Optimization by Self-Organized Criticality

Failure in a population: Tauopathy disrupts homeostatic set-points in emergent dynamics despite stability in the constituent neurons

Homeostatic regulation of neuronal activity is essential for robust computation; set-points, such as firing rate, are actively stabilized to compensate for perturbations. The disruption of brain function central to neurodegenerative disease likely arises from impairments of computationally essential set-points. Here, we systematically investigated the effects of tau-mediated neurodegeneration on all known set-points in neuronal activity. We continuously tracked hippocampal neuronal activity across the lifetime of a mouse model of tauopathy. We were unable to detect effects of disease in measures of single-neuron firing activity. By contrast, as tauopathy progressed, there was disruption of network-level neuronal activity, quantified by measuring neuronal pairwise interactions and criticality, a homeostatically controlled, ideal computational regime. Deviations in criticality correlated with symptoms, predicted underlying anatomical pathology, occurred in a sleep-wake-dependent manner, and could be used to reliably classify an animal's genotype. This work illustrates how neurodegeneration may disrupt the computational capacity of neurobiological systems.

Tauopathy severely disrupts homeostatic set-points in emergent neural dynamics but not in the activity of individual neurons

The homeostatic regulation of neuronal activity is essential for robust computation; key set-points, such as firing rate, are actively stabilized to compensate for perturbations. From this perspective, the disruption of brain function central to neurodegenerative disease should reflect impairments of computationally essential set-points. Despite connecting neurodegeneration to functional outcomes, the impact of disease on set-points in neuronal activity is unknown. Here we present a comprehensive, theory-driven investigation of the effects of tau-mediated neurodegeneration on homeostatic set-points in neuronal activity. In a mouse model of tauopathy, we examine 27,000 hours of hippocampal recordings during free behavior throughout disease progression. Contrary to our initial hypothesis that tauopathy would impact set-points in spike rate and variance, we found that cell-level set-points are resilient to even the latest stages of disease. Instead, we find that tauopathy disrupts neuronal activity at the network-level, which we quantify using both pairwise measures of neuron interactions as well as measurement of the network's nearness to criticality, an ideal computational regime that is known to be a homeostatic set-point. We find that shifts in network criticality 1) track with symptoms, 2) predict underlying anatomical and molecular pathology, 3) occur in a sleep/wake dependent manner, and 4) can be used to reliably classify an animal's genotype. Our data suggest that the critical set-point is intact, but that homeostatic machinery is progressively incapable of stabilizing hippocampal networks, particularly during waking. This work illustrates how neurodegenerative processes can impact the computational capacity of neurobiological systems, and suggest an important connection between molecular pathology, circuit function, and animal behavior.

Brain Criticality EEG analysis for tracking neurodevelopment from Childhood to Adolescence

The brain criticality hypothesis suggests that neural networks and multiple aspects of brain activity self-organize into a critical state, and criticality marks the transition between ordered and disordered states. This hypothesis is appealing from computer science perspective because neural networks at criticality exhibit optimal processing and computing properties while having implications in clinical applications to neurological disorders. In this paper, we introduced brain criticality analysis to track neurodevelopment from childhood to adolescence using the electroencephalogram (EEG) data of 662 subjects aged 5 to 16 years from the Child Mind Institute. We computed brain criticality from long-range temporal correlation (LRTC) using detrended fluctuation analysis (DFA). We also compared the brain criticality analysis with standard EEG power analysis. The results showed a statistically significant increase in brain criticality from childhood to adolescence in the alpha band. A decreasing trend was observed in theta band from EEG power analysis, but a much higher variance was observed compared to the brain criticality analysis. However, the significant results were only observed in some EEG channels, and not observed if the analysis were performed separately with eyes-open and eyes-close condition. Nonetheless, the results suggest that brain criticality may serve as a biomarker of brain development and maturation, but further research is needed to improve brain criticality algorithms and EEG analysis methods.Clinical Relevance- The brain criticality analysis may be used to characterize and predict neurodevelopment in early childhood.

