Differential effects of propofol and ketamine on critical brain dynamics

Whether the brain operates at a critical “tipping” point is a long standing scientific question, with evidence from both cellular and systems-scale studies suggesting that the brain does sit in, or near, a critical regime. Neuroimaging studies of humans in altered states of consciousness have prompted the suggestion that maintenance of critical dynamics is necessary for the emergence of consciousness and complex cognition, and that reduced or disorganized consciousness may be associated with deviations from criticality. Unfortunately, many of the cellular-level studies reporting signs of criticality were performed in non-conscious systems (in vitro neuronal cultures) or unconscious animals (e.g. anaesthetized rats). Here we attempted to address this knowledge gap by exploring critical brain dynamics in invasive ECoG recordings from multiple sessions with a single macaque as the animal transitioned from consciousness to unconsciousness under different anaesthetics (ketamine and propofol). We use a previously-validated test of criticality: avalanche dynamics to assess the differences in brain dynamics between normal consciousness and both drug-states. Propofol and ketamine were selected due to their differential effects on consciousness (ketamine, but not propofol, is known to induce an unusual state known as “dissociative anaesthesia”). Our analyses indicate that propofol dramatically restricted the size and duration of avalanches, while ketamine allowed for more awake-like dynamics to persist. In addition, propofol, but not ketamine, triggered a large reduction in the complexity of brain dynamics. All states, however, showed some signs of persistent criticality when testing for exponent relations and universal shape-collapse. Further, maintenance of critical brain dynamics may be important for regulation and control of conscious awareness.     

Finite-size transitions in complex membranes

The lipid-raft hypothesis postulates that cell membranes possess some degree of lateral organization. The hypothesis has attracted much attention while remaining controversial, with an underlying mechanism that remains elusive. One idea that supports rafts relies on the membrane lying near a critical point. Although supported by experimental evidence, holding a many-component membrane at criticality requires a delicate tuning of all components—a daunting task. Here, we propose a coherent framework to reconcile critical behavior and lipid regulation. Using a lattice model, we show that lipid regulation of a complex membrane, i.e., allowing composition to fluctuate based on relative chemical potentials, can lead to critical behavior. The results are robust against specific values of the chemical potentials. Instead of a conventional transition point, criticality is observed over a large temperature range. This surprising behavior arises from finite-size effects, causing nonequivalent time and space averages. The instantaneous lipid distribution effectively develops a translational symmetry, which we relate to long-wavelength Goldstone modes. The framework is robust and reproduces important experimental trends; membrane-demixing temperature closely follows cell-growth temperature. It also ensures criticality of fixed-composition extracts, such as giant plasma membrane vesicles. Our clear picture provides a strong argument in favor of the critical-membrane hypothesis, without the need for specific sensing mechanisms.     

Maximizing Sensory Dynamic Range by Tuning the Cortical State to Criticality

Modulation of interactions among neurons can manifest as dramatic changes in the state of population dynamics in cerebral cortex. How such transitions in cortical state impact the information processing performed by cortical circuits is not clear. Here we performed experiments and computational modeling to determine how somatosensory dynamic range depends on cortical state. We used microelectrode arrays to record ongoing and whisker stimulus-evoked population spiking activity in somatosensory cortex of urethane anesthetized rats. We observed a continuum of different cortical states; at one extreme population activity exhibited small scale variability and was weakly correlated, the other extreme had large scale fluctuations and strong correlations. In experiments, shifts along the continuum often occurred naturally, without direct manipulation. In addition, in both the experiment and the model we directly tuned the cortical state by manipulating inhibitory synaptic interactions. Our principal finding was that somatosensory dynamic range was maximized in a specific cortical state, called criticality, near the tipping point midway between the ends of the continuum. The optimal cortical state was uniquely characterized by scale-free ongoing population dynamics and moderate correlations, in line with theoretical predictions about criticality. However, to reproduce our experimental findings, we found that existing theory required modifications which account for activity-dependent depression. In conclusion, our experiments indicate that in vivo sensory dynamic range is maximized near criticality and our model revealed an unanticipated role for activity-dependent depression in this basic principle of cortical function.     

Avalanches in Self-Organized Critical Neural Networks: A Minimal Model for the Neural SOC Universality Class

The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. Thus the model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that may include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain.     

