Determination of Krogh Coefficient for Oxygen Consumption Measurement from Thin Slices of Rodent Cortical Tissue Using a Fick's Law Model of Diffusion.

To investigate the impact of experimental interventions on living biological tissue, ex vivo rodent brain slices are often used as a more controllable alternative to a live animal model. However, for meaningful results, the biological sample must be known to be healthy and viable. One of the gold-standard approaches to identifying tissue viability status is to measure the rate of tissue oxygen consumption under specific controlled conditions. Here, we work with thin (400 µm) slices of mouse cortical brain tissue which are sustained by a steady flow of oxygenated artificial cerebralspinal fluid (aCSF) at room temperature. To quantify tissue oxygen consumption (Q), we measure oxygen partial pressure (pO2) as a function of probe depth. The curvature of the obtained parabolic (or parabola-like) pO2 profiles can be used to extract Q, providing one knows the Krogh coefficient Kt, for the tissue. The oxygen trends are well described by a Fick's law diffusion-consumption model developed by Ivanova and Simeonov, and expressed in terms of ratio (Q/K), being the rate of oxygen consumption in tissue divided by the Krogh coefficient (oxygen diffusivity × oxygen solubility) for tissue. If the fluid immediately adjacent to the tissue can be assumed to be stationary (i.e., nonflowing), one may invoke conservation of oxygen flux K·(∂P/∂x) across the interface to deduce (Kt/Kf), the ratio of Krogh coefficients for tissue and fluid. Using published interpolation formulas for the effect of salt content and temperature on oxygen diffusivity and solubility for pure water, we estimate Kf, the Krogh coefficient for aCSF, and hence deduce the Kt coefficient for tissue. We distinguish experimental uncertainty from natural biological variability by using pairs of repeated profiles at the same tissue location. We report a dimensionless Krogh ratio (Kt/Kf)=0.562±0.088 (mean ± SD), corresponding to a Krogh coefficient Kt=(1.29±0.21)×10-14 mol/(m·s·Pa) for mouse cortical tissue at room temperature, but acknowledge the experimental limitation of being unable to verify that the fluid boundary layer is truly stationary. We compare our results with those reported in the literature, and comment on the challenges and ambiguities caused by the extensive use of 'biologically convenient' non-SI units for tissue Krogh coefficient.

Analysis of the Hindriks and van Putten model for propofol anesthesia: Limitations and extensions.

We present a detailed analysis of the Hindriks and van Putten thalamocortical mean-field model for propofol anesthesia [NeuroImage 60(23), 2012]. The Hindriks and van Putten (HvP) model predicts increases in delta and alpha power for moderate (up to 130%) prolongation of GABAA inhibitory response, corresponding to light anesthetic sedation. Our analysis reveals that, for deeper anesthetic effect, the model exhibits an unexpected abrupt jump in cortical activity from a low-firing state to an extremely high-firing stable state (∼250 spikes/s), and remains locked there even at GABAA prolongations as high as 300% which would be expected to induce full comatose suppression of all firing activity. We demonstrate that this unphysiological behavior can be completely suppressed with appropriate tuning of the parameters controlling the sigmoidal functions that map soma voltage to firing rate for the excitatory and inhibitory neural populations, coupled with elimination of the putative population-dependent anesthetic efficacies introduced in the HvP model. The modifications reported here constrain the anesthetized brain activity into a biologically plausible range in which the cortex now has access to a moderate-firing state ("awake") and a low-firing ("anesthetized") state such that the brain can transition from "awake" to "anesthetized" states at a critical level of drug concentration. The modified HvP model predicts a drug-effect hysteresis in which the drug concentration required for induction is larger than that at emergence. In addition, the revised model shows a decrease in the intensity and frequency of alpha-band fluctuations, transitioning to delta-band dominance, with deepening anesthesia. These predicted drug concentration-dependent changes in EEG dynamics are consistent with clinical reports.

Cooperative Conformational Transitions Underpin the Activation Heat Capacity in the Temperature Dependence of Enzyme Catalysis.

