Information Flow in the Brain: Ordered Sequences of Metastable States

: In this brief overview paper, we analyse information ﬂow in the brain. Although Shannon’s information concept, in its pure algebraic form, has made a number of valuable contributions to neuroscience, information dynamics within the brain is not fully captured by its classical description. These additional dynamics consist of self-organisation, interplay of stability/instability, timing of sequential processing, coordination of multiple sequential streams, circular causality between bottom-up and top-down operations, and information creation. Importantly, all of these processes are dynamic, hierarchically nested and correspond to continuous brain state change, even if the external environment remains constant. This is where metastable coordination comes into play. In a metastable regime of brain functioning, as a result of the simultaneous co-existence of tendencies for independence and cooperation, information is continuously created, preserved for some time and then dissipated through the formation of dynamical and nested spatio-temporal coalitions among simple neuronal assemblies and larger coupled conglomerates of them—so-called delocalised operational modules.


Introduction
An issue of crucial importance in the studying and understanding of higher cognitive operations in normal and pathological brain states and eventually the nature of consciousness is the origin and dynamics of information flow in the brain [1][2][3].The concept of information as a mathematical framework was first proposed in 1948 by the engineer and mathematician Claude Shannon [4] and was the birth to Information Theory [5].It was originally intended for the analysis of telecommunication systems, but soon branched out into many other fields [6], including neuroscience [7].
From the very beginning, Shannon's information concept was used [8] to estimate the limits of information transmission capacity in neurons, which then laid the foundation for "Neural Information Flow" theory [9,10].Further, Attneave [11], Barlow [12] and later Shlens and colleagues [13,14] and Schneidman et al. [15] used the information concept as a mutual constraint in studying the structure and function of the neural system [7].At the same time, despite these and many other valuable contributions to neuroscience, information dynamics within the brain is not adequately captured by the classical description of information [3].The non-classical aspects of information dynamics include self-organisation [1,16], the interplay of stability/instability [17,18], timing of sequential processing [2,19,20], coordination of the multiple sequential streams [21,22], circular causality between bottom-up and top-down operations [23][24][25], and information creation [3].Importantly, all of these processes are dynamic, hierarchically nested and correspond to continuous change of brain states, even when the external environment remains constant [26][27][28][29].
According to Tognoli and Kelso [25], "(. . . ) it seems that transmission principles do not scale well upward from simple 'channels' of synaptic interactions to the larger and more complex web of evolved brains.Thus, it is without surprise that the brain betrays an essential communicational etiquette: its parts do not behave in a sequential-one-talks-at-a-time-manner (. . .).It is also overwhelmingly clear that 'inputs' from the environment do not enter a silent system.Brain parts constantly exchange information about their current and past affairs, and what comes in at a given time works more as a 'perturbation' to an already established ballet, an event that weaves itself within a broader scheme of coordinated brain behaviour rather than the sole commander of all things present" ( [25], p. 3).All of these nuances show how difficult it is to keep within the Shannonian spirit when applying the information principle to the brain.
The observations above resonate with an ongoing shift in brain informatics paradigm.Since the brain is an active system that retains the characteristics of a complex, nonlinear system with nonequilibrium dynamics [28], reflected in transient evolution of transient states in the form of discrete frames of activity [30] and phase transitions between micro-and macro-levels [31,32], evidenced by the presence of spontaneous neuronal avalanches [33,34]-it creates or generates information as a result of sequential instabilities.Furthermore, such transient instabilities take place on multiple brain scales (micro-, meso-, and macro-) in a nested hierarchy of multiple coordinative processes, where autonomous tendencies coexist together with the interdependent tendencies [18].The cornerstone of such coordination dynamics is synergetic self-organization [35], which is described through circular causality of adaptive, informationally meaningful, bidirectional couplings on multiple levels [25,36].If one is to consider this multivariability of brain functioning as a whole, wherein the dynamic self-assembling process neuronal masses engage and disengage over time in the form of transient neuronal assemblies, thus allowing the brain to perceive objects or scenes, manipulate mental images and separate remembered parts of an experience, and finally to bind them all together into a coherent whole, then a new and peculiar principle emerges-metastability of brain functioning [18].