Dynamics of Mechanically Coupled Hair-Cell Bundles of the Inner Ear

The high sensitivity and effective frequency discrimination of sound detection performed by the auditory system rely on the dynamics of a system of hair cells. In the inner ear, these acoustic receptors are primarily attached to an overlying structure that provides mechanical coupling between the hair bundles. Although the dynamics of individual hair bundles has been extensively investigated, the influence of mechanical coupling on the motility of the system of bundles remains underdetermined. We developed a technique of mechanically coupling two active hair bundles, enabling us to probe the dynamics of the coupled system experimentally. We demonstrated that the coupling could enhance the coherence of hair bundles’ spontaneous oscillation, as well as their phase-locked response to sinusoidal stimuli, at the calcium concentration in the surrounding fluid near the physiological level. The empirical data were consistent with numerical results from a model of two coupled nonisochronous oscillators, each displaying a supercritical Hopf bifurcation. The model revealed that a weak coupling can poise the system of unstable oscillators closer to the bifurcation by a shift in the critical point. In addition, the dynamics of strongly coupled oscillators far from criticality suggested that individual hair bundles may be regarded as nonisochronous oscillators. An optimal degree of nonisochronicity was required for the observed tuning behavior in the coherence of autonomous motion of the coupled system.     

Minimal model of plasma membrane heterogeneity requires coupling cortical actin to criticality

We present a minimal model of plasma membrane heterogeneity that combines criticality with connectivity to cortical cytoskeleton. The development of this model was motivated by recent observations of micron-sized critical fluctuations in plasma membrane vesicles that are detached from their cortical cytoskeleton. We incorporate criticality using a conserved order parameter Ising model coupled to a simple actin cytoskeleton interacting through point-like pinning sites. Using this minimal model, we recapitulate several experimental observations of plasma membrane raft heterogeneity. Small (r ∼ 20 nm) and dynamic fluctuations at physiological temperatures arise from criticality. Including connectivity to the cortical cytoskeleton disrupts large fluctuations, prevents macroscopic phase separation at low temperatures (T ≤ 22°C), and provides a template for long-lived fluctuations at physiological temperature (T = 37°C). Cytoskeleton-stabilized fluctuations produce significant barriers to the diffusion of some membrane components in a manner that is weakly dependent on the number of pinning sites and strongly dependent on criticality. More generally, we demonstrate that critical fluctuations provide a physical mechanism for organizing and spatially segregating membrane components by providing channels for interaction over large distances.     

Global Genetic Response in a Cancer Cell: Self-Organized Coherent Expression Dynamics

Understanding the basic mechanism of the spatio-temporal self-control of genome-wide gene expression engaged with the complex epigenetic molecular assembly is one of major challenges in current biological science. In this study, the genome-wide dynamical profile of gene expression was analyzed for MCF-7 breast cancer cells induced by two distinct ErbB receptor ligands: epidermal growth factor (EGF) and heregulin (HRG), which drive cell proliferation and differentiation, respectively. We focused our attention to elucidate how global genetic responses emerge and to decipher what is an underlying principle for dynamic self-control of genome-wide gene expression. The whole mRNA expression was classified into about a hundred groups according to the root mean square fluctuation (rmsf). These expression groups showed characteristic time-dependent correlations, indicating the existence of collective behaviors on the ensemble of genes with respect to mRNA expression and also to temporal changes in expression. All-or-none responses were observed for HRG and EGF (biphasic statistics) at around 10–20 min. The emergence of time-dependent collective behaviors of expression occurred through bifurcation of a coherent expression state (CES). In the ensemble of mRNA expression, the self-organized CESs reveals distinct characteristic expression domains for biphasic statistics, which exhibits notably the presence of criticality in the expression profile as a route for genomic transition. In time-dependent changes in the expression domains, the dynamics of CES reveals that the temporal development of the characteristic domains is characterized as autonomous bistable switch, which exhibits dynamic criticality (the temporal development of criticality) in the genome-wide coherent expression dynamics. It is expected that elucidation of the biophysical origin for such critical behavior sheds light on the underlying mechanism of the control of whole genome.     

Irregularly Appearing Early Afterdepolarizations in Cardiac Myocytes: Random Fluctuations or Dynamical Chaos?