Many enzymes display non-Arrhenius behavior with curved Arrhenius plots in the absence of denaturation. There has been significant debate about the origin of this behavior and recently the role of the activation heat capacity (ΔCP⧧) has been widely discussed. If enzyme-catalyzed reactions occur with appreciable negative values of ΔCP⧧ (arising from narrowing of the conformational space along the reaction coordinate), then curved Arrhenius plots are a consequence. To investigate these phenomena in detail, we have collected high precision temperature-rate data over a wide temperature interval for a model glycosidase enzyme MalL, and a series of mutants that change the temperature-dependence of the enzyme-catalyzed rate. We use these data to test a range of models including macromolecular rate theory (MMRT) and an equilibrium model. In addition, we have performed extensive molecular dynamics (MD) simulations to characterize the conformational landscape traversed by MalL in the enzyme-substrate complex and an enzyme-transition state complex. We have crystallized the enzyme in a transition state-like conformation in the absence of a ligand and determined an X-ray crystal structure at very high resolution (1.10 Å). We show (using simulation) that this enzyme-transition state conformation has a more restricted conformational landscape than the wildtype enzyme. We coin the term "transition state-like conformation (TLC)" to apply to this state of the enzyme. Together, these results imply a cooperative conformational transition between an enzyme-substrate conformation (ES) and a transition-state-like conformation (TLC) that precedes the chemical step. We present a two-state model as an extension of MMRT (MMRT-2S) that describes the data along with a convenient approximation with linear temperature dependence of the activation heat capacity (MMRT-1L) that can be used where fewer data points are available. Our model rationalizes disparate behavior seen for MalL and previous results for a thermophilic alcohol dehydrogenase and is consistent with a raft of data for other enzymes. Our model can be used to characterize the conformational changes required for enzyme catalysis and provides insights into the role of cooperative conformational changes in transition state stabilization that are accompanied by changes in heat capacity for the system along the reaction coordinate. TLCs are likely to be of wide importance in understanding the temperature dependence of enzyme activity and other aspects of enzyme catalysis.

Evidence for a short-lived resonance state in enzyme catalysis via rate-equation convolution.

At the cellular level, all biological function relies on enzymes to provide catalytic acceleration of essential biochemical processes driving cellular metabolism. The enzyme is presumed to lower the activation energy barrier separating reactants from products, but the precise mechanism remains unresolved. Here we examine the temperature dependence of the enzyme-catalyzed dissociation of p-nitrophenyl-α-D-glucopyranoside (pNPG), a chromogenic analog for maltose, isomaltose, and sucrose disaccharide sugars, into p-nitrophenol (pNP) and glucose (monosaccharide). The enzymes of interest are the wild type and mutant forms of glucosidase MalL produced by the probiotic bacterium Bacillus subtilis. The per-enzyme production rates k(T) for the pNPG→ glucose reaction all show a characteristic temperature profile with an Arrhenius-like (approximately exponential) slow acceleration at low temperatures, rising through a point of inflexion to reach a maximum, then turning over to decline steeply towards zero production at high temperatures. This asymmetric profile is found to be well fitted by convolving an exponential growth function f(T) with a Gaussian temperature distribution g(T) to produce an exponentially modified Gaussian function h(T). To give a physical interpretation of the convolution components, we make the temperature mapping Θ≡T_{ref}-T where T_{ref} marks the temperature at which a given mutant becomes fully denatured (unfolded) and therefore inactive, then convert the convolution components to probability density functions which obey the convolution theorem of statistics. Working in Θ space, we identify f(Θ) as the density function for an Arrhenius-like transition from ground-state A to metastable-state B, and g(Θ) as the Gaussian distribution of offset-temperature fluctuations for the metastable state. By mapping the standard thermodynamic relations for temperature and energy fluctuations to the enzyme frame of reference, we are able to derive an expression for the lifetime for the metastable B state. For the 15 enzyme experiments, we obtain a mean value 〈Δt〉≳(29.0±1.3)×10^{-15}s, in remarkably good agreement with the ∼30-fs estimate for the period of glycosidic bond oscillations extracted from published infrared spectroscopy. We suggest that the metastable B state provides a low-energy target that has the effect of lowering the activation energy barrier by presenting an alternative axis for the reaction coordinate.

The molecular dynamics of possible inhibitors for SARS-CoV-2.

