What kind of brain network? Overlapping and dynamic

In a highly networked system like the brain, we need to shift from thinking in terms of isolated brain regions, and adopt the language of networks: Networks of brain regions collectively support behaviors. The network itself is the unit, not the brain area (Figure 1). Consequently, processes that support behavior are not implemented by an individual area, but depend on the interaction of multiple areas, which are dynamically recruited into multi-region assemblies (more on dynamic aspects below).

Figure 1. What’s the rightful functional unit of interest? Historically, the brain area took center spot. A better unit is a network of brain regions working together.

Functional networks are based on the relationships of the signals in disparate parts of the brain, not on the status of their physical connections. The spatial scale of functional circuits varies considerably, from those linking nearby areas to large ones crisscrossing the brain. The most intriguing networks are possibly those discovered with functional MRI. To identify networks, investigators capitalize on “clustering methods”, general computer science algorithms that sort basic elements (here, areas) into different groups. The objective is to subdivide a set of elements into natural clusters, also known as communities. (These are also called modules by network researchers, but this is confusing in the case of neuroscience given the meaning of “modularity”).

Intuitively, a community should have more internal than external associations. For example, if we consider the set of all actors in the US, we can group them into theater and film clusters (theater actors work with and know each other more so than they work/know film actors). This notion can be formalized: communities are determined by subdividing a set of objects by maximizing the number of within-group connections, and minimizing the number of between-group connections. Remember that a connection in a graph is a link between two elements that share the relationship in question, such as between two theater actors who’ve worked together, or two actors that were in the same movie. Thus, theater actors will tend to group with other theater actors, and less so with film actors, and vice versa.

The most popular partitioning schemes parse individual elements (brain regions in a brain network, persons in a social network, etc.) into unique groupings – a node belongs to one and exactly one community. Based on functional MRI data at rest, the study by Yeo and colleagues discussed above described a seven-community division of the entire cortex, where each local patch of tissue belongs to a single community. In other words, the overall space is broken into disjoint communities. Their elegant work has been very influential and their 7-network partition was adopted as a sort of canonical subdivision of the cortex (see Figure 2). (Intriguingly, they also described an alternative 17-community subdivision of the cortex, but this one didn’t become very popular, likely because 17 is “too large” for neuroscientists to wrap their heads around.) Whereas discrete clusters simplify the description of a system, are they too inflexible, leading to the loss of valuable information?

Figure 2. Seven-network parcellation of Yeo et al. The organization of the human cerebral cortex estimated by intrinsic functional connectivity. J Neurophysiol 106: 1125–1165.

Think about the actors mentioned above. Perhaps they neatly subdivide into theater and film groups, and perhaps into some other clear subgroups (Broadway and Off-Broadway theater performers?). Yet, real-world groupings are seldom this simple, and in this case a particular artist might belong to more than one set (acting in both theater and film, say). In fact, several scientific disciplines, including sociology and biology, have realized the potential of overlapping network organization. For example, the study of chemical interactions reveals that a substantial fraction of proteins interact with several protein groups, indicating that actual networks are made of interwoven sets of overlapping communities. How about the brain?

Consider the versions of the connectivity “core” discussed previously, which contains regions distributed across the cortex, or across the entire brain. These areas are not only strongly interconnected, but also linked with many other parts of the brain. Put another way, by definition, regions of the core are those talking to lots of other ones. Traditional disjoint network partitioning schemes emphasize the within community grouping while minimizing the between community interactions. But regions of the core are both very highly interconnected and linked with disparate parts of the brain. So, how should we think about them?

Network science has additional tools that come to the help. One of them is to think of nodes as having a spectrum of computational properties. Both how well connected a node is, and how vastly distributed its links are matter. Nodes that are particularly well connected are called hubs (with a meaning similar to that in “airport hub”), a property that is formally captured by a mathematical measure called centrality. Hubs come in many different flavors, such as connector hubs that have links to many communities, and provincial hubs that are well connected within their particular community. We can thus think of the former nodes as more “central” in the overall system than the latter.

Nodes that work as connector hubs are distinctly interesting because they have the potential to integrate diverse types of signals if they receive connections from disparate sources, and/or to distribute signals widely if they project to disparate targets. They are a particularly good reminder that communities are not islands; nodes within a community have connections both within their community and to other clusters.

Networks are overlapping

We suggested that a better brain unit is a network, not a region. But in highly interconnected systems like the brain, subdividing the whole system into discrete and separate networks still seems too constraining. (The approach is more satisfactory in engineering systems, which are often designed with the goal of being relatively modular). An alternative is to consider networks as inherently overlapping. In this type of description, collections of brain regions – networks – are still the rightful unit, but a given region can participate in several of these, like the actors discussed previously. thinking more generally, we can even describe a system in terms of communities but allow every one of its nodes to belong to all communities, simultaneously. How would this work (Figure 3)?