Irregularly occurring early afterdepolarizations (EADs) in cardiac myocytes are traditionally hypothesized to be caused by random ion channel fluctuations. In this study, we combined 1), patch-clamp experiments in which action potentials were recorded at different pacing cycle lengths from isolated rabbit ventricular myocytes under several experimental conditions inducing EADs, including oxidative stress with hydrogen peroxide, calcium overload with BayK8644, and ionic stress with hypokalemia; 2), computer simulations using a physiologically detailed rabbit ventricular action potential model, in which repolarization reserve was reduced to generate EADs and random ion channel or path cycle length fluctuations were implemented; and 3), iterated maps with or without noise. By comparing experimental, modeling, and bifurcation analyses, we present evidence that noise-induced transitions between bistable states (i.e., between an action potential with and without an EAD) is not sufficient to account for the large variation in action potential duration fluctuations observed in experimental studies. We conclude that the irregular dynamics of EADs is intrinsically chaotic, with random fluctuations playing a nonessential, auxiliary role potentiating the complex dynamics.     

scGET: Predicting Cell Fate Transition During Early Embryonic Development by Single-cell Graph Entropy

During early embryonic development, cell fate commitment represents a critical transition or"tipping point"of embryonic differentiation, at which there is a drastic and qualitative shift of the cell populations. In this study, we presented a computational approach, scGET, to explore the gene–gene associations based on single-cell RNA sequencing (scRNA-seq) data for critical transition prediction. Specifically, by transforming the gene expression data to the local network entropy, the single-cell graph entropy (SGE) value quantitatively characterizes the stability and criticality of gene regu-latory networks among cell populations and thus can be employed to detect the critical signal of cell fate or lineage commitment at the single-cell level. Being applied to five scRNA-seq datasets of embryonic differentiation, scGET accurately predicts all the impending cell fate transitions. After identifying the"dark genes"that are non-differentially expressed genes but sensitive to the SGE value, the underlying signaling mechanisms were revealed, suggesting that the synergy of dark genes and their downstream targets may play a key role in various cell development processes. The application in all five datasets demonstrates the effectiveness of scGET in analyzing scRNA-seq data from a network perspective and its potential to track the dynamics of cell differentiation. The source code of scGET is accessible at https://github.com/zhongjiayuna/scGET_Project.     

Failure of adaptive self-organized criticality during epileptic seizure attacks

Critical dynamics are assumed to be an attractive mode for normal brain functioning as information processing and computational capabilities are found to be optimal in the critical state. Recent experimental observations of neuronal activity patterns following power-law distributions, a hallmark of systems at a critical state, have led to the hypothesis that human brain dynamics could be poised at a phase transition between ordered and disordered activity. A so far unresolved question concerns the medical significance of critical brain activity and how it relates to pathological conditions. Using data from invasive electroencephalogram recordings from humans we show that during epileptic seizure attacks neuronal activity patterns deviate from the normally observed power-law distribution characterizing critical dynamics. The comparison of these observations to results from a computational model exhibiting self-organized criticality (SOC) based on adaptive networks allows further insights into the underlying dynamics. Together these results suggest that brain dynamics deviates from criticality during seizures caused by the failure of adaptive SOC.     

Stable long-period cycling and complex dynamics in a single-locus fertility model with genomic imprinting

Although long-period population size cycles and chaotic fluctuations in abundance are common in ecological models, such dynamics are uncommon in simple population-genetic models where convergence to a fixed equilibrium is most typical. When genotype-frequency cycling does occur, it is most often due to frequency-dependent selection that results from individual or species interactions. In this paper, we demonstrate that fertility selection and genomic imprinting are sufficient to generate a Hopf bifurcation and complex genotype-frequency cycling in a single-locus population-genetic model. Previous studies have shown that on its own, fertility selection can yield stable two-cycles but not long-period cycling characteristic of a Hopf bifurcation. Genomic imprinting, a molecular mechanism by which the expression of an allele depends on the sex of the donating parent, allows fitness matrices to be nonsymmetric, and this additional flexibility is crucial to the complex dynamics we observe in this fertility selection model. Additionally, we find under certain conditions that stable oscillations and a stable equilibrium point can coexist. These dynamics are characteristic of a Chenciner (generalized Hopf) bifurcation. We believe this model to be the simplest population-genetic model with such dynamics.     