The novel coronavirus SARS-CoV-2, responsible for the present COVID-19 global pandemic, is known to bind to the angiotensin converting enzyme-2 (ACE2) receptor in human cells. A possible treatment of COVID-19 could involve blocking ACE2 and/or disabling the spike protein on the virus. Here, molecular dynamics simulations were performed to test the binding affinities of nine candidate compounds. Of these, three drugs showed significant therapeutic potential that warrant further investigation: SN35563, a ketamine ester analogue, was found to bind strongly to the ACE2 receptor but weakly within the spike receptor-binding domain (RBD); in contrast, arbidol and hydroxychloroquine bound preferentially with the spike RBD rather than ACE2. A fourth drug, remdesivir, bound approximately equally to both the ACE2 and viral spike RBD, thus potentially increasing risk of viral infection by bringing the spike protein into closer proximity to the ACE2 receptor. We suggest more experimental investigations to test that SN35563-in combination with arbidol or hydroxychloroquine-might act synergistically to block viral cell entry by providing therapeutic blockade of the host ACE2 simultaneous with reduction of viral spike receptor-binding; and that this combination therapy would allow the use of smaller doses of each drug.Communicated by Ramaswamy H. Sarma.

A mechanism for ultra-slow oscillations in the cortical default network.

When the brain is in its noncognitive "idling" state, functional MRI measurements reveal the activation of default cortical networks whose activity is suppressed during cognitive processing. This default or background mode is characterized by ultra-slow BOLD oscillations (∼0.05 Hz), signaling extremely slow cycling in cortical metabolic demand across distinct cortical regions. Here we describe a model of the cortex which predicts that slow cycling of cortical activity can arise naturally as a result of nonlinear interactions between temporal (Hopf) and spatial (Turing) instabilities. The Hopf instability is triggered by delays in the inhibitory postsynaptic response, while the Turing instability is precipitated by increases in the strength of the gap-junction coupling between interneurons. We comment on possible implications for slow dendritic computation and information processing.

An analysis of the transitions between down and up states of the cortical slow oscillation under urethane anaesthesia.

We study the dynamics of the transition between the low- and high-firing states of the cortical slow oscillation by using intracellular recordings of the membrane potential from cortical neurons of rats. We investigate the evidence for a bistability in assemblies of cortical neurons playing a major role in the maintenance of this oscillation. We show that the trajectory of a typical transition takes an approximately exponential form, equivalent to the response of a resistor-capacitor circuit to a step-change in input. The time constant for the transition is negatively correlated with the membrane potential of the low-firing state, and values are broadly equivalent to neural time constants measured elsewhere. Overall, the results do not strongly support the hypothesis of a bistability in cortical neurons; rather, they suggest the cortical manifestation of the oscillation is a result of a step-change in input to the cortical neurons. Since there is evidence from previous work that a phase transition exists, we speculate that the step-change may be a result of a bistability within other brain areas, such as the thalamus, or a bistability among only a small subset of cortical neurons, or as a result of more complicated brain dynamics.

Efficacy of three neuroprotective drugs in secondary progressive multiple sclerosis (MS-SMART): a phase 2b, multiarm, double-blind, randomised placebo-controlled trial.