While metastability is a well-established concept in physics, it was first formulated in relation to a neural system by Kelso [37], who framed it within a classical model of coordination dynamics called the extended HKB [38] (where HKB stands for Haken, Kelso and Bunz [39]).Metastability in the brain refers to competition of complementary tendencies of cooperative integration and autonomous fragmentation among multiple distributed neuronal assemblies [1,18,[40][41][42][43][44].The interplay of these two tendencies (autonomy and integration) constitutes the metastable regime of brain functioning [1,18], where local (autonomous) and global (integrated) processes coexist not as antagonists but as a complementary pair [45] at all hierarchically nested levels of the brain functional organisation [23].Such a metastable regime in the brain arises when "the parts are no longer perfect clones of one another (e.g., as in computational models built from collections of identical neurons) [and] when symmetry is broken and interacting parts are recognized in the diversity of their intrinsic behavior" ( [25], p. 3) (see also [21,26,27,[46][47][48][49]).As a result, information is continuously created, preserved for some time and then dissipated by means of transient spatio-temporal coalitions among multiple neuronal assemblies and their operations associated with the emergence or decay of self-organized operational structures in the brain [23].Thus, we conclude that ordered sequences of metastable states across multiple spatial and temporal scales constitute information flow in the brain.
No other neurobiological theory is comparable to the Operational Architectonics (OA) theory of brain-mind functioning [2,18,[22][23][24]41,42] in its adherence to metastability as the overall phenomenon [1,44] and concrete versions of it such as a sequence of stable transient states [3,27,30] or transient coordination of autonomous processes [48,49].The OA theory provides a new and comprehensive framework for outlining information emergence and flow in the brain and mind.In this brief review paper, we will use an informal way of description, leaving the modeling and mathematical aspects as well as computational results out because they are largely still to be devised and to maintain intelligibility for the broad audience of this Special Issue.

The Operational Architectonics (OA) Theory of Brain-Mind Functioning
In a series of publications [2,18,[22][23][24]41,42], we have presented a theory of brain OA.This theory states that the simplest mental/cognitive operations that are responsible for qualia or simple computations are presented in the brain in the form of local three-dimensional fields produced by transient functional neuronal assemblies, while the complex operations that are responsible for complex operations, objects, images or thoughts are instantiated by coordinated/synchronized simple operations (temporal coupling of local 3D fields) in the form of so-called operational modules (OM) that may be of varied complexity and life-span.As such, brain OA is presented as a highly structured and dynamic extracellular electric field nested in spatial and temporal domains [23,24] and over a range of frequencies [50], thus forming a particular operational space-time (OST) [23].This OST exists within brain internal physical space-time (IPST) and the best way to capture it is through the electroencephalogram (EEG) measurement [51,52].The main property of this OST level of brain organization is that it intervenes between IPST level, where it literally resides, and the experiential/subjective phenomenal space-time (PST) level, to which it is isomorphic [23,41].Furthermore, the OST level has emergent properties relatively independent from the neurophysiological/neuroanatomical properties of the IPST level; however, it has one-to-one correspondence with the PST level that supervenes on the OST level and is ontologically inseparable from it [23,24].
According to the OA theory and in agreement with the metastability principle, OMs (that are produced by repetitive synchronization of lower-order operations performed by many neuronal assemblies along the cortex, with scale-free, power-law dynamics) are metastable because of intrinsic differences (including semantic) in the activity between neuronal assemblies that constitute every given OM: each neuronal assembly is autonomous by doing its own job, while at the same time still retaining a tendency to be coordinated together within the same OM in order to execute a given macro-operation [23,24,53].A metastable regime gives tremendous functional advantages for the brain-mind system, for example, speed, flexibility, resilience [21,44] and a tremendous increase in the number of available transient states within and between different levels of a nested functional hierarchy and spanning over several time scales [18,29,54], thus allowing an expression of virtually unlimited diversity of informationally-rich and sophisticated mental and cognitive states [25,53].