Nonstationary but quasisteady states in self-organized criticality

The notion of self-organized criticality (SOC) was conceived to interpret the spontaneous emergence of long-range correlations in nature. Since then many different models have been introduced to study SOC. All of them have a few common features: externally driven dynamical systems self-organize themselves to nonequilibrium stationary states exhibiting fluctuations of all length scales as the signatures of criticality. In contrast, we have studied here in the framework of the sandpile model a system that has mass inflow but no outflow. There is no boundary, and particles cannot escape from the system by any means. Therefore, there is no current balance, and consequently it is not expected that the system would arrive at a stationary state. In spite of that, it is observed that the bulk of the system self-organizes to a quasisteady state where the grain density is maintained at a nearly constant value. Power law distributed fluctuations of all lengths and time scales have been observed, which are the signatures of criticality. Our detailed computer simulation study gives the set of critical exponents whose values are very close to their counterparts in the original sandpile model. This study indicates that (i) a physical boundary and (ii) the stationary state, though sufficient, may not be the necessary criteria for achieving SOC.

Integrated world modeling theory expanded: Implications for the future of consciousness

Integrated world modeling theory (IWMT) is a synthetic theory of consciousness that uses the free energy principle and active inference (FEP-AI) framework to combine insights from integrated information theory (IIT) and global neuronal workspace theory (GNWT). Here, I first review philosophical principles and neural systems contributing to IWMT's integrative perspective. I then go on to describe predictive processing models of brains and their connections to machine learning architectures, with particular emphasis on autoencoders (perceptual and active inference), turbo-codes (establishment of shared latent spaces for multi-modal integration and inferential synergy), and graph neural networks (spatial and somatic modeling and control). Future directions for IIT and GNWT are considered by exploring ways in which modules and workspaces may be evaluated as both complexes of integrated information and arenas for iterated Bayesian model selection. Based on these considerations, I suggest novel ways in which integrated information might be estimated using concepts from probabilistic graphical models, flow networks, and game theory. Mechanistic and computational principles are also considered with respect to the ongoing debate between IIT and GNWT regarding the physical substrates of different kinds of conscious and unconscious phenomena. I further explore how these ideas might relate to the "Bayesian blur problem," or how it is that a seemingly discrete experience can be generated from probabilistic modeling, with some consideration of analogies from quantum mechanics as potentially revealing different varieties of inferential dynamics. I go on to describe potential means of addressing critiques of causal structure theories based on network unfolding, and the seeming absurdity of conscious expander graphs (without cybernetic symbol grounding). Finally, I discuss future directions for work centered on attentional selection and the evolutionary origins of consciousness as facilitated "unlimited associative learning." While not quite solving the Hard problem, this article expands on IWMT as a unifying model of consciousness and the potential future evolution of minds.

How critical is brain criticality?

Criticality is the singular state of complex systems poised at the brink of a phase transition between order and randomness. Such systems display remarkable information-processing capabilities, evoking the compelling hypothesis that the brain may itself be critical. This foundational idea is now drawing renewed interest thanks to high-density data and converging cross-disciplinary knowledge. Together, these lines of inquiry have shed light on the intimate link between criticality, computation, and cognition. Here, we review these emerging trends in criticality neuroscience, highlighting new data pertaining to the edge of chaos and near-criticality, and making a case for the distance to criticality as a useful metric for probing cognitive states and mental illness. This unfolding progress in the field contributes to establishing criticality theory as a powerful mechanistic framework for studying emergent function and its efficiency in both biological and artificial neural networks.

Self-Organized Criticality of Precipitation in the Rainy Season in East China

Based on daily precipitation data from 1960 to 2017 in the rainy season in east China, to a given percentile threshold of one observation station, the time that precipitation spends below threshold is defined as quiet time τ. The probability density functions τ in different thresholds follow power-law distributions with exponent β of approximately 1.2 in the day, pentad and ten-day period time scales, respectively. The probability density functions τ in different regions follow the same rules, too. Compared with sandpile model, Γ function describing the collapse behavior can effectively scale the quiet time distribution of precipitation events. These results confirm the assumption that for observation station data and low-resolution precipitation data, even in China, affected by complex weather and climate systems, precipitation is still a real world example of self-organized criticality in synoptic. Moreover, exponent β of the probability density function τ, mean quiet time τ¯q and hazard function Hq of quiet times can give sensitive regions of precipitation events in China. Usual intensity precipitation events (UPEs) easily occur and cluster mainly in the middle Yangtze River basin, east of the Sichuan Province and north of the Gansu Province. Extreme intensity precipitation events (EPEs) more easily occur in northern China in the rainy season. UPEs in the Hubei Province and the Hunan Province are more likely to occur in the future. EPEs in the eastern Sichuan Province, the Guizhou Province, the Guangxi Province and Northeast China are more likely to occur.