BACKGROUND: Neurodegeneration is the pathological substrate that causes major disability in secondary progressive multiple sclerosis. A synthesis of preclinical and clinical research identified three neuroprotective drugs acting on different axonal pathobiologies. We aimed to test the efficacy of these drugs in an efficient manner with respect to time, cost, and patient resource. METHODS: We did a phase 2b, multiarm, parallel group, double-blind, randomised placebo-controlled trial at 13 clinical neuroscience centres in the UK. We recruited patients (aged 25-65 years) with secondary progressive multiple sclerosis who were not on disease-modifying treatment and who had an Expanded Disability Status Scale (EDSS) score of 4·0-6·5. Participants were randomly assigned (1:1:1:1) at baseline, by a research nurse using a centralised web-based service, to receive twice-daily oral treatment of either amiloride 5 mg, fluoxetine 20 mg, riluzole 50 mg, or placebo for 96 weeks. The randomisation procedure included minimisation based on sex, age, EDSS score at randomisation, and trial site. Capsules were identical in appearance to achieve masking. Patients, investigators, and MRI readers were unaware of treatment allocation. The primary outcome measure was volumetric MRI percentage brain volume change (PBVC) from baseline to 96 weeks, analysed using multiple regression, adjusting for baseline normalised brain volume and minimisation criteria. The primary analysis was a complete-case analysis based on the intention-to-treat population (all patients with data at week 96). This trial is registered with ClinicalTrials.gov, NCT01910259. FINDINGS: Between Jan 29, 2015, and June 22, 2016, 445 patients were randomly allocated amiloride (n=111), fluoxetine (n=111), riluzole (n=111), or placebo (n=112). The primary analysis included 393 patients who were allocated amiloride (n=99), fluoxetine (n=96), riluzole (n=99), and placebo (n=99). No difference was noted between any active treatment and placebo in PBVC (amiloride vs placebo, 0·0% [95% CI -0·4 to 0·5; p=0·99]; fluoxetine vs placebo -0·1% [-0·5 to 0·3; p=0·86]; riluzole vs placebo -0·1% [-0·6 to 0·3; p=0·77]). No emergent safety issues were reported. The incidence of serious adverse events was low and similar across study groups (ten [9%] patients in the amiloride group, seven [6%] in the fluoxetine group, 12 [11%] in the riluzole group, and 13 [12%] in the placebo group). The most common serious adverse events were infections and infestations. Three patients died during the study, from causes judged unrelated to active treatment; one patient assigned amiloride died from metastatic lung cancer, one patient assigned riluzole died from ischaemic heart disease and coronary artery thrombosis, and one patient assigned fluoxetine had a sudden death (primary cause) with multiple sclerosis and obesity listed as secondary causes. INTERPRETATION: The absence of evidence for neuroprotection in this adequately powered trial indicates that exclusively targeting these aspects of axonal pathobiology in patients with secondary progressive multiple sclerosis is insufficient to mitigate neuroaxonal loss. These findings argue for investigation of different mechanistic targets and future consideration of combination treatment trials. This trial provides a template for future simultaneous testing of multiple disease-modifying medicines in neurological medicine. FUNDING: Efficacy and Mechanism Evaluation (EME) Programme, an MRC and NIHR partnership, UK Multiple Sclerosis Society, and US National Multiple Sclerosis Society.

Modeling brain activation patterns for the default and cognitive states.

We argue that spatial patterns of cortical activation observed with EEG, MEG and fMRI might arise from spontaneous self-organisation of interacting populations of excitatory and inhibitory neurons. We examine the dynamical behavior of a mean-field cortical model that includes chemical and electrical (gap-junction) synapses, focusing on two limiting cases: the "slow-soma" limit with slow voltage feedback from soma to dendrite, and the "fast-soma" limit in which the feedback action of soma voltage onto dendrite reversal potentials is instantaneous. For slow soma-dendrite feedback, we find a low-frequency (approximately 1 Hz) dynamic Hopf instability, and a stationary Turing instability that catalyzes formation of patterned distributions of cortical firing-rate activity with pattern wavelength approximately 2 cm. Turing instability can only be triggered when gap-junction diffusion between inhibitory neurons is strong, but patterning is destroyed if the tonic level of subcortical excitation is raised sufficiently. Interaction between the Hopf and Turing instabilities may describe the non-cognitive background or "default" state of the brain, as observed by BOLD imaging. In the fast-soma limit, the model predicts a high-frequency Hopf (approximately 35 Hz) instability, and a traveling-wave gamma-band instability that manifests as a 2-D standing-wave pattern oscillating in place at approximately 30 Hz. Small levels of inhibitory diffusion enhance and broaden the definition of the gamma antinodal regions by suppressing higher-frequency spatial modes, but gamma emergence is not contingent on the presence of inhibitory gap junctions; higher levels of diffusion suppress gamma activity. Fast-soma instabilities are enhanced by increased subcortical stimulation. Prompt soma-dendrite feedback may be an essential component of the genesis and large-scale cortical synchrony of gamma activity observed at the point of cognition.

Excitatory effects of gap junction blockers on cerebral cortex seizure-like activity in rats and mice.

PURPOSE: The role of gap junctions in seizures is an area of intense research. Many groups have reported anticonvulsant effects of gap junction blockade, strengthening the case for a role for gap junctions in ictogenesis. The cerebral cortex is underrepresented in this body of research. We have investigated the effect of gap junction blockade on seizure-like activity in rat and mouse cerebral cortex slices. METHODS: Seizure-like activity was induced by perfusing with low-magnesium artificial cerebrospinal fluid. The effect of three gap junction blockers was investigated in rat cortical slices; quinine (200 and 400 microm), quinidine (100 and 200 microm), and carbenoxolone (100 and 200 microm). In addition, the effect of mefloquine was investigated in wild-type mice and connexin36 knockout mice. The data were analyzed for the effect on frequency and amplitude of seizure-like events. RESULTS: Paradoxical excitatory effects on seizure-like activity were observed for all three agents in rat cortical slices. Quinine (200 microm) and carbenoxolone (100 microm) increased both the frequency and amplitude of seizure-like events. Quinidine (100 microm) increased the frequency of events. Higher doses of quinine (400 microm) and carbenoxolone (200 microm) had biphasic excitatory-inhibitory effects. Similar excitatory effects were observed in adult wild-type mouse cortical slices perfused with mefloquine (5 microm or 10 microm), but were absent in slices from connexin36-deficient mice. DISCUSSION: In conclusion, we have shown a paradoxical proseizure effect of pharmacologic gap junction blockade in a cortical model of seizure-like activity. We suggest that this effect is probably due to a disruption of inhibitory interneuron coupling secondary to connexin36 blockade.

