Abstract

Introduction

The brain learns and adapts to environmental change, while showing resilience to local perturbation and damage. Complex adaptive systems seem to follow common organizational principles across many levels of scale, from subcellular components to social systems that resolve the tension between adaptability and resilience [1–4]. Here, we focus on two of these principles that illuminate the organization of the brain at the systems level: (i) The importance of multiple controlling variables, and (ii) the small-world architecture of efficient information-processing networks.

Complex biological and social systems are often driven by several separate control mechanisms with distinct functional properties [1]. Because the number of controlling variables is usually at least two, but fewer than ten, this principle has been named the ‘rule of hand’ [1]. The different controlling variables often affect the overall state of the system through distinct mechanisms that operate on separable temporal scales [5,6]. Systems with distinct rapid-acting and more slowly changing controlling variables can simultaneously be highly stable, yet flexible. For example, the ecological state of a forest can be rapidly affected by changes in the number of leaf-eating insects and more slowly by changes in the growth of large tree species. The presence of multiple control mechanisms also increases the resilience of a system to perturbation. For example, our sense of balance is supported in parallel by the vestibular system, the visual system and peripheral joint-position sensors. If any one of these three control variables is impaired, some level of balance is still maintained by the remaining mechanisms.

Information flow through complex networks of nodes can be made efficient by structuring the flow between the nodes in certain ways. Networks consisting of multiple densely connected clusters with small numbers of connections between clusters (i.e. small-world networks) are more efficient at information transmission (Figure 1) than are either randomly connected or highly regular lattice networks [2,3,7]. Such ‘small-world’ networks are ubiquitous. For example, the anatomical connections of the macaque visual system and the neuronal connections of Caenorhabditis elegans have both been described as small-world networks [2].

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Figure 1

Schematic depicting regular, small-world and random graphs. Small-world graphs can be generated by replacing local connections in regular (lattice) graphs with longer-range short-cuts. (a) Sample regular graph (lattice) containing 22 nodes and 52 edges. In regular graphs, each node is only connected to the next n nodes around the ring in a regular pattern. Regular graphs have long Lp and high Cp. (b) Data-derived graph containing 22 nodes [regions of interest (ROIs)] and 52 edges (functional connections) that seems small-world-like. Densely intraconnected clusters (black, yellow and blue) are linked through long-range short cuts (highlighted in red). Small-world networks are ’clumpy’, as reflected by high Cp and much shorter Lp than regular graphs. This type of network organization enables faster information transfer between any pair of nodes. (c) Sample random graph containing 22 nodes and 52 edges. Random graphs have moderately short Lp and low Cp. Functional connectivity diagrams of actual brain regions are neither regular nor random but more small-world like.

Here, we propose that the human brain implements top-down control in ways consistent with the complex systems principles of using multiple controllers and small-world-like architecture. We have chosen the study of top-down control as our example [8,9] because it is a complex function, probably supported by sets of interrelated brain regions that configure downstream processing in accordance with conscious goals [10,11].

Earlier studies [12,13] most commonly ascribed top-down control to several prefrontal regions, mainly the dorsolateral prefrontal cortex (dlPFC) and dorsal anterior cingulate cortex/medial superior frontal cortex (dACC/msFC). By contrast, we argue that top-down control is not implemented by such a limited number of regions but rather by a larger collection of functionally related regions. Second, based on both functional studies and recently developed ‘functional connectivity’ methods [3,4,11,14–17] (Box 1), we make the case that these regions are organized into relatively separate networks. Further, we present evidence that these separate control networks function at different timescales, making different contributions to the adaptability and stability of top-down control, respectively. Lastly, we argue that the network structure of these regions develops and embodies efficient small-world information processing.

Control implemented by a large set of distributed brain regions

Many single-unit and functional magnetic resonance imaging (fMRI) studies, showing that the dlPFC can maintain task-relevant information during the delay between a cue and a subsequent trial, have triggered intense focus on the lateral prefrontal cortex as a top-down controller [12,18]. However, a series of recent event-related, and mixed blocked/event-related human fMRI studies have shown that a large collection of lateral and medial frontal, prefrontal and parietal brain regions also have important roles in top-down control [11,19–26] (Figure 2).

