Extracellular potassium alters frequency and profile of retinal spreading depression waves

Migraine Visual Aura and Cortical Spreading Depression-Linking Mathematical Models to Empirical Evidence

This review describes the subjective experience of visual aura in migraine, outlines theoretical models of this phenomenon, and explores how these may be linked to neurochemical, electrophysiological, and psychophysical differences in sensory processing that have been reported in migraine with aura. Reaction-diffusion models have been used to model the hallucinations thought to arise from cortical spreading depolarisation and depression in migraine aura. One aim of this review is to make the underlying principles of these models accessible to a general readership. Cortical spreading depolarisation and depression in these models depends on the balance of the diffusion rate between excitation and inhibition and the occurrence of a large spike in activity to initiate spontaneous pattern formation. We review experimental evidence, including recordings of brain activity made during the aura and attack phase, self-reported triggers of migraine, and psychophysical studies of visual processing in migraine with aura, and how these might relate to mechanisms of excitability that make some people susceptible to aura. Increased cortical excitability, increased neural noise, and fluctuations in oscillatory activity across the migraine cycle are all factors that are likely to contribute to the occurrence of migraine aura. There remain many outstanding questions relating to the current limitations of both models and experimental evidence. Nevertheless, reaction-diffusion models, by providing an integrative theoretical framework, support the generation of testable experimental hypotheses to guide future research.

Metabolic basis of brain-like electrical signalling in bacterial communities

Information processing in the mammalian brain relies on a careful regulation of the membrane potential dynamics of its constituent neurons, which propagates across the neuronal tissue via electrical signalling. We recently reported the existence of electrical signalling in a much simpler organism, the bacterium Bacillus subtilis. In dense bacterial communities known as biofilms, nutrient-deprived B. subtilis cells in the interior of the colony use electrical communication to transmit stress signals to the periphery, which interfere with the growth of peripheral cells and reduce nutrient consumption, thereby relieving stress from the interior. Here, we explicitly address the interplay between metabolism and electrophysiology in bacterial biofilms, by introducing a spatially extended mathematical model that combines the metabolic and electrical components of the phenomenon in a discretized reaction-diffusion scheme. The model is experimentally validated by environmental and genetic perturbations, and confirms that metabolic stress is transmitted through the bacterial population via a potassium wave. Interestingly, this behaviour is reminiscent of cortical spreading depression in the brain, characterized by a wave of electrical activity mediated by potassium diffusion that has been linked to various neurological disorders, calling for future studies on the evolutionary link between the two phenomena. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Dynamics from seconds to hours in Hodgkin-Huxley model with time-dependent ion concentrations and buffer reservoirs

The classical Hodgkin-Huxley (HH) model neglects the time-dependence of ion concentrations in spiking dynamics. The dynamics is therefore limited to a time scale of milliseconds, which is determined by the membrane capacitance multiplied by the resistance of the ion channels, and by the gating time constants. We study slow dynamics in an extended HH framework that includes time-dependent ion concentrations, pumps, and buffers. Fluxes across the neuronal membrane change intra- and extracellular ion concentrations, whereby the latter can also change through contact to reservoirs in the surroundings. Ion gain and loss of the system is identified as a bifurcation parameter whose essential importance was not realized in earlier studies. Our systematic study of the bifurcation structure and thus the phase space structure helps to understand activation and inhibition of a new excitability in ion homeostasis which emerges in such extended models. Also modulatory mechanisms that regulate the spiking rate can be explained by bifurcations. The dynamics on three distinct slow times scales is determined by the cell volume-to-surface-area ratio and the membrane permeability (seconds), the buffer time constants (tens of seconds), and the slower backward buffering (minutes to hours). The modulatory dynamics and the newly emerging excitable dynamics corresponds to pathological conditions observed in epileptiform burst activity, and spreading depression in migraine aura and stroke, respectively.

Relevance of excitable media theory and retinal spreading depression experiments in preclinical pharmacological research

In preclinical neuropharmacological research, molecular, cell-based, and systems using animals are well established. On the tissue level the situation is less comfortable, although during the last decades some effort went into establishing such systems, i.e. using slices of the vertebrate brain together with optical and electrophysiological techniques. However, these methods are neither fast, nor can they be automated or upscaled. By contrast, the chicken retina can be used as a suitable model. It is easy accessible and can be kept alive in vitro for hours up to days. Due to its structure, in addition the retina displays remarkable intrinsic optical signals, which can be easily used in experiments. Also to electrophysiological methods the retina is well accessible. In excitable tissue, to which the brain and the retina belong, propagating excitation waves can be expected, and the spreading depression is such a phenomenon. It has been first observed in the forties of the last century. Later, Martins-Ferreira established it in the chicken retina (retinal spreading depression or RSD). The electrophysiological characteristics of it are identical with those of the cortical SD. The metabolic differences are known and can be taken into account. The experimental advantage of the RSD compared to the cortical SD is the pronounced intrinsic optical signal (IOS) associated with the travelling wave. This is due to the maximum transparency of retinal tissue in the functional state; thus any physiological event will change it markedly and therefore can be easily seen even by naked eye. The theory can explain wave spread in one (action potentials), two (RSDs) and three dimensions (one heart beat). In this review we present the experimental and the excitable media context for the data interpretation using as example the cholinergic pharmacology in relation to functional syndromes. We also discuss the intrinsic optical signal and how to use it in pre-clinical research.

Radial, spiral and reverberating waves of spreading depolarization occur in the gyrencephalic brain

OBJECTIVES

The detection of the hemodynamic and propagation patterns of spreading depolarizations (SDs) in the gyrencephalic brain using intrinsic optical signal imaging (IOS).

METHODS

The convexity of the brain surface was surgically exposed in fourteen male swine. Within the boundaries of this window, brains were immersed and preconditioned with an elevated K(+) concentration (7 mmol/l) in the standard Ringer lactate solution for 30-40 min. SDs were triggered using 3-5 μl of 1 mol/l KCl solution. Changes in tissue absorbency or reflection were registered with a CCD camera at a wavelength of 564 nm (14 nm FWHM), which was mounted 25 cm above the exposed cortex. Additional monitoring by electrocorticography and laser-Doppler was used in a subset of animals (n=7) to validate the detection of SD.

RESULTS

Of 198 SDs quantified in all of the experiments, 187 SDs appeared as radial waves that developed semi-planar fronts. The morphology was affected by the surface of the gyri, the sulci and the pial vessels. Other SD patterns such as spirals and reverberating waves, which have not been described before in gyrencephalic brains, were also observed. Diffusion gradients created in the cortex surface (i.e., KCl concentrations), sulci, vessels and SD-SD interactions make the gyrencephalic brain prