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Background: The brain reserve hypothesis posits that larger maximal lifetime brain growth (MLBG) may confer protection against physical disability in multiple sclerosis (MS). Larger MLBG as a proxy for brain reserve, has been associated with reduced progression of physical disability in patients with early MS; however, it is unknown whether this association remains once in the secondary progressive phase of MS (SPMS). Our aim was to assess whether larger MLBG is associated with decreased physical disability progression in SPMS. Methods: We conducted a post hoc analysis of participants in the MS-Secondary Progressive Multi-Arm Randomisation Trial (NCT01910259), a multicentre randomised placebo-controlled trial of the neuroprotective potential of three agents in SPMS. Physical disability was measured by Expanded Disability Status Scale (EDSS), 9-hole peg test (9HPT) and 25-foot timed walk test (T25FW) at baseline, 48 and 96 weeks. MLBG was estimated by baseline intracranial volume (ICV). Multivariable time-varying Cox regression models were used to investigate the association between MLBG and physical disability progression. Results: 383 participants (mean age 54.5 years, 298 female) were followed up over 96 weeks. Median baseline EDSS was 6.0 (range 4.0-6.5). Adjusted for covariates, larger MLBG was associated with a reduced risk of EDSS progression (HR 0.84,95% CI:0.72 to 0.99;p=0.04). MLBG was not independently associated with time to progression as measured by 9HPT or T25FW. Conclusion: Larger MLBG is independently associated with physical disability progression over 96 weeks as measured by EDSS in SPMS. This suggests that MLBG as a proxy for brain reserve may continue to confer protection against disability when in the secondary progression phase of MS. Trail registration number: NCT01910259.
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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.
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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 pNPGâ 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 ãΔtãâ³(29.0±1.3)×10^{-15}s, in remarkably good agreement with the â¼30-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.
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Glucosa , Calor , Temperatura , Termodinámica , Catálisis , CinéticaRESUMEN
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.
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Oxígeno , Roedores , Animales , Ratones , Difusión , Pruebas de Función Respiratoria , Consumo de OxígenoRESUMEN
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.
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Enzima Convertidora de Angiotensina 2 , Antivirales , Receptores Virales , SARS-CoV-2 , Glicoproteína de la Espiga del Coronavirus , Humanos , Enzima Convertidora de Angiotensina 2/antagonistas & inhibidores , Enzima Convertidora de Angiotensina 2/química , Sitios de Unión , COVID-19 , Hidroxicloroquina/farmacología , Simulación de Dinámica Molecular , Unión Proteica , Receptores Virales/antagonistas & inhibidores , Receptores Virales/química , SARS-CoV-2/efectos de los fármacos , Glicoproteína de la Espiga del Coronavirus/antagonistas & inhibidores , Glicoproteína de la Espiga del Coronavirus/química , Antivirales/farmacologíaRESUMEN
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 (â¼250 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.
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Anestésicos Intravenosos/farmacología , Corteza Cerebral/efectos de los fármacos , Modelos Neurológicos , Red Nerviosa/efectos de los fármacos , Inhibición Neural/efectos de los fármacos , Neuronas/efectos de los fármacos , Propofol/farmacología , Corteza Cerebral/fisiología , Humanos , Red Nerviosa/fisiología , Inhibición Neural/fisiología , Neuronas/fisiologíaRESUMEN
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.
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Esclerosis Múltiple Crónica Progresiva/tratamiento farmacológico , Fármacos Neuroprotectores/uso terapéutico , Administración Oral , Adulto , Amilorida/uso terapéutico , Encéfalo , Progresión de la Enfermedad , Método Doble Ciego , Femenino , Fluoxetina/uso terapéutico , Humanos , Imagen por Resonancia Magnética , Masculino , Persona de Mediana Edad , Esclerosis Múltiple/tratamiento farmacológico , Riluzol/uso terapéutico , Resultado del TratamientoRESUMEN
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 â¼4cm/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].
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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.
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Amilorida/uso terapéutico , Fluoxetina/uso terapéutico , Esclerosis Múltiple Crónica Progresiva/tratamiento farmacológico , Fármacos Neuroprotectores/uso terapéutico , Riluzol/uso terapéutico , Adulto , Método Doble Ciego , Femenino , Humanos , Masculino , Persona de Mediana Edad , Resultado del TratamientoRESUMEN
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.
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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.
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Ecología , Peces , Modelos Teóricos , AnimalesRESUMEN
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 â≈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 Bâ, with Bâ«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.
