demands. Simple tasks may even be hindered by critical dynamics, whereas demanding tasks benefit from them [54], implying that the “distance to criticality” is itself a tunable control variable. Arousal and vigilance are known to shift this distance [55], and resting-state fMRI—particularly in eyes-closed conditions—captures drifting mixtures of wakefulness and light sleep [56]. This body of work suggests that the brain’s DWP is inherently nonstationary, wandering across a wide swath of state space, such that small fluctuations in arousal can produce disproportionately large changes in FC. This may explain why linear models approximate static FC well [47–49] (S13 Fig) but systematically fail to capture the temporal richness of time-resolved FC.

Our fitted simulations reveal how such wandering arises: slow fluctuations in a global excitability-like parameter (captured by the scaling term (G)) repeatedly move the system toward and away from rate-instability transitions (Fig 6). Although several model parameters can, in principle, induce critical transitions, perturbation analyses consistently identified (G) as the dominant determinant of FCD temporal structure. Biologically, this resonates with the diffuse ascending projections of major neuromodulatory systems, which act as global gain controllers and are well positioned to modulate large-scale excitability [25,26,57]. Nonetheless, neuromodulatory influences are not isolated control knobs but coordinated, low-dimensional patterns of receptor- and state-dependent action. The strong explanatory power of (G) therefore likely reflects a projection of this low-dimensional biological manifold onto model space, rather than the dominance of any single biophysical mechanism. Importantly, the nonlinear structure of the model endows it with a rich phase space, within which modulations of parameters such as G or noise amplitude () can induce transitions across regimes and give rise to phenomena such as stochastic resonance. As a result, FCD can exhibit nonmonotonic (U-shaped) dependencies—for instance in FCD speed—reflecting an optimal intermediate regime between overly stable and overly labile dynamics (for example, see Fig 2F). Such behavior is consistent with empirically observed reorganizations of brain activity and resonates with classical principles such as the Yerkes–Dodson law [58], highlighting how complex, arousal-like effects can emerge from generic nonlinear dynamics. Moreover, incorporating realistic spatial gradients of neuromodulatory receptor densities—known to be systematic across cortex [40,59]—may further enhance the model’s ability to capture fine-grained spatial structure in MC, which we considered here only in distributional form.

Our findings also carry important implications for the fMRI community, which has long debated the extent to which resting-state FCD is shaped—or contaminated—by arousal-related fluctuations [27,60]. The present framework offers a principled, dynamical-systems–based method for quantifying these contributions. In particular, it provides a mechanistic counterpart to the distinction proposed by Laumann and colleagues [27], who separated neural contributions to FCD into components related to spontaneous cognition versus arousal. Within our modeling scheme, this dichotomy maps naturally onto autonomous versus nonautonomous dynamics: the former capturing intrinsic, cognition-related fluctuations, and the latter reflecting slow, state-dependent modulations driven by arousal systems.

Several additional observations warrant consideration. First, we turn to the role of negative correlations (anti-correlations) in FCD, which are increasingly recognized as functionally meaningful [61]. A limitation of our framework is that neuromodulatory effects are modeled as uniform modulations of the model parameters, which biases the system toward increased positive correlations due to shared fluctuations across regions. Applying GSR partially mitigates this effect and introduces negative values in the tail of the MC distribution (Figs 3, 4); however, these anti-correlations cannot be unambiguously attributed to intrinsic dynamics, as GSR itself is known to induce such effects [62]. Notably, the static MFM already exhibits negative MC tails even in the absence of GSR (see S7 Fig), suggesting that at least part of this phenomenon may arise from the underlying nonlinear dynamics. Disentangling these contributions represents an important direction for future work. One potential avenue to mitigate the need for GSR, and reduce common-input effects, is to introduce parametric heterogeneity—for example, by incorporating spatial gradients of receptor densities.