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Figure 2

Distinct fronto-parietal and cingulo-opercular control networks. (a) The network structure of human control networks is displayed in a two-dimensional graph layout. Black lines indicate strong resting state functional connections between brain regions. The thickness of the lines indicates the relative connection strength (r). A spring-embedding algorithm (Net-Draw) was used to generate the 2D graph layout [17]. This algorithm treats each connection as a spring; thus, brain regions with similar patterns of connections are brought closer together in 2D space. This method arranges the nodes of a graph in ‘connection space’ rather than anatomical space. Regions sharing connections are placed close together, whereas minimally connected regions are spatially distant. For example, the left and right IPS have similar connectivity profiles and are therefore positioned closely adjacent in the network graph. For each region (circle), the central color indicates which network it belongs to (black = cingulo-opercular; blue = cerebellar and yellow = fronto-parietal). The outer color indicates the predominant control signal type of each region (red = set-maintenance; blue = error-related and yellow = start cue-related). At the displayed correlation threshold (r ≥ 0.15), the cingulo-opercular and fronto-parietal networks are not directly connected to each other but each network is connected to the cerebellar error-network through regions that also carry error information (the thalamus, dlPFC and IPL). This architecture suggests that both networks might be communicating error signals (or codes) to and from the cerebellum, in parallel. (b) Distinct cingulo-opercular (black) and fronto-parietal (yellow) control networks, in addition to cerebellar regions (blue circles) are shown on an inflated surface rendering of the human brain [55].

Other fMRI, single-unit, event-related potentials and transcranial magnetic stimulation studies support this broader view [27–30]. For example, several investigators have shown that brain regions, including the inferior parietal lobule (IPL) [21,22,31] and anterior prefrontal cortex (aPFC) [11,24,25,32,33], maintain task and context information. In addition, fMRI studies have shown that the anterior insula/frontal operculum (aI/fO) and dACC/msFC carry a variety of control signals [11,20,23,26–28,34–36].

Posner and Petersen’s [10] classic model of attentional control proposed that different control regions carry out distinct functions. Consistent with this idea, our cross-studies analyses of mixed blocked/event-related fMRI data, which examined three different types of control signals, showed that one set of control regions carried task set-maintenance signals [aI/fO, dACC/msFC, anterior prefrontal cortex (aPFC)], whereas other regions showed predominantly feedback and adjustment (the dlPFC and IPL), or control initiation activity [the intraparietal sulcus (IPS) and dorsal frontal cortex (dFC)] [11].

Control regions separate into fronto-parietal and cingulo-opercular networks

Cataloging functional differences between brain regions alone provides limited insight into how these regions relate to one another in information processing terms. Hence, recent studies have used resting state functional connectivity MRI (rs-fcMRI) to examine functional relationships between sets of regions [16]. Two recent studies employing rs-fcMRI, one using graph theory and hierarchical clustering [8] and the other using independent component analysis (ICA) [37], have shown that the control regions of the brain separate into distinct networks. Along with the identification of these networks using ICA [37], visualization of network structure across different correlation thresholds demonstrates that the separation is independent of specific graph definition thresholds (see supplementary material, Movie 1).

Here, we refer to the two distinct control networks as the ‘fronto-parietal’ and ‘cingulo-opercular’ networks. The fronto-parietal network consists of the dlPFC, IPL, dFC, IPS, precuneus and middle cingulate cortex (mCC). The cingulo-opercular network includes the aPFC, aI/fO, dACC/msFC and thalamus (Figure 2). Our functional connectivity analyses also showed that the cerebellum forms a separate but related cluster of regions that is interposed between the fronto-parietal and cingulo-opercular networks (Figure 2a; see supplementary material, Movie 1).

Distinct functions of control networks: adaptive control and set-maintenance

Mixed blocked/event-related fMRI designs can separate brain signals based on differences in their temporal profiles [14,38]. In our mixed blocked/event-related fMRI analyses [11], the fronto-parietal network contains signals that potentially initiate and adjust control on a trial-to-trial basis, whereas the cingulo-opercular network provides stable ‘set-maintenance’ over the entire task epoch.

Regions in the fronto-parietal control network respond to cues signifying task onset. In addition, they respond differentially to events that carry performance feedback information (e.g. correct versus error trials) [11]. The fronto-parietal control network seems to include parts of the dorsal attention network proposed by Corbetta and Shulman [39], and also additional regions commonly associated with top-down control in cue-delay-trial paradigms (the dlPFC and IPL) [12,18,31]. The fronto-parietal control network, then, seems to combine brain regions that initiate attentional control in response to cues with regions that process performance feedback on a trial-by-trial basis to adjust control settings [8,9,37].