The electrocortical effects of enflurane: experiment and theory.

BACKGROUND: High concentrations of enflurane will induce a characteristic electroencephalogram pattern consisting of periods of suppression alternating with large short paroxysmal epileptiform discharges (PEDs). In this study, we compared a theoretical computer model of this activity with real local field potential (LFP) data obtained from anesthetized rats. METHODS: After implantation of a high-density 8 x 8 electrode array in the visual cortex, the patterns of LFP and multiunit spike activity were recorded in rats during 0.5, 1.0, 1.5, and 2.0 minimum alveolar anesthetic concentration (MAC) enflurane anesthesia. These recordings were compared with computer simulations from a mean field model of neocortical dynamics. The neuronal effect of increasing enflurane concentration was simulated by prolonging the decay time constant of the inhibitory postsynaptic potential (IPSP). The amplitude of the excitatory postsynaptic potential (EPSP) was modulated, inverse to the neocortical firing rate. RESULTS: In the anesthetized rats, increasing enflurane concentrations consistently caused the appearance of suppression pattern (>1.5 MAC) in the LFP recordings. The mean rate of multiunit spike activity decreased from 2.54/s (0.5 MAC) to 0.19/s (2.0 MAC). At high MAC, the majority of the multiunit action potential events became synchronous with the PED. In the theoretical model, prolongation of the IPSP decay time and activity-dependent EPSP modulation resulted in output that was similar in morphology to that obtained from the experimental data. The propensity for rhythmic seizure-like activity in the model could be determined by analysis of the eigenvalues of the equations. CONCLUSION: It is possible to use a mean field theory of neocortical dynamics to replicate the PED pattern observed in LFPs in rats under enflurane anesthesia. This pattern requires a combination of a moderately increased total area under the IPSP, prolonged IPSP decay time, and also activity-dependent modulation of EPSP amplitude.

Spinodal decomposition in a mean-field model of the cortex: Emergence of hexagonally symmetric activation patterns.

Spinodal decomposition is a well-known pattern-forming mechanism in metallurgic alloys, semiconductor crystals, and colloidal gels. In metallurgy, if a heated sample of a homogeneous Zn-Al alloy is suddenly quenched below a critical temperature, then the sample can spontaneously precipitate into inhomogenous textures of Zn- and Al-rich regions with significantly altered material properties such as ductility and hardness. Here we report on our recent discovery that a two-dimensional model of the human cortex with inhibitory diffusion can, under particular homogeneous initial conditions, exhibit a form of nonconserved spinodal decomposition in which regions of the cortex self-organize into hexagonally distributed binary patches of activity and inactivity. Fine-scale patterns precipitate rapidly, and then the dynamics slows to render coarser-scale shapes which can ripen into a range of slowly evolving patterns including mazelike labyrinths, hexagonal islands and continents, nucleating "mitotic cells" which grow to a critical size then subdivide, and inverse nucleations in which quiescent islands are surrounded by a sea of activity. One interesting class of activity coalesces into a soliton-like narrow ribbon of depolarization that traverses the cortex at ∼4cm/s. We speculate that this may correspond to the thus far unexplained interictal waves of cortical activation that precede grand-mal seizure in an epileptic event. We note that spinodal decomposition is quite distinct from the Turing mechanism for symmetry breaking in cortex investigated in earlier work by the authors [Steyn-Ross et al., Phys. Rev. E 76, 011916 (2007)PLEEE81539-375510.1103/PhysRevE.76.011916].

Anesthesia modifies subthreshold critical slowing down in a stochastic Hodgkin-Huxley-like model with inhibitory synaptic input.