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Modelos Neurológicos , Neuronas/citología , Membrana Celular/metabolismo , Difusión , Fenómenos Electrofisiológicos , Uniones Comunicantes/metabolismoRESUMEN
The dynamics of a spiking neuron approaching threshold is investigated in the framework of Markov-chain models describing the random state-transitions of the underlying ion-channel proteins. We characterize subthreshold channel-noise-induced transmembrane potential fluctuations in both type-I (integrator) and type-II (resonator) parametrizations of the classic conductance-based Hodgkin-Huxley equations. As each neuron approaches spiking threshold from below, numerical simulations of stochastic trajectories demonstrate pronounced growth in amplitude simultaneous with decay in frequency of membrane voltage fluctuations induced by ion-channel state transitions. To explore this progression of fluctuation statistics, we approximate the exact Markov treatment with a 12-variable channel-based stochastic differential equation (SDE) and its Ornstein-Uhlenbeck (OU) linearization and show excellent agreement between Markov and SDE numerical simulations. Predictions of the OU theory with respect to membrane potential fluctuation variance, autocorrelation, correlation time, and spectral density are also in agreement and illustrate the close connection between the eigenvalue structure of the associated deterministic bifurcations and the observed behavior of the noisy Markov traces on close approach to threshold for both integrator and resonator point-neuron varieties.
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Modelos Neurológicos , Neuronas/citología , Neuronas/metabolismo , Canales Iónicos/metabolismo , Cadenas de Markov , Procesos EstocásticosRESUMEN
The Wilson-Cowan neural field equations describe the dynamical behavior of a 1-D continuum of excitatory and inhibitory cortical neural aggregates, using a pair of coupled integro-differential equations. Here we use bifurcation theory and small-noise linear stochastics to study the range of a phase transitions-sudden qualitative changes in the state of a dynamical system emerging from a bifurcation-accessible to the Wilson-Cowan network. Specifically, we examine saddle-node, Hopf, Turing, and Turing-Hopf instabilities. We introduce stochasticity by adding small-amplitude spatio-temporal white noise, and analyze the resulting subthreshold fluctuations using an Ornstein-Uhlenbeck linearization. This analysis predicts divergent changes in correlation and spectral characteristics of neural activity during close approach to bifurcation from below. We validate these theoretical predictions using numerical simulations. The results demonstrate the role of noise in the emergence of critically slowed precursors in both space and time, and suggest that these early-warning signals are a universal feature of a neural system close to bifurcation. In particular, these precursor signals are likely to have neurobiological significance as early warnings of impending state change in the cortex. We support this claim with an analysis of the in vitro local field potentials recorded from slices of mouse-brain tissue. We show that in the period leading up to emergence of spontaneous seizure-like events, the mouse field potentials show a characteristic spectral focusing toward lower frequencies concomitant with a growth in fluctuation variance, consistent with critical slowing near a bifurcation point. This observation of biological criticality has clear implications regarding the feasibility of seizure prediction.
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Characterizing brain dynamics during anesthesia is a main current challenge in anesthesia study. Several single channel electroencephalogram (EEG)-based commercial monitors like the Bispectral index (BIS) have suggested to examine EEG signal. But, the BIS index has obtained numerous critiques. In this study, we evaluate the concentration-dependent effect of the propofol on long-range frontal-temporal synchronization of EEG signals collected from eight subjects during a controlled induction and recovery design. We used order patterns cross recurrence plot and provide an index named order pattern laminarity (OPL) to assess changes in neuronal synchronization as the mechanism forming the foundation of conscious perception. The prediction probability of 0.9 and 0.84 for OPL and BIS specified that the OPL index correlated more strongly with effect-site propofol concentration. Also, our new index makes faster reaction to transients in EEG recordings based on pharmacokinetic and pharmacodynamic model parameters and demonstrates less variability at the point of loss of consciousness (standard deviation of 0.04 for OPL compared with 0.09 for BIS index). The result show that the OPL index can estimate anesthetic state of patient more efficiently than the BIS index in lightly sedated state with more tolerant of artifacts.
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Anestesia , Anestésicos Intravenosos , Sincronización de Fase en Electroencefalografía/fisiología , Propofol , Adolescente , Adulto , Periodo de Recuperación de la Anestesia , Anestésicos Intravenosos/farmacocinética , Sedación Consciente , Monitores de Conciencia , Relación Dosis-Respuesta a Droga , Femenino , Humanos , Masculino , Neuronas/fisiología , Percepción/fisiología , Propofol/farmacocinética , Adulto JovenRESUMEN
The electroencephalogram (EEG) patterns recorded during general anesthetic-induced coma are closely similar to those seen during slow-wave sleep, the deepest stage of natural sleep; both states show patterns dominated by large amplitude slow waves. Slow oscillations are believed to be important for memory consolidation during natural sleep. Tracking the emergence of slow-wave oscillations during transition to unconsciousness may help us to identify drug-induced alterations of the underlying brain state, and provide insight into the mechanisms of general anesthesia. Although cellular-based mechanisms have been proposed, the origin of the slow oscillation has not yet been unambiguously established. A recent theoretical study by Steyn-Ross et al. (2013) proposes that the slow oscillation is a network, rather than cellular phenomenon. Modeling anesthesia as a moderate reduction in gap-junction interneuronal coupling, they predict an unconscious state signposted by emergent low-frequency oscillations with chaotic dynamics in space and time. They suggest that anesthetic slow-waves arise from a competitive interaction between symmetry-breaking instabilities in space (Turing) and time (Hopf), modulated by gap-junction coupling strength. A significant prediction of their model is that EEG phase coherence will decrease as the cortex transits from Turing-Hopf balance (wake) to Hopf-dominated chaotic slow-waves (unconsciousness). Here, we investigate changes in phase coherence during induction of general anesthesia. After examining 128-channel EEG traces recorded from five volunteers undergoing propofol anesthesia, we report a significant drop in sub-delta band (0.05-1.5 Hz) slow-wave coherence between frontal, occipital, and frontal-occipital electrode pairs, with the most pronounced wake-vs.-unconscious coherence changes occurring at the frontal cortex.