On the Importance of Being Flexible: Dynamic Brain Networks and Their Potential Functional Significances

In this theoretical review, we begin by discussing brains and minds from a dynamical systems perspective, and then go on to describe methods for characterizing the flexibility of dynamic networks. We discuss how varying degrees and kinds of flexibility may be adaptive (or maladaptive) in different contexts, specifically focusing on measures related to either more disjoint or cohesive dynamics. While disjointed flexibility may be useful for assessing neural entropy, cohesive flexibility may potentially serve as a proxy for self-organized criticality as a fundamental property enabling adaptive behavior in complex systems. Particular attention is given to recent studies in which flexibility methods have been used to investigate neurological and cognitive maturation, as well as the breakdown of conscious processing under varying levels of anesthesia. We further discuss how these findings and methods might be contextualized within the Free Energy Principle with respect to the fundamentals of brain organization and biological functioning more generally, and describe potential methodological advances from this paradigm. Finally, with relevance to computational psychiatry, we propose a research program for obtaining a better understanding of ways that dynamic networks may relate to different forms of psychological flexibility, which may be the single most important factor for ensuring human flourishing.

Neuronal avalanches in Watts-Strogatz networks of stochastic spiking neurons

Networks of stochastic leaky integrate-and-fire neurons, both at the mean-field level and in square lattices, present a continuous absorbing phase transition with power-law neuronal avalanches at the critical point. Here we complement these results showing that small-world Watts-Strogatz networks have mean-field critical exponents for any rewiring probability p>0. For the ring (p=0), the exponents are the same from the dimension d=1 of the directed-percolation class. In the model, firings are stochastic and occur in discrete time steps, based on a sigmoidal firing probability function. Each neuron has a membrane potential that integrates the signals received from its neighbors. The membrane potentials are subject to a leakage parameter. We study topologies with a varied number of neuron connections and different values of the leakage parameter. Results indicate that the dynamic range is larger for p=0. We also study a homeostatic synaptic depression mechanism to self-organize the network towards the critical region. These stochastic oscillations are characteristic of the so-called self-organized quasicriticality.

Collective and synchronous dynamics of photonic spiking neurons

Nonlinear dynamics of spiking neural networks have recently attracted much interest as an approach to understand possible information processing in the brain and apply it to artificial intelligence. Since information can be processed by collective spiking dynamics of neurons, the fine control of spiking dynamics is desirable for neuromorphic devices. Here we show that photonic spiking neurons implemented with paired nonlinear optical oscillators can be controlled to generate two modes of bio-realistic spiking dynamics by changing optical-pump amplitude. When the photonic neurons are coupled in a network, the interaction between them induces an effective change in the pump amplitude depending on the order parameter that characterizes synchronization. The experimental results show that the effective change causes spontaneous modification of the spiking modes and firing rates of clustered neurons, and such collective dynamics can be utilized to realize efficient heuristics for solving NP-hard combinatorial optimization problems.

Nonlocal self-organization of a dissipative system

We study the self-organization process induced by a nonlocal critical field, in analogy with the electric field that is derived from the global spatial profile of electric charge density during a discharge. In this nontrivial extension of standard sandpilelike models of intermittent dissipation, the charges move in a similar manner to grains of sand when the threshold condition on the field is achieved. Here we focus our attention on the long term statistics of events, so that we consider an extremely simplified model in close similarity with sandpiles, avoiding some of the extremely interesting complexities that occur in three-dimensional electric discharges. For the observed avalanches (discharges in this case) we analyze four characteristic quantities: current, charge discharged, energy discharged, and duration of the discharge. We have run several simulations to explore the parameter space and found in general that they exhibit well defined power law event statistics spanning for one to three decades in general. For some parameter values we observe the existence of large or global events, in addition to the power law statistics, some of which may be related to finite size effects due to the size of the simulation box. This is the first step in understanding the long term statistics of systems with avalanches or discharges, when the criticality is controlled by nonlocality, as there are a number systems, such as lightning discharges or heat transport in tokamaks, where this type of dynamics is expected to occur.