Figure 3. Community organization in the brain.
(A) Standard communities are disjoint (inset: colors indicate separate communities), as illustrated via three types of representation. The representation on the right corresponds to a schematic correlation matrix.
(B) Overlapping communities are interdigitated, such that brain regions belong to multiple communities simultaneously (inset: community overlap shown on the brain indicated by intersection colors).
From: Najafi, M., McMenamin, B. W., Simon, J. Z., & Pessoa, L. (2016). Overlapping communities reveal rich structure in large-scale brain networks during rest and task conditions. Neuroimage, 135, 92-106.

In a study in my lab, we allowed each brain region to participate in a community in a graded fashion, which was captured by membership values varying continuously between 0 and 1; 0 indicated that the node did not belong to a community, and 1 that it belonged uniquely to a community. One can think of membership values as the strength of participation of a node in each community. It’s also useful to conceive of membership as a finite resource, such that it sums to 1. For example, in the case of acting professionals, a performer could belong to the theater cluster with membership 0.7 and to the film cluster with membership 0.3 to indicate the relative degree of participation in the two. In my lab’s study, we found that it was reasonable to subdivide cortical and subcortical regions into 5, 6, or 7 communities, like other algorithms have suggested in the past. But we also uncovered dense community overlap which was not limited to “special” hubs. In many cases, the entire community was clearly a meaningful functional unit, while at the same time most of its nodes still interacted non-trivially with a large set of brain regions in other networks.

The results of our study, and related ones by other groups, suggest that densely overlapping communities are well suited to capture the flexible and task dependent mapping between brain regions and their functions. The upshot is that it’s very difficult to subdivide a highly interconnected system without losing a lot of important information. What we need is a set of tools that allow us to do this in sophisticated ways. And we need them both to think about how networks are organized in space, as discussed in this section, and in time, to which we turn next.

Networks are dynamic

The brain is not frozen in place but is a dynamic, constantly moving object. Accordingly, its networks are not static but evolve temporally. As an individual matures from infancy to adolescence to adulthood and old age the brain changes structurally. But the changes that I want to emphasize here are those occurring at much faster time scales, those that accompany the production of behaviors as they unfold across seconds to minutes.

Functional connections between regions – the degree to which their signals covary – are constantly fluctuating based on cognitive, emotional, and motivational demands. When someone pays attention to a stimulus that is emotionally significant (it was paired with mild shock in the past, say), increased functionally connectivity is detected between the visual cortex and the amygdala. When she performs a challenging task in which an advance cue indicates that she may earn extra cash for performing it correctly, increased functional connectivity is observed between parietal/frontal cortex (important for performing the task) and the ventral striatum (which participates in reward-related processes). And so on. Consequently, network functional organization must be understood dynamically (Figure 4). In the past decade, researchers have created methods to delineate how networks change across time, informing how we view social, technological, and biological systems.

Figure 4. Brain networks are dynamic. (a,b) Specific network properties (‘network index’) evolve across time. (c,d) A region’s grouping with multiple networks evolves across time as indicated by the ‘membership index’ (inset: purple region and its functional connections to multiple networks). The region indicated in purple increases its coupling with one of the networks and stays coupled with it for the remainder of the time.

Brain networks are dynamic. For example, the fronto-parietal network mentioned previously is engaged by many challenging tasks, such as paying attention to an object, maintaining information in mind, or withholding a prepotent response. If a person transitions mentally from, say, listening passively to music to engaging in one of these functions (say, she needs to remember the name of a book just recommended to her), the state of the frontal-parietal network will correspondingly evolve, such that the signals in areas across the network will increasingly synchronize, supporting the task at hand (holding information in mind).

There’s a second, more radical, way in which networks are dynamic. That’s when they are viewed not as fixed collections of regions, but instead as coalitions that form and dissolve to meet computational needs. For instance, at time t1 regions R1, R2, R7, and R9 might form a natural cluster; at a later time t2 regions R2, R7, and R17 might coalesce. This shift in perspective challenges the notion of a network as a coherent unit, at least for longer periods of time. At what point does a coalition of regions become something other than community X? For example, the brain areas comprising the fronto-parietal network exist irrespective of the current mental operation; for one, the person could actually be sleeping or under anesthesia. The areas in question may not be strongly communicating with each other at all. Should it be viewed as a functional unit? When the regions become engaged by a mental operation, their signals become more strongly synchronized. But when along this process should the network be viewed as “active”? As the mind fluctuates from state to state, we can view networks cohering and dissolving correspondingly – not unlike a group of dancers merging and separating as an act progresses. The temporal evolution of their joint states is what is important.