Review articleCriticality in the brain: A synthesis of neurobiology, models and cognition
Introduction
Enormous strides have been achieved in neuroscience across a hierarchy of scales of enquiry, from the variety of neural cell types and their molecular biology, through the function of cortical circuits and, in recent years, to the complex architecture of large-scale brain networks. Much of this success has been achieved within research silos, with a focus on scale-specific phenomena, partly mandated by the apertures of various imaging technologies and partly by the training and cultures within the various neuroscientific disciplines. Research in neuroscience also proceeds within a largely descriptive world-view, with increasing emphasis on the collation and statistical characterization of “big data” (Biswal et al., 2010, Markram et al., 2015). Whilst specific mechanisms have been elucidated across an array of basic and clinical neuroscience domains, important challenges remain to be addressed: First, since correlations between behaviour and neuronal activity have been documented at almost every scale of analysis, it seems unlikely that a description of the brain at any particular scale will be sufficient to describe brain function. How is neural activity integrated across scales to give rise to cognitive function? What are the mechanisms linking activity across scales? Second, brain function does not only rely upon the execution of particular functions, but also on adaptive switching from one function to another, depending on context and goals. What are the fundamental principles underlying such complex, flexible neuronal dynamics? Third, what are the major theoretical frameworks to explain and unify the properties of all the large volumes of data currently being accrued? Fourth, how is information encoded by neurons – in the entropy of individual spikes, or via likelihood functions encoded by the distributions of population activity?
The principles that unify brain function across spatial and temporal scales remain largely unknown. However, comparable multi-scale challenges exist in other scientific disciplines. Meteorology, for example, spans scales from local wind gusts through regional weather systems up to global climate patterns. Each scale is nested within a larger scale, such that the local variance in wind gusts depends upon the regional weather, which is likewise constrained by global trends such as El Niño. Mathematicians and physicists have developed a considerable armoury of analytic tools to address multi-scale dynamics in a host of physical, biological and chemical systems (Bak et al., 1987). Chief amongst these is the notion of criticality, an umbrella term that denotes the behaviour of a system perched between order (such as slow, laminar fluid flow) and disorder [such as the turbulence of a fast-flowing fluid, (Shih et al., 2016)]. A critical system shows scale-free fluctuations that stretch from the smallest to the largest scale, and which may spontaneously jump between different spatiotemporal patterns. Despite their apparent random nature, the fluctuations in these systems are highly structured, obeying deep physical principles that show commonality from one system to the other (so-called universality). They can hence be subject to robust statistical analysis and modelling.
Critical systems thus display the type of cross-scale effects and dynamic instabilities linking activity at different scales that is typical of brain functioning. An emerging literature suggests that brain function may be supported by critical neural dynamics, with original research that continues to flourish (Deco and Jirsa, 2012, Kelso et al., 1992, Priesemann et al., 2014, Scott et al., 2014) on the background of an existing body of reviews and syntheses (Beggs and Timme, 2012, Chialvo, 2010, Deco and Jirsa, 2012, Boonstra et al., 2013, Hesse and Gross, 2014, Kelso et al., 1992, Plenz and Thiagarajan, 2007, Priesemann et al., 2014, Schuster et al., 2014, Scott et al., 2014, Shew and Plenz, 2013). The principles supporting the emergence of these patterns of activity are not yet fully understood but recent studies using neuroimaging techniques such as functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG) (Deco et al., 2009, Linkenkaer-Hansen et al., 2001, Stam and de Bruin, 2004) have added to earlier work in slice preparations (Beggs and Plenz, 2003). Computational models also show that neural systems have maximum adaptability to accommodate incoming processing demands when they are close to a critical point (Friston et al., 2012b, Friston, 2000, Gollo and Breakspear, 2014, Kastner et al., 2015, Shew et al., 2009, Yang et al., 2012). Conversely, brain disorders, as diverse as epilepsy, encephalopathy, bipolar disorder and schizophrenia may correspond to excursions from such an optimal critical point.