Radiolysis generates a complex organosynthetic chemical network

The architectural features of cellular life and its ecologies at larger scales are built upon foundational networks of reactions between molecules that avoid a collapse to equilibrium. The search for life’s origins is, in some respects, a search for biotic network attributes in abiotic chemical systems. Radiation chemistry has long been employed to model prebiotic reaction networks, and here we report network-level analyses carried out on a compiled database of radiolysis reactions, acquired by the scientific community over decades of research. The resulting network shows robust connections between abundant geochemical reservoirs and the production of carboxylic acids, amino acids, and ribonucleotide precursors—the chemistry of which is predominantly dependent on radicals. Moreover, the network exhibits the following measurable attributes associated with biological systems: (1) the species connectivity histogram exhibits a heterogeneous (heavy-tailed) distribution, (2) overlapping families of closed-loop cycles, and (3) a hierarchical arrangement of chemical species with a bottom-heavy energy-size spectrum. The latter attribute is implicated with stability and entropy production in complex systems, notably in ecology where it is known as a trophic pyramid. Radiolysis is implicated as a driver of abiotic chemical organization and could provide insights about the complex and perhaps radical-dependent mechanisms associated with life’s origins.

Effect of the Adaptive Response on the Wear Behavior of PVD and CVD Coated Cutting Tools during Machining with Built Up Edge Formation

The relationship between the wear process and the adaptive response of the coated cutting tool to external stimuli is demonstrated in this review paper. The goal of the featured case studies is to achieve control over the behavior of the tool/workpiece tribo-system, using an example of severe tribological conditions present under machining with intensive built-up edge (BUE) formation. The built-ups developed during the machining process are dynamic structures with a dual role. On one hand they exhibit protective functions but, on the other hand, the process of built-up edge formation is similar to an avalanche. Periodical growth and breakage of BUE eventually leads to tooltip failure and catastrophe of the entire tribo-system. The process of BUE formation is governed by the stick-slip phenomenon occurring at the chip/tool interface which is associated with the self-organized critical process (SOC). This process could be potentially brought under control through the engineered adaptive response of the tribo-system, with the goal of reducing the scale and frequency of the occurring avalanches (built-ups). A number of multiscale frictional processes could be used to achieve this task. Such processes are associated with the strongly non-equilibrium process of self-organization during friction (nano-scale tribo-films formation) as well as physical-chemical and mechanical processes that develop on a microscopic scale inside the coating layer and the carbide substrate. Various strategies for achieving control over wear behavior are presented in this paper using specific machining case studies of several hard-to-cut materials such as stainless steels, titanium alloy (TiAl6V4), compacted graphitic iron (CGI), each of which typically undergoes strong built-up edge formation. Various categories of hard coatings deposited by different physical vapor deposition (PVD) and chemical vapor deposition (CVD) methods are applied on cutting tools and the results of their tribological and wear performance studies are presented. Future research trends are outlined as well.

Why Brain Criticality Is Clinically Relevant: A Scoping Review

The past 25 years have seen a strong increase in the number of publications related to criticality in different areas of neuroscience. The potential of criticality to explain various brain properties, including optimal information processing, has made it an increasingly exciting area of investigation for neuroscientists. Recent reviews on this topic, sometimes termed brain criticality, make brief mention of clinical applications of these findings to several neurological disorders such as epilepsy, neurodegenerative disease, and neonatal hypoxia. Other clinicallyrelevant domains - including anesthesia, sleep medicine, developmental-behavioral pediatrics, and psychiatry - are seldom discussed in review papers of brain criticality. Thorough assessments of these application areas and their relevance for clinicians have also yet to be published. In this scoping review, studies of brain criticality involving human data of all ages are evaluated for their current and future clinical relevance. To make the results of these studies understandable to a more clinical audience, a review of the key concepts behind criticality (e.g., phase transitions, long-range temporal correlation, self-organized criticality, power laws, branching processes) precedes the discussion of human clinical studies. Open questions and forthcoming areas of investigation are also considered.