In addition to the control initiation and adjustment signals also seen in the fronto-parietal network, the cingulo-opercular network carries set-maintenance activity that extends across the performance of many trials of a task. Hence, the hallmark feature of the cingulo-opercular network is set-maintenance activity that spans the entire task epoch [11]. Consistent with our data, several other fMRI studies have also associated the aPFC, dACC/msFC and aI/fO with important task control functions [24,27,33,36,40]. Several recent studies have implicated the dACC/msFC [36,41], in addition to the aI/fO and aPFC, in decision making [40]. It stands to reason that some of the same brain regions that safely maintain task goals are also involved in making (and/or monitoring) choices in accordance with those task goals.

In our mixed blocked/event-related fMRI studies [11], a set of cerebellar regions displayed only error-related activity, consistent with the view that the cerebellum processes error information in the service of performance optimization [42,43]. Interestingly, the cerebellar error regions were connected to the dlPFC and IPL in the fronto-parietal network, and to the thalamus in the cingulo-opercular network, all regions characterized by error-related (feedback and adjustment) activity [44] (Figure 2). These results suggest that the cerebellum sends error codes to both networks and/or that it receives error information from one or both of the control networks of the brain.

Dual-networks model of top-down control

The combination of studies outlined earlier [8,11,37,45] suggests that human behavior draws on two different types of top-down control (Figure 3). The fronto-parietal and cingulo-opercular systems both seem to maintain task-relevant information, but for different purposes and using different mechanisms [11,18,23,25,32,33,46–49]. Hence, we argue that more adaptive control (fronto-parietal) and stable set-maintenance (cingulo-opercular) rely on distinct types of ‘sustained’ activity.

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Figure 3

Model of proposed parallel rapid-adaptive and set-maintenance networks for human top-down control. Thin arrows schematize strong functional connections and boxed arrows schematize putative flow of information. The fronto-parietal and cingulo-opercular control networks might be organized in parallel. Both networks would thus interpret cues, implement top-down control and process bottom-up feedback. The fronto-parietal network might maintain task-relevant information in a more readily accessible form to adjust control rapidly. The cingulo-opercular network might stably maintain task sets across entire task epochs [9], perhaps in a less easily accessible, or remote, form. Adapted, with permission, from [9] Proceedings of the National Academy of Sciences. Copyright (2007) National Academy of Sciences, U.S.A.

The fronto-parietal network seems to actively maintain task-relevant information about one or a small number of trials, to implement control parameter adjustments more rapidly (Figure 3). We believe that cue-delay-target paradigms [12] detect this type of task control information as ‘sustained’ activity between a cue and the following target. The fronto-parietal network might also use error-related information to affect processing on the subsequent trial or for a limited number of subsequent trials.

Distinct from the maintenance activity seen between a cue and the following target in cue-delay-target paradigms, the cingulo-opercular network carries sustained activity that spans across the trials in a task epoch. The feedback signals received by the cingulo-opercular network, rather than causing immediate adjustments, might perhaps be integrated over many repetitions in a more protracted iterative fashion [36,50] (Figure 3).

Our dual-networks model of control (Figure 3) thus stands in contrast to several earlier models that ascribed top-down control functions primarily to the lateral PFC [18,49,51]. We argue that the lateral PFC does not constitute the lone top-down controller of the brain [18,51]. Instead, we contend that functionally and anatomically distinguishable regions of prefrontal (the dlPFC and aPFC), frontal (the dFC, dACC/msFC and aI/fO) and parietal cortex (the IPL, IPS and precuneus) contribute specific individual control functions [11] as nodes within two separate control networks [8,9,37,52]. Our proposed dual-networks model can account for the recent finding by Rossi et al. [53] that large lateral PFC lesions (apparently sparing the aPFC, dACC/msFC and, possibly, the aI/fO) severely impair the ability of a macaque to adjust behavior in response to frequent cue changes, whereas its ability to maintain set seems to be unaffected. By comparison, these results seem to be problematic for single-mechanism lateral PFC accounts of top-down control.

Furthermore, the finding that spatially adjacent prefrontal, frontal and parietal regions are separated into different clusters [9,11,37] seems inconsistent with the proposal that the PFC contains a single hierarchically organized mechanism that implements increasingly more abstract forms of control along a caudo-rostral gradient [13,49]. If the control system of the brain formed a single hierarchy, we would expect its functional connectivity to be more regular (Figure 1), such that each level was connected locally to the levels above and below.