Such a metastable mode of brain-mind functioning [23,24,53] introduces hierarchical coupling [51,55] between the brain and mind while simultaneously allowing them to retain their individuality (for a conceptual discussion see [53]).When examined from this perspective, mind, cognition, and behavior, as well as brain activity, are all seen as dynamic processes that rapidly evolve through a series of informationally consistent, spatially and temporally organized, transient coordination states.In each moment of time, these states (of varying complexity) are defined by the selective coordination of local cortical neuronal assemblies that are interacting by virtue of synchrony of their local electromagnetic fields (frames of activity) which are equivalent to functional operations (OST-level) within the large-scale anatomical structure of the cortex (IPST-level) [23,24,41].
In analyzing the OA framework in physical terms, it could be proposed that such nested architectonics of brain-mind operations (presented as OMs of different complexity) can be described in terms of nested energy frames as analyzed within the Dynamic Universe theory [56], where the flow of information is viewed as the flow of energy [57] with abrupt transients (or rapid transitive periods, RTPs [23,24]) between frames of energy [58].Such RTPs (fast transitions) among the frames are typically associated with a fast memory drop in the dynamics, so that each self-organized single-frame state is often independent from another and the RTPs themselves.This property is mathematically denoted as a renewal condition; then, the sequence of RTPs as a renewal point process [59][60][61] is typically associated with the ability of the system to trigger a sequence of complex self-organized metastable structures.Why the long-range memory yielded by self-organization is in fact compatible with the memory-resetting properties of renewal events is discussed by Allegrini et al. [62].In relation to the brain operational architectonics, this means that within the RTP between two consequent metastable OMs, there is a biphasic transitive process: in the first brief phase, there is a drastic and abrupt increase in degrees of freedom among participating neuronal assemblies that is accompanied by a sudden increase in entropy, information and dimensionality [24].This first phase of RTP is followed by a second brief phase with a quick reduction in the degrees of freedom of neuronal assemblies and rapid decrease in entropy, information and dimensionality, indicating the self-organization of a new informational state expressed in the form of a new OM within brain OST [24].Such a new OM (new state) presents the new complex operation, phenomenal image or a thought (for a general conceptualization see [23,24]).

Empirical Support
As follows from the previous discussion, the ordered sequences of metastable states likely depend on (1) repertoire (how many types of states exist); (2) probability of occurrence (functional importance of states of a different type); (3) relative incidence of state type changes (how often the state types change); (4) life-span (maintenance of the relative stability in the neurodynamics within a particular time interval); (5) sequence hierarchy (consistent groupings of state types-steady bundle with one another-that comprise more integral blocks of structural organization).If these characteristics consistently change in a non-random fashion (functional relevance) along with the changes in the functional brain states, cognitive tasks and/or different psychopathological changes, then they indeed constitute information flow in the brain.As was already noted, the most adequate way to study sequences of metastable states is through EEG measurement [51,52].
It is well established that local EEG signals have a piecewise stationary structure which could be presented as a sequence of "glued" stationary processes with different probability characteristics (for the reviews see [2,26,43]).In this context, every quasi-stationary EEG segment (frame) reflects the oscillatory state of the underlying neurodynamical system i.e., transient neuronal assembly [2,43] which signifies a local functional cortical state [63].In its turn, every EEG oscillatory state is characterized by multiple EEG oscillations where these oscillations are mixed in different proportions depending on the level of vigilance as well as on perceptual, cognitive and mental operations.In this sense, a particular configuration of EEG oscillations (their repertoire and proportions) characterises/reflects a particular type (or class) of neurons' activities.Thus, a local EEG oscillatory state is a steady, transient and self-organised operational unit which has been proposed, based on the experimental research, to present the basic building block of cortical activity [64].Empirical EEG studies demonstrate that increased functional loading (multistage memory task) causes a statistically significant (a) increase in state type transition between neighboring EEG epochs/frames of the same EEG-signal and (b) decrease of life-span of these states [63].Perhaps these changes indicate that during increased functional loading, the brain's operations are completed more dynamically and that there exists a transition to a more differential organization in the electromagnetic field [65].Moreover, not all functional states occur with the same probability; some of them seem to be "preferred" during a particular condition [63].Psychopharmacological influence, psychopathology, or cognitive load alterations result in the changes of (a) number of oscillatory types of local EEG states; (b) percentage of dominant oscillatory types of local EEG states; (c) transition probability between distinct oscillatory types of functional states; (d) duration of functional states and (e) parameters of the temporal coincidence of the transitions from one functional state type to another registered in different cortex areas [64].It is important to note that all of these characteristics (repertoire, probability occurrence, relative incidence, life-span and sequence hierarchy) differ significantly from random processes, and are thus functionally relevant, reflecting different real aspects of information flow within the brain.