The dynamics of a stochastic type-I Hodgkin-Huxley-like point neuron model exposed to inhibitory synaptic noise are investigated as a function of distance from spiking threshold and the inhibitory influence of the general anesthetic agent propofol. The model is biologically motivated and includes the effects of intrinsic ion-channel noise via a stochastic differential equation description as well as inhibitory synaptic noise modeled as multiple Poisson-distributed impulse trains with saturating response functions. The effect of propofol on these synapses is incorporated through this drug's principal influence on fast inhibitory neurotransmission mediated by γ-aminobutyric acid (GABA) type-A receptors via reduction of the synaptic response decay rate. As the neuron model approaches spiking threshold from below, we track membrane voltage fluctuation statistics of numerically simulated stochastic trajectories. We find that for a given distance from spiking threshold, increasing the magnitude of anesthetic-induced inhibition is associated with augmented signatures of critical slowing: fluctuation amplitudes and correlation times grow as spectral power is increasingly focused at 0 Hz. Furthermore, as a function of distance from threshold, anesthesia significantly modifies the power-law exponents for variance and correlation time divergences observable in stochastic trajectories. Compared to the inverse square root power-law scaling of these quantities anticipated for the saddle-node bifurcation of type-I neurons in the absence of anesthesia, increasing anesthetic-induced inhibition results in an observable exponent <-0.5 for variance and >-0.5 for correlation time divergences. However, these behaviors eventually break down as distance from threshold goes to zero with both the variance and correlation time converging to common values independent of anesthesia. Compared to the case of no synaptic input, linearization of an approximating multivariate Ornstein-Uhlenbeck model reveals these effects to be the consequence of an additional slow eigenvalue associated with synaptic activity that competes with those of the underlying point neuron in a manner that depends on distance from spiking threshold.

Multiple Sclerosis-Secondary Progressive Multi-Arm Randomisation Trial (MS-SMART): a multiarm phase IIb randomised, double-blind, placebo-controlled clinical trial comparing the efficacy of three neuroprotective drugs in secondary progressive multiple sclerosis.

INTRODUCTION: The major unmet need in multiple sclerosis (MS) is for neuroprotective therapies that can slow (or ideally stop) the rate of disease progression. The UK MS Society Clinical Trials Network (CTN) was initiated in 2007 with the purpose of developing a national, efficient, multiarm trial of repurposed drugs. Key underpinning work was commissioned by the CTN to inform the design, outcome selection and drug choice including animal models and a systematic review. This identified seven leading oral agents for repurposing as neuroprotective therapies in secondary progressive MS (SPMS). The purpose of the Multiple Sclerosis-Secondary Progressive Multi-Arm Randomisation Trial (MS-SMART) will be to evaluate the neuroprotective efficacy of three of these drugs, selected with distinct mechanistic actions and previous evidence of likely efficacy, against a common placebo arm. The interventions chosen were: amiloride (acid-sensing ion channel antagonist); fluoxetine (selective serotonin reuptake inhibitor) and riluzole (glutamate antagonist). METHODS AND ANALYSIS: Patients with progressing SPMS will be randomised 1:1:1:1 to amiloride, fluoxetine, riluzole or matched placebo and followed for 96 weeks. The primary outcome will be the percentage brain volume change (PBVC) between baseline and 96 weeks, derived from structural MR brain imaging data using the Structural Image Evaluation, using Normalisation, of Atrophy method. With a sample size of 90 per arm, this will give 90% power to detect a 40% reduction in PBVC in any active arm compared with placebo and 80% power to detect a 35% reduction (analysing by analysis of covariance and with adjustment for multiple comparisons of three 1.67% two-sided tests), giving a 5% overall two-sided significance level. MS-SMART is not powered to detect differences between the three active treatment arms. Allowing for a 20% dropout rate, 110 patients per arm will be randomised. The study will take place at Neuroscience centres in England and Scotland. ETHICS AND DISSEMINATION: MS-SMART was approved by the Scotland A Research Ethics Committee on 13 January 2013 (REC reference: 13/SS/0007). Results of the study will be submitted for publication in a peer-reviewed journal. TRIAL REGISTRATION NUMBERS: NCT01910259; 2012-005394-31; ISRCTN28440672.

Gap junctions mediate large-scale Turing structures in a mean-field cortex driven by subcortical noise.