The adaptive control and set-maintenance systems we propose are not only functionally, but also cytoarchitectonically distinct. Only the cingulo-opercular network contains von Economo neurons [54] – large layer V projection neurons found most abundantly in humans. This cytoarchitectonic dissociation suggests that the cingulo-opercular and fronto-parietal networks might have taken different evolutionary paths [54–56] (Box 2).

Please note that although we propose that control processes can be broken down into at least two basic types: rapid-adapting and set-maintenance, we do not feel that the control regions are interchangeable. We maintain that different nodes within each network carry out specialized processes that contribute to the overall functions of the networks.

Small-world control network architecture supports efficient information processing

Watts and Strogatz [2] highlighted that the connectional topology of many complex systems is neither completely regular (lattice) nor completely random. In a lattice, a given node or brain region is only locally connected to the next n nodes. Local connectivity is high and nodes are well clustered, but any signal traveling far across the network is significantly slowed because it has to cross too many nodes. One can think of a regular network as a system with only a local bus line that makes every stop (Figure 1).

By replacing some of the short-range links with long-range connections, Watts and Strogatz preserved local clustering, while also introducing between-cluster short cuts. Such a small-world network has a local bus line in addition to an express bus that directly connects different clusters without unnecessary stops.

These architectures can be described mathematically in terms of clustering coefficient (Cp) and characteristic path length (Lp). Cp describes the density of local clustering by measuring the fraction of neighbors of a given node that are also neighbors of each other, whereas Lp counts how many connections information has to traverse, on average, when traveling across the network.

Several investigators have suggested that the brain is organized in such a way that clusters of regions with similar functions segregate into networks, whereas sparse connections between networks enable the effective functional integration of processing streams [3,57–59]. Resting state connectivity studies [60], including our own [8,9], support this notion. Consistent with these observations, our graph-theoretical analyses of control networks revealed small-world organization, as indicated by relatively high Cp and small Lp [8].

Recent developmental rs-fcMRI data suggest that the structure of inter-regional networks in children is characterized by an abundance of local (short-range) connections. Over development, some local connections regress, whereas the strength of some long-range connections (short cuts) increase [9], mimicking the progression from a more lattice-like to a small-world structure [2] (Figure 1). In children aged between seven and nine years, the rs-fcMRI connectivity between the control regions of the brain correlates strongly with anatomical proximity. For example, in children, the dlPFC is more closely connected to the anatomically adjacent aPFC than to the IPL, even though the dlPFC and IPL are functionally more closely related in adults [9]. Consistent with the original description of small-world dynamics by Watts and Strogatz, the adult dual-networks control architecture emerges from a more regular organization [9] (Figure 1).

Conclusions and future directions

Evidence suggests that the principles of (i) multiple controlling variables and (ii) small-world connectivity hold true for the human brain, in particular for higher cognitive functions, such as top-down control.

In contradistinction to prior models, we argue that top-down control is driven by a fairly large collection of brain regions. These regions are distributed throughout the prefrontal, frontal and parietal cortex, in addition to the insula, cerebellum and thalamus.

Although previous models [18] treated control as a single continuously measurable entity, we believe top-down control in typical populations to be an amalgam of distinct processes, carried out by different brain regions, grouped into at least two separate control networks.

We propose that human behavior is, at the same time, flexible and highly stable because it can rely on at least two fairly parallel control networks: one optimized for rapid adaptive control (fronto-parietal) and the other for stable set-maintenance (cingulo-opercular). It stands to reason that the dual-networks control architecture is additionally advantageous because it increases the overall resilience of top-down control to damage or other perturbations. Although we have identified two control networks, it seems likely that additional controllers might exist, operating at other temporal and/or spatial scales.

In the future, our approach for studying top-down control networks should be expanded to include many more brain regions and functions. Similar to others who have advocated the elucidation of the human structural connectome [61], our final goal would be the visualization of all major functional relationships between all of the functional areas of the brain – a human functional connectome [61]. A human connectome based on both structural and functional connectivity data could then be annotated using activation studies that provide additional functional context. The development of the human connectome could be charted from birth to old age, and also examined in special populations [62], such as attention-deficit hyperactivity disorder [63], obsessive-compulsive disorder, Tourette syndrome, stroke [64] and traumatic brain injury patients, to better understand the systems-level pathophysiology of these important disorders.

Supplementary Material

Acknowledgements

Footnotes

References