Evidently, the brain's informational processes dynamic may be reflected in the transformations of a small number of packages of relatively stable patterns within the cortex field oscillatory activity [50].It is suggested that particular temporal sequences of several EEG patterns appear in consistent groupings (steady bundle with one another) and comprise more integral blocks of local EEG structural organization.The idea that there may exist stable "super-segments/frames" in the individual/local EEG (steady combinations of particular segment/frame types as, for example, type "A" always follows type "F") was first shown by Jansen [66] and was replicated by other researchers [63,64,67,68].
As a parallel process to sequential dynamics, it has been demonstrated that a set of local bioelectrical (EEG) fields (produced by transient neuronal assemblies that are located in distinct brain areas) can rapidly couple with one another, thus demarcating the establishment of a particular more global or global metastable spatio-temporal OM in the volumetric OST continuum of the brain (see for review [22]).It was shown that the probability that a particular number of cortical areas are recruited into an OM (defined as the temporal RTP coincidences) is governed by power-law statistics [69].Such dependency is characteristic for non-ergodic systems, thus suggesting, in contrast to a traditional understanding of the brain as an ergodic system [27], that brain functional activity is rather non-ergodic [70,71].Further, our analysis revealed that such stabilized spatiotemporal OM configurations also have the transient dynamic which is expressed as a series of sudden transitions between OMs [22].From an information-theory point of view, one may suppose that OMs that cover most or the whole cortex and are long-lasting are not efficient in the healthy brain [72] because context-dependent information transfer is necessarily very dynamic and it would require very quick and flexible reconfiguration of many co-existent OMs.Empirical evidence supports this intuition [22]: it has been shown that the average life-span of OMs is longest for small OMs that are formed by two neuronal assemblies (~30 s) and shortest for large OMs that span most or the whole cortex (~100 milliseconds).In this context, the brain operates as a highly dynamic system where large metastable spatial-temporal patterns of stabilized activity (indexed as OMs) formed only for very brief episodes and then quickly dissipated allowing the brain (as a whole) to have more degrees of freedom to form new metastable OMs needed to execute newly immediately-emerged and ever-changing operations of different complexity [22].This dynamic can be significantly altered during pharmacological influence, neurological or psychiatric pathology or as result of traumatic brain damage when consciousness (including self-awareness) is minimal or lost completely [73][74][75][76].It may also be intentionally altered through mental training such as meditation [77,78].

Conclusions
Based on the theoretical conceptualizations and empirical data, we propose that information flow within the brain has to be organized in a specific temporal order along a chain of metastable states within and between different levels of a nested functional architecture of the brain.Such dynamic organisation is also isomorphic to the dynamics of phenomenal/subjective experience [53].Therefore, it is proposed that the ordered sequence of metastable states is a core component of informational flow in such a complex system as the brain-mind system.This perspective seriously considers repetitions of spatial-temporal patterns (indexed as metastable OMs) at all functional levels, thus capturing both dynamic as well as hierarchical complexities of brain activity that are nested within a multi-scale operational architecture [22][23][24].

IPST
Internal physical space-time PST Phenomenal (subjective) space-time HKB Stands for Haken, Kelso and Bunz