Despite the ubiquity of criticality in many branches of science, its application to neuroscience is relatively recent and unknown to many neuroscientists. When it is used, it is often invoked metaphorically; a practice which risks mixing distinct processes incorrectly into a rubric term. Research into criticality has much to offer neuroscientists, but needs to be used in accordance with its well-defined operational criteria. Accumulating evidence should also be viewed cautiously according to emerging pitfalls. Here, we first revisit the core notion of critical phenomenon and provide examples from the physical sciences. We then review the classic and recent studies of neuronal criticality. We finally consider emerging applications that advance new theories of healthy and maladaptive cognition using the innovative tools that criticality provides.
Section snippets
Criticality in physical systems
Criticality refers to the appearance of erratic fluctuations in a dynamical system that is close to losing dynamic stability (Box 1 and Box 2). Because the nature of the instability can vary (as we review below), criticality is a broad umbrella term that subsumes several related phenomena but also excludes others. In this section, we present a brief pedagogical account of criticality. We first consider critical fluctuations that occur close to instability in systems consisting of only a few
Criticality in the brain
The role of criticality and multistability in neurophysiological systems of the brain was first articulated over 3 decades ago by Walter Freeman following detailed empirical analyses and computational models of the rabbit olfactory bulb (Fig. 1g). In particular, Freeman proposed that the process of inhalation and exhalation acted, via modulation of the gain of excitatory neurons, to sweep the activity of the olfactory bulb through a sub-critical bifurcation and hence through a zone of
Challenges and pitfalls of the criticality hypothesis
Despite this recent emergence of criticality research in neuroscience, lessons learned in other branches of science raise important pitfalls and caveats. First, inferring the presence of scale-free statistics in neuroscience data has classically rested upon fitting a power-law (or Pareto) regression to the probability distribution of the size of the temporal or spatial fluctuations (Fig. 1, Fig. 2). The statistical principles underlying this exercise were critiqued in a highly influential
Emerging role of criticality in cognition
Notwithstanding the aforementioned caveats, growing empirical and modelling research clearly supports the view that neural dynamics likely occur near critical instabilities. The recognition of the limitations of this new field simply shows that it has matured beyond the “proof of principle” stage (Feyerabend, 1993). The scene is thus set for the translation of criticality into cognitive and clinical brain research.
In Section 3.1, we noted a canonical example of critical fluctuations near the
Bifurcations and seizures
Whereas the role of criticality in cognition is relatively nascent, casting seizures as dynamic disorders that arise out of critical instabilities is supported by an appreciable body of evidence (Da Silva et al., 2003, Meisel et al., 2012). The primary generalized seizures of childhood – Absence seizures – correspond to the presence of high amplitude 3 Hz spike-and-wave oscillations that appear and terminate equally quickly. These seizures have been modelled as critical bifurcations in
Summary
Evidence for the widespread occurrence of criticality in nature, and its corresponding computational advantages, has triggered the interest of scientists in many different fields. The list of advantages associated with criticality spans many systems and different measurable quantities (Assis and Copelli, 2008, Boedecker et al., 2012, Deco et al., 2013, Gollo et al., 2013, Haldeman and Beggs, 2005, Hidalgo et al., 2014, Kastner et al., 2015, Legenstein and Maass, 2007, Livi et al., 2017,
Conflicts of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Acknowledgments
Dedicated to the memory of Walter Freeman whose seminal early work inspired us and shaped the field. The authors thank the very helpful feedback from the anonymous reviewers. L.C., L.L.G, A.Z and M.B. were supported by the Australian National Health Medical Research Council (L.C. APP1099082, L.L.G. APP1110975, A.Z. APP1047648, M.B. APP1037196 and APP1118153). This work was also supported by the Australian Research Council Centre of Excellence for Integrative Brain Function (M.B., ARC Centre
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