One of the grand puzzles in neuroscience is establishing the link between cognition and the disparate patterns of spontaneous and task-induced brain activity that can be measured clinically using a wide range of detection modalities such as scalp electrodes and imaging tomography. High-level brain function is not a single-neuron property, yet emerges as a cooperative phenomenon of multiply-interacting populations of neurons. Therefore a fruitful modeling approach is to picture the cerebral cortex as a continuum characterized by parameters that have been averaged over a small volume of cortical tissue. Such mean-field cortical models have been used to investigate gross patterns of brain behavior such as anesthesia, the cycles of natural sleep, memory and erasure in slow-wave sleep, and epilepsy. There is persuasive and accumulating evidence that direct gap-junction connections between inhibitory neurons promote synchronous oscillatory behavior both locally and across distances of some centimeters, but, to date, continuum models have ignored gap-junction connectivity. In this paper we employ simple mean-field arguments to derive an expression for D2, the diffusive coupling strength arising from gap-junction connections between inhibitory neurons. Using recent neurophysiological measurements reported by Fukuda [J. Neurosci. 26, 3434 (2006)], we estimate an upper limit of D2 approximately 0.6cm2. We apply a linear stability analysis to a standard mean-field cortical model, augmented with gap-junction diffusion, and find this value for the diffusive coupling strength to be close to the critical value required to destabilize the homogeneous steady state. Computer simulations demonstrate that larger values of D2 cause the noise-driven model cortex to spontaneously crystalize into random mazelike Turing structures: centimeter-scale spatial patterns in which regions of high-firing activity are intermixed with regions of low-firing activity. These structures are consistent with the spatial variations in brain activity patterns detected with the BOLD (blood oxygen-level-dependent) signal detected with magnetic resonance imaging, and may provide a natural substrate for synchronous gamma-band rhythms observed across separated EEG (electroencephalogram) electrodes.

White-noise susceptibility and critical slowing in neurons near spiking threshold.

We present mathematical and simulation analyses of the below-threshold noisy response of two biophysically motivated models for excitable membrane due to H. R. Wilson: a squid axon ("resonator") and a human cortical neuron ("integrator"). When stimulated with a low-intensity white noise superimposed on a dc control current, both membrane types generate voltage fluctuations that exhibit critical slowing down--that is, the voltage responsiveness to noisy input currents grows in amplitude while slowing in frequency--as the membrane approaches spiking threshold from below. We define threshold unambiguously as that dc current that renders a zero real eigenvalue for the Jacobian matrix for the integrator neuron, and, for the resonator neuron, as the dc current that gives a complex eigenvalue pair whose real part is zero. Using a linear Ornstein-Uhlenbeck analysis, we give exact small-noise expressions for the variance, power spectrum, and correlation function of the voltage fluctuations, and we derive the scaling laws for the divergence of susceptibility and correlation times for approach to threshold. We compare these predictions with numerical simulations of the nonlinear stochastic equations, and demonstrate that, provided the white-noise perturbations are kept sufficiently small, the linearized theory works well. These predictions should be testable in the laboratory using a current-clamped cell configuration. If confirmed, then the proximity of a neuron to its spike-transition point can be judged by measuring its subthreshold susceptibility to white-noise stimulation. We postulate that such temporally correlated fluctuations could provide a means of subthreshold signaling via gap-junction connections with neighboring neurons.

From individual spiking neurons to population behavior: Systematic elimination of short-wavelength spatial modes.

Mean-field models of the brain approximate spiking dynamics by assuming that each neuron responds to its neighbors via a naive spatial average that neglects local fluctuations and correlations in firing activity. In this paper we address this issue by introducing a rigorous formalism to enable spatial coarse-graining of spiking dynamics, scaling from the microscopic level of a single type 1 (integrator) neuron to a macroscopic assembly of spiking neurons that are interconnected by chemical synapses and nearest-neighbor gap junctions. Spiking behavior at the single-neuron scale ℓ≈10µm is described by Wilson's two-variable conductance-based equations [H. R. Wilson, J. Theor. Biol. 200, 375 (1999)], driven by fields of incoming neural activity from neighboring neurons. We map these equations to a coarser spatial resolution of grid length Bℓ, with B≫1 being the blocking ratio linking micro and macro scales. Our method systematically eliminates high-frequency (short-wavelength) spatial modes q(->) in favor of low-frequency spatial modes Q(->) using an adiabatic elimination procedure that has been shown to be equivalent to the path-integral coarse graining applied to renormalization group theory of critical phenomena. This bottom-up neural regridding allows us to track the percolation of synaptic and ion-channel noise from the single neuron up to the scale of macroscopic population-average variables. Anticipated applications of neural regridding include extraction of the current-to-firing-rate transfer function, investigation of fluctuation criticality near phase-transition tipping points, determination of spatial scaling laws for avalanche events, and prediction of the spatial extent of self-organized macrocolumnar structures. As a first-order exemplar of the method, we recover nonlinear corrections for a coarse-grained Wilson spiking neuron embedded in a network of identical diffusively coupled neurons whose chemical synapses have been disabled. Intriguingly, we find that reblocking transforms the original type 1 Wilson integrator into a type 2 resonator whose spike-rate transfer function exhibits abrupt spiking onset with near-vertical takeoff and chaotic dynamics just above threshold.