Criticality in the conformational phase transition among self-similar groups in intrinsically disordered proteins: Probed by salt-bridge dynamics

Intrinsically disordered proteins (IDP) serve as one of the key components in the global proteome. In contrast to globular proteins, they harbor an enormous amount of physical flexibility enforcing them to be retained in conformational ensembles rather than stable folds. Previous studies in an aligned direction have revealed the importance of transient dynamical phenomena like that of salt-bridge formation in IDPs to support their physical flexibility and have further highlighted their functional relevance. For this characteristic flexibility, IDPs remain amenable and accessible to different ordered binding partners, supporting their potential multi-functionality. The current study further addresses this complex structure-functional interplay in IDPs using phase transition dynamics to conceptualize the underlying (avalanche type) mechanism of their being distributed across and hopping around degenerate structural states (conformational ensembles). For this purpose, extensive molecular dynamics simulations have been done and the data analyzed from a statistical physics perspective. Investigation of the plausible scope of 'self-organized criticality' (SOC) to fit into the complex dynamics of IDPs was found to be assertive, relating the conformational degeneracy of these proteins to their functional multiplicity. In accordance with the transient nature of 'salt-bridge dynamics', the study further uses it as a probe to explain the structural basis of the proposed criticality in the conformational phase transition among self-similar groups in IDPs. The analysis reveal scale-invariant self-similar fractal geometries in the structural conformations of different IDPs. The insights from the study has the potential to be extended further to benefit structural tinkering of IDPs in their functional characterization and drugging.

An Integrated World Modeling Theory (IWMT) of Consciousness: Combining Integrated Information and Global Neuronal Workspace Theories With the Free Energy Principle and Active Inference Framework; Toward Solving the Hard Problem and Characterizing Agentic Causation

The Free Energy Principle and Active Inference Framework (FEP-AI) begins with the understanding that persisting systems must regulate environmental exchanges and prevent entropic accumulation. In FEP-AI, minds and brains are predictive controllers for autonomous systems, where action-driven perception is realized as probabilistic inference. Integrated Information Theory (IIT) begins with considering the preconditions for a system to intrinsically exist, as well as axioms regarding the nature of consciousness. IIT has produced controversy because of its surprising entailments: quasi-panpsychism; subjectivity without referents or dynamics; and the possibility of fully-intelligent-yet-unconscious brain simulations. Here, I describe how these controversies might be resolved by integrating IIT with FEP-AI, where integrated information only entails consciousness for systems with perspectival reference frames capable of generating models with spatial, temporal, and causal coherence for self and world. Without that connection with external reality, systems could have arbitrarily high amounts of integrated information, but nonetheless would not entail subjective experience. I further describe how an integration of these frameworks may contribute to their evolution as unified systems theories and models of emergent causation. Then, inspired by both Global Neuronal Workspace Theory (GNWT) and the Harmonic Brain Modes framework, I describe how streams of consciousness may emerge as an evolving generation of sensorimotor predictions, with the precise composition of experiences depending on the integration abilities of synchronous complexes as self-organizing harmonic modes (SOHMs). These integrating dynamics may be particularly likely to occur via richly connected subnetworks affording body-centric sources of phenomenal binding and executive control. Along these connectivity backbones, SOHMs are proposed to implement turbo coding via loopy message-passing over predictive (autoencoding) networks, thus generating maximum a posteriori estimates as coherent vectors governing neural evolution, with alpha frequencies generating basic awareness, and cross-frequency phase-coupling within theta frequencies for access consciousness and volitional control. These dynamic cores of integrated information also function as global workspaces, centered on posterior cortices, but capable of being entrained with frontal cortices and interoceptive hierarchies, thus affording agentic causation. Integrated World Modeling Theory (IWMT) represents a synthetic approach to understanding minds that reveals compatibility between leading theories of consciousness, thus enabling inferential synergy.

Seven Properties of Self-Organization in the Human Brain

The principle of self-organization has acquired a fundamental significance in the newly emerging field of computational philosophy. Self-organizing systems have been described in various domains in science and philosophy including physics, neuroscience, biology and medicine, ecology, and sociology. While system architecture and their general purpose may depend on domain-specific concepts and definitions, there are (at least) seven key properties of self-organization clearly identified in brain systems: (1) modular connectivity, (2) unsupervised learning, (3) adaptive ability, (4) functional resiliency, (5) functional plasticity, (6) from-local-to-global functional organization, and (7) dynamic system growth. These are defined here in the light of insight from neurobiology, cognitive neuroscience and Adaptive Resonance Theory (ART), and physics to show that self-organization achieves stability and functional plasticity while minimizing structural system complexity. A specific example informed by empirical research is discussed to illustrate how modularity, adaptive learning, and dynamic network growth enable stable yet plastic somatosensory representation for human grip force control. Implications for the design of “strong” artificial intelligence in robotics are brought forward.