Secondly, while the predominant dynamical motif across participants consisted of fast-regime trajectories interrupted by intermittent excursions into the slow regime, we also observed substantial inter-individual heterogeneity. In a subset of individuals, trajectories originated within the slow regime and periodically crossed rate-instability boundaries, suggesting that different brains may occupy systematically distinct positions along an arousal–excitability manifold. Such alternative dynamical pathways may reflect stable differences in baseline arousal, neuromodulatory responsiveness, or cognitive style, and may ultimately map onto meaningful behavioral, age-related, or clinical phenotypes [52,63–65]. Converging evidence from neuropathology, imaging, and clinical studies indicates that neurodegenerative disorders—most notably Alzheimer’s disease (AD)—are characterized by early and progressive disruption of ascending neuromodulatory systems. Degeneration of basal forebrain cholinergic nuclei is a hallmark of AD and underlies the long-standing cholinergic hypothesis, with loss of cholinergic neurons and cortical innervation closely tracking cognitive decline [66,67]. Similarly, the noradrenergic locus coeruleus shows pronounced vulnerability, often degenerating prior to overt cortical pathology and clinical symptoms [68]. Because these systems exert diffuse control over local cortical parameters, their degeneration is expected to constrain the brain’s ability to dynamically traverse critical regimes of network dynamics. Within the framework developed here, such neuromodulatory loss would restrict excursions across dynamical phase boundaries, narrowing the accessible repertoire of functional network states. This may provide a parsimonious mechanistic account of the reduced dynamical fluidity [69], impaired FCD [11], and diminished metastability [70] consistently reported in AD, and suggests that neuromodulatory decline contributes to cognitive impairment by producing a fundamental impoverishment of large-scale brain dynamics.

We offer potential customizations of the pipeline proposed here. First, although our implementation relied on the bistable Wong–Wang neural mass—a widely used model for large-scale fMRI dynamics [15,40,41]—the broader framework we introduce is not tied to this specific formulation. Oscillatory mechanisms, which are central to EEG, MEG, and LFP signals, could be readily incorporated using Stuart–Landau oscillators or next-generation neural mass models such as the Montbrió mean-field reduction [71,72]. Extending the framework into these oscillatory regimes may offer a principled route for unifying fast electrophysiological rhythms with slow arousal fluctuations [30,73]. Similarly, node dynamics could be extended to include additional targets of neuromodulatory action. In particular, mean-field models incorporating spike-frequency adaptation—known to be modulated by acetylcholine—provide a biologically grounded mechanism for shaping large-scale dynamics, including the emergence of Up–Down state transitions characteristic of NREM sleep. Such extensions could be implemented using mean-field reductions of models like the Adaptive Exponential Integrate-and-Fire model, enabling a more mechanistic investigation of how neuromodulation influences FCD [74,75].

Second, we adopted a GA for model fitting because it robustly accommodates noisy, computationally expensive simulations and multi-objective optimization without requiring gradient information [46]. This makes it particularly well suited to whole-brain models, whose parameter spaces are often highly nonlinear and characterized by sharp dynamical transitions. By treating the model as a black box, this approach avoids explicit assumptions about likelihood functions or the need for specialized training datasets. Recent work has explored simulation-based inference [76,77] for parameter estimation in whole-brain models, and systematic comparisons of these complementary approaches—in terms of performance, scalability, and interpretability—represent an important direction for future research. Finally, the whole-brain modeling community has increasingly leveraged PET-derived neurotransmitter maps to incorporate spatial heterogeneity in neuromodulatory influences [78–82]. When combined with the temporal framework introduced here, such spatially informed approaches could provide unprecedented insight into how distinct neuromodulatory systems shape the spatiotemporal organization of large-scale network dynamics, enabling a rich repertoire of functional configurations to emerge from a fixed structural scaffold. The temporal dynamics of arousal could be further informed by diverse data streams that serve as arousal proxies such as pupil diameter and electrophysiological markers of arousal [30,83]. These multimodal measures provide a natural testbed for evaluating and refining the mechanistic hypotheses proposed here, and the present model—while intentionally coarse—can be readily augmented to incorporate such information in future extensions.

Together, our findings offer a unified framework in which neuromodulation shapes large-scale brain dynamics by continuously steering the system across inter-critical regions of state space. Rather than treating resting-state activity as noise around a fixed operating point, our results support a view of the brain as an adaptive dynamical system whose working point fluidly evolves on slow timescales, enabling it to flexibly explore, sample, and reorganize its FC landscape. This perspective provides a foundation for mechanistically linking arousal, critical dynamics, and spontaneous cognition—and for understanding how their disruption contributes to aging, neuropsychiatric conditions, and altered states of consciousness.

Methods

Supporting information

Acknowledgments

The authors thank Romain Goutagny, James Shine, and Dietmar Plenz for insightful discussions and valuable feedback that helped shape this work.

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