Exploring the Mechanisms of Differentiation,Dedifferentiation, Reprogramming and Transdifferentiation

We explored the underlying mechanisms of differentiation, dedifferentiation, reprogramming and transdifferentiation (cell type switchings) from landscape and flux perspectives. Lineage reprogramming is a new regenerative method to convert a matured cell into another cell including direct transdifferentiation without undergoing a pluripotent cell state and indirect transdifferentiation with an initial dedifferentiation-reversion (reprogramming) to a pluripotent cell state. Each cell type is quantified by a distinct valley on the potential landscape with higher probability. We investigated three driving forces for cell fate decision making: stochastic fluctuations, gene regulation and induction, which can lead to cell type switchings. We showed that under the driving forces the direct transdifferentiation process proceeds from a differentiated cell valley to another differentiated cell valley through either a distinct stable intermediate state or a certain series of unstable indeterminate states. The dedifferentiation process proceeds through a pluripotent cell state. Barrier height and the corresponding escape time from the valley on the landscape can be used to quantify the stability and efficiency of cell type switchings. We also uncovered the mechanisms of the underlying processes by quantifying the dominant biological paths of cell type switchings on the potential landscape. The dynamics of cell type switchings are determined by both landscape gradient and flux. The flux can lead to the deviations of the dominant biological paths for cell type switchings from the naively expected landscape gradient path. As a result, the corresponding dominant paths of cell type switchings are irreversible. We also classified the mechanisms of cell fate development from our landscape theory: super-critical pitchfork bifurcation, sub-critical pitchfork bifurcation, sub-critical pitchfork with two saddle-node bifurcation, and saddle-node bifurcation. Our model showed good agreements with the experiments. It provides a general framework to explore the mechanisms of differentiation, dedifferentiation, reprogramming and transdifferentiation.     

Regulative differentiation as bifurcation of interacting cell population

In multicellular organisms, several cell states coexist. For determining each cell type, cell-cell interactions are often essential, in addition to intracellular gene expression dynamics. Based on dynamical systems theory, we propose a mechanism for cell differentiation with regulation of populations of each cell type by taking simple cell models with gene expression dynamics. By incorporating several interaction kinetics, we found that the cell models with a single intracellular positive-feedback loop exhibit a cell fate switching, with a change in the total number of cells. The number of a given cell type or the population ratio of each cell type is preserved against the change in the total number of cells, depending on the form of cell-cell interaction. The differentiation is a result of bifurcation of cell states via the intercellular interactions, while the population regulation is explained by self-consistent determination of the bifurcation parameter through cell-cell interactions. The relevance of this mechanism to development and differentiation in several multicellular systems is discussed.     

Robustness of circadian rhythms in the presence of molecular fluctuations: an investigation based on a mechanistic, statistical theory and a simulation algorithm

After a very brief introduction to a mechanistic and statistical theory of molecular fluctuations in chemical reactions developed by Joel Keizer, we explore the robustness of a circadian rhythm model by using the theory and the exact stochastic simulation (ESS). The comparative study shows that the theory reflects the effects of the dynamics of the model on the robustness more than ESS does. Even though the theory is a macroscopic one, the robustness of the model compares well with that computed from the ESS when the system size is larger than 50. The robustness increases nonlinearly with the system size and it reaches an asymptotic value at higher system sizes. As we can expect from the dynamics of the system, the robustness is minimum near the bifurcation point and as the most sensitive parameter increases away from the bifurcation point the robustness according to the theory as well as the ESS increases and then reaches to a steady value.     

Full system bifurcation analysis of endocrine bursting models

Plateau bursting is typical of many electrically excitable cells, such as endocrine cells that secrete hormones and some types of neurons that secrete neurotransmitters. Although in many of these cell types the bursting patterns are regulated by the interplay between voltage-gated calcium channels and calcium-sensitive potassium channels, they can be very different. We investigate so-called square-wave and pseudo-plateau bursting patterns found in endocrine cell models that are characterized by a super- or subcritical Hopf bifurcation in the fast subsystem, respectively. By using the polynomial model of Hindmarsh and Rose (Proceedings of the Royal Society of London B 221 (1222) 87-102), which preserves the main properties of the biophysical class of models that we consider, we perform a detailed bifurcation analysis of the full fast-slow system for both bursting patterns. We find that both cases lead to the same possibility of two routes to bursting, that is, the criticality of the Hopf bifurcation is not relevant for characterizing the route to bursting. The actual route depends on the relative location of the full-system's fixed point with respect to a homoclinic bifurcation of the fast subsystem. Our full-system bifurcation analysis reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis.     