Which System Variables Carry Robust Early Signs of Upcoming Phase Transition? An Ecological Example.

Growth of critical fluctuations prior to catastrophic state transition is generally regarded as a universal phenomenon, providing a valuable early warning signal in dynamical systems. Using an ecological fisheries model of three populations (juvenile prey J, adult prey A and predator P), a recent study has reported silent early warning signals obtained from P and A populations prior to saddle-node (SN) bifurcation, and thus concluded that early warning signals are not universal. By performing a full eigenvalue analysis of the same system we demonstrate that while J and P populations undergo SN bifurcation, A does not jump to a new state, so it is not expected to carry early warning signs. In contrast with the previous study, we capture a significant increase in the noise-induced fluctuations in the P population, but only on close approach to the bifurcation point; it is not clear why the P variance initially shows a decaying trend. Here we resolve this puzzle using observability measures from control theory. By computing the observability coefficient for the system from the recordings of each population considered one at a time, we are able to quantify their ability to describe changing internal dynamics. We demonstrate that precursor fluctuations are best observed using only the J variable, and also P variable if close to transition. Using observability analysis we are able to describe why a poorly observable variable (P) has poor forecasting capabilities although a full eigenvalue analysis shows that this variable undergoes a bifurcation. We conclude that observability analysis provides complementary information to identify the variables carrying early-warning signs about impending state transition.

Modelling general anaesthesia as a first-order phase transition in the cortex.

Since 1997 we have been developing a theoretical foundation for general anaesthesia. We have been able to demonstrate that the abrupt change in brain state brought on by anaesthetic drugs can be characterized as a first-order phase transition in the population-average membrane voltage of the cortical neurons. The theory predicts that, as the critical point of phase change into unconsciousness is approached, the electrical fluctuations in cortical activity will grow strongly in amplitude while slowing in frequency, becoming more correlated both in time and in space. Thus the bio-electrical change of brain-state has deep similarities with thermodynamic phase changes of classical physics. The theory further predicts the existence of a second critical point, hysteretically separated from the first, corresponding to the return path from comatose unconsciousness back to normal responsiveness. There is a steadily accumulating body of clinical evidence in support of all of the phase-transition predictions: low-frequency power surge in EEG activity; increased correlation time and correlation length in EEG fluctuations; hysteresis separation, with respect to drug concentration, between the point of induction and the point of emergence.

Proposed mechanism for learning and memory erasure in a white-noise-driven sleeping cortex.

Understanding the structure and purpose of sleep remains one of the grand challenges of neurobiology. Here we use a mean-field linearized theory of the sleeping cortex to derive statistics for synaptic learning and memory erasure. The growth in correlated low-frequency high-amplitude voltage fluctuations during slow-wave sleep (SWS) is characterized by a probability density function that becomes broader and shallower as the transition into rapid-eye-movement (REM) sleep is approached. At transition, the Shannon information entropy of the fluctuations is maximized. If we assume Hebbian-learning rules apply to the cortex, then its correlated response to white-noise stimulation during SWS provides a natural mechanism for a synaptic weight change that will tend to shut down reverberant neural activity. In contrast, during REM sleep the weights will evolve in a direction that encourages excitatory activity. These entropy and weight-change predictions lead us to identify the final portion of deep SWS that occurs immediately prior to transition into REM sleep as a time of enhanced erasure of labile memory. We draw a link between the sleeping cortex and Landauer's dissipation theorem for irreversible computing [R. Landauer, IBM J. Res. Devel. 5, 183 (1961)], arguing that because information erasure is an irreversible computation, there is an inherent entropy cost as the cortex transits from SWS into REM sleep.