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BACKGROUND: Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system's set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This "code-based" approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. RESULTS: As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. CONCLUSIONS: The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming skills, and the graphical interface lends itself to easy modification and use by non-experts.
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Biología Computacional/métodos , Modelos Biológicos , Programas Informáticos , Corteza Cerebral/citología , Corteza Cerebral/fisiología , Difusión , Humanos , Neuronas/citología , Neuronas/metabolismo , Dinámicas no LinealesRESUMEN
General anaesthetics have been hypothesised to ablate consciousness by decoupling intracortical neural connectivity. We explored this by investigating the effect of etomidate and ketamine on coupling of neural population activity using the low magnesium neocortical slice model. Four extracellular electrodes (50 µm) were positioned in mouse neocortical slices (400 µm thick) with varying separation. The effect of etomidate (24 µM) and ketamine (16 µM) on the timing of population activity recorded between channels was analysed. No decoupling was observed at the closest electrode separation of 0.2 mm. At 4mm separation, decoupling was observed in 50% and 42% of slices during etomidate and ketamine delivery, respectively (P<0.0001 and P=0.002, compared to 0.2 mm separation). A lower rate of decoupling was observed with 1mm separation (21% and 8%, respectively, P<0.03 for etomidate compared to 0.2mm separation). The data support the hypothesis that mechanistically diverse general anaesthetics disrupt neuronal connectivity across widely distributed intracortical networks.
Asunto(s)
Potenciales de Acción/efectos de los fármacos , Anestésicos Generales/farmacología , Etomidato/farmacología , Ketamina/farmacología , Neocórtex/efectos de los fármacos , Neuronas/efectos de los fármacos , Potenciales de Acción/fisiología , Animales , Femenino , Masculino , Ratones , Ratones de la Cepa 129 , Ratones Endogámicos C57BL , Neocórtex/citología , Neocórtex/fisiología , Neuronas/fisiología , Técnicas de Cultivo de ÓrganosRESUMEN
During slow-wave sleep, general anesthesia, and generalized seizures, there is an absence of consciousness. These states are characterized by low-frequency large-amplitude traveling waves in scalp electroencephalogram. Therefore the oscillatory state might be an indication of failure to form coherent neuronal assemblies necessary for consciousness. A generalized seizure event is a pathological brain state that is the clearest manifestation of waves of synchronized neuronal activity. Since gap junctions provide a direct electrical connection between adjoining neurons, thus enhancing synchronous behavior, reducing gap-junction conductance should suppress seizures; however there is no clear experimental evidence for this. Here we report theoretical predictions for a physiologically-based cortical model that describes the general anesthetic phase transition from consciousness to coma, and includes both chemical synaptic and direct electrotonic synapses. The model dynamics exhibits both Hopf (temporal) and Turing (spatial) instabilities; the Hopf instability corresponds to the slow (â²8 Hz) oscillatory states similar to those seen in slow-wave sleep, general anesthesia, and seizures. We argue that a delicately balanced interplay between Hopf and Turing modes provides a canonical mechanism for the default non-cognitive rest state of the brain. We show that the Turing mode, set by gap-junction diffusion, is generally protective against entering oscillatory modes; and that weakening the Turing mode by reducing gap conduction can release an uncontrolled Hopf oscillation and hence an increased propensity for seizure and simultaneously an increased sensitivity to GABAergic anesthesia.
RESUMEN
Clinically, anesthetic drugs show hysteresis in the plasma drug concentrations at induction versus emergence from anesthesia induced unconsciousness. This is assumed to be the result of pharmacokinetic lag between the plasma and brain effect-site and vice versa. However, recent mathematical and experimental studies demonstrate that anesthetic hysteresis might be due in part to lag in the brain physiology, independent of drug transport delay - so-called "neural inertia". The aim of this study was to investigate neural inertia in the reduced neocortical mouse slice model. Seizure-like event (SLE) activity was generated by exposing cortical slices to no-magnesium artificial cerebrospinal fluid (aCSF). Concentration-effect loops were generated by manipulating SLE frequency, using the general anesthetic drug etomidate and by altering the aCSF magnesium concentration. The etomidate (24 µM) concentration-effect relationship showed a clear hysteresis, consistent with the slow diffusion of etomidate into slice tissue. Manipulation of tissue excitability, using either carbachol (50 µM) or elevated potassium (5mM vs 2.5mM) did not significantly alter the size of etomidate hysteresis loops. Hysteresis in the magnesium concentration-effect relationship was evident, but only when the starting condition was magnesium-containing "normal" aCSF. The in vitro cortical slice manifests pathway-dependent "neural inertia" and may be a valuable model for future investigations into the mechanisms of neural inertia in the cerebral cortex.