25 years of criticality in neuroscience - established results, open controversies, novel concepts

Twenty-five years ago, Dunkelmann and Radons (1994) showed that neural networks can self-organize to a critical state. In models, the critical state offers a number of computational advantages. Thus this hypothesis, and in particular the experimental work by Beggs and Plenz (2003), has triggered an avalanche of research, with thousands of studies referring to it. Nonetheless, experimental results are still contradictory. How is it possible, that a hypothesis has attracted active research for decades, but nonetheless remains controversial? We discuss the experimental and conceptual controversy, and then present a parsimonious solution that (i) unifies the contradictory experimental results, (ii) avoids disadvantages of a critical state, and (iii) enables rapid, adaptive tuning of network properties to task requirements.

Connectomics of Morphogenetically Engineered Neurons as a Predictor of Functional Integration in the Ischemic Brain

Recent advances in cell reprogramming technologies enable the in vitro generation of theoretically unlimited numbers of cells, including cells of neural lineage and specific neuronal subtypes from human, including patient-specific, somatic cells. Similarly, as demonstrated in recent animal studies, by applying morphogenetic neuroengineering principles in situ, it is possible to reprogram resident brain cells to the desired phenotype. These developments open new exciting possibilities for cell replacement therapy in stroke, albeit not without caveats. Main challenges include the successful integration of engineered cells in the ischemic brain to promote functional restoration as well as the fact that the underlying mechanisms of action are not fully understood. In this review, we aim to provide new insights to the above in the context of connectomics of morphogenetically engineered neural networks. Specifically, we discuss the relevance of combining advanced interdisciplinary approaches to: validate the functionality of engineered neurons by studying their self-organizing behavior into neural networks as well as responses to stroke-related pathology in vitro; derive structural and functional connectomes from these networks in healthy and perturbed conditions; and identify and extract key elements regulating neural network dynamics, which might predict the behavior of grafted engineered neurons post-transplantation in the stroke-injured brain.

Exploring Criticality as a Generic Adaptive Mechanism

The activity of many biological and cognitive systems is not poised deep within a specific regime of activity. Instead, they operate near points of critical behavior located at the boundary between different phases. Certain authors link some of the properties of criticality with the ability of living systems to generate autonomous or intrinsically generated behavior. However, these claims remain highly speculative. In this paper, we intend to explore the connection between criticality and autonomous behavior through conceptual models that show how embodied agents may adapt themselves toward critical points. We propose to exploit maximum entropy models and their formal descriptions of indicators of criticality to present a learning model that drives generic agents toward critical points. Specifically, we derive such a learning model in an embodied Boltzmann machine by implementing a gradient ascent rule that maximizes the heat capacity of the controller in order to make the network maximally sensitive to external perturbations. We test and corroborate the model by implementing an embodied agent in the Mountain Car benchmark test, which is controlled by a Boltzmann machine that adjusts its weights according to the model. We find that the neural controller reaches an apparent point of criticality, which coincides with a transition point of the behavior of the agent between two regimes of behavior, maximizing the synergistic information between its sensors and the combination of hidden and motor neurons. Finally, we discuss the potential of our learning model to answer questions about the connection between criticality and the capabilities of living systems to autonomously generate intrinsic constraints on their behavior. We suggest that these “critical agents” are able to acquire flexible behavioral patterns that are useful for the development of successful strategies in different contexts.

Thermodynamic Scaling of Interfering Hemoglobin Strain Field Waves

Hemoglobin (Hgb) forms tetramers (dimerized α-β dimers), which enhance its globular stability and may also facilitate small gas molecule transport, as shown by recent all-atom Newtonian solvated simulations. Hydropathic bioinformatic thermodynamic scaling enables close comparisons of hemoglobin dimers with myoglobin and neuroglobin, and reveals many nonlocal wave-like features of strained Hgb structures at the coarse-grained amino acid level. The thermodynamic analysis employs two hydropathic scales, one describing abrupt first-order unfolding transitions, the other continuous second-order transitions. Small molecule exchange at hemes is a first-order process. Wave-like collective tetrameric features appropriate to ligand absorption and release, seen in optical experiments (short times), are identified thermodynamically at long times. Strain fields localized near hemes interfere with extended strain fields associated with dimer interfacial misfit, resulting in novel wavelength dependent dimer correlation function Fano antiresonances.