The future in and of criticality assessments

In recent literature, the concept of criticality aspires to provide a multifaceted risk assessment of resource supply shortage. However, most existing methodologies for the criticality assessment of raw materials are restricted to a fixed temporal and spatial reference system. They provide a snapshot in time of the equilibrium between supply and demand/economic importance and do not account for temporal changes of their indicators. The static character of criticality assessments limits the use of criticality methodologies to short‐term policy making of raw materials. In the current paper, we argue for an enhancement of the criticality framework to account for three key dynamic characteristics, namely changes of social, technical, and economic features; consideration of the spatial dimension in site‐specific assessments; and impact of changing governance frameworks. We illustrate how these issues were addressed in studies outside of the field of criticality and identify the dynamic parameters that influence resource supply and demand based on a review of studies that belong to the general field of resource supply and demand. The parameters are grouped in seven categories: extraction, social, economic, technical, policy, market dynamics, and environmental. We explore how these parameters were considered in the reviewed studies and propose ways and specific examples of addressing the dynamic effects in the criticality indicators. Furthermore, we discuss the current work on future scenarios to provide reference points for indicator benchmarks. The insights and guidelines derived from the review and our recommendations for future research set the foundations for an enhanced dynamic and site‐specific criticality assessment framework.     

Membrane dynamics correlate with formation of signaling clusters during cell spreading

The morphology and duration of contacts between cells and adhesive surfaces play a key role in several biological processes, such as cell migration, cell differentiation, and the immune response. The interaction of receptors on the cell membrane with ligands on the adhesive surface leads to triggering of signaling pathways, which allow cytoskeletal rearrangement, and large-scale deformation of the cell membrane, which allows the cell to spread over the substrate. Despite numerous studies of cell spreading, the nanometer-scale dynamics of the membrane during formation of contacts, spreading, and initiation of signaling are not well understood. Using interference reflection microscopy, we study the kinetics of cell spreading at the micron scale, as well as the topography and fluctuations of the membrane at the nanometer scale during spreading of Jurkat T cells on antibody-coated substrates. We observed two modes of spreading, which were characterized by dramatic differences in membrane dynamics and topography. Formation of signaling clusters was closely related to the movement and morphology of the membrane in contact with the activating surface. Our results suggest that cell membrane morphology may be a critical constraint on signaling at the cell-substrate interface.     

Criticality Is an Emergent Property of Genetic Networks that Exhibit Evolvability

Accumulating experimental evidence suggests that the gene regulatory networks of living organisms operate in the critical phase, namely, at the transition between ordered and chaotic dynamics. Such critical dynamics of the network permits the coexistence of robustness and flexibility which are necessary to ensure homeostatic stability (of a given phenotype) while allowing for switching between multiple phenotypes (network states) as occurs in development and in response to environmental change. However, the mechanisms through which genetic networks evolve such critical behavior have remained elusive. Here we present an evolutionary model in which criticality naturally emerges from the need to balance between the two essential components of evolvability: phenotype conservation and phenotype innovation under mutations. We simulated the Darwinian evolution of random Boolean networks that mutate gene regulatory interactions and grow by gene duplication. The mutating networks were subjected to selection for networks that both (i) preserve all the already acquired phenotypes (dynamical attractor states) and (ii) generate new ones. Our results show that this interplay between extending the phenotypic landscape (innovation) while conserving the existing phenotypes (conservation) suffices to cause the evolution of all the networks in a population towards criticality. Furthermore, the networks produced by this evolutionary process exhibit structures with hubs (global regulators) similar to the observed topology of real gene regulatory networks. Thus, dynamical criticality and certain elementary topological properties of gene regulatory networks can emerge as a byproduct of the evolvability of the phenotypic landscape.     

Fluctuations in continuous mammalian cell bioreactors with retention.

Continuous flow bioreactors with cell retention have been increasingly used for the cultivation of mammalian cells. The potential advantages of such bioreactors are high cell concentrations and volumetric productivities. In many reported cases, these systems have shown fluctuations in cell concentrations of various frequency and magnitude. To analyze the dynamics of the fluctuations, a model-based approach is followed. Simulations showed that large fluctuations in biomass resulted in response to fluctuations in the retention ratio when the system is operated at high dilution rate and high cell retention. The dependence of cell concentration fluctuations on variations in dilution rate and retention ratio was established by a cross-correlation statistical analysis on available experimental data. The slower dynamics and the fluctuation propensity of retention systems suggest that continuous culture without retention is more convenient for kinetic studies. In all likelihood, continuous culture with retention can be stabilized by controlling both the retention ratio and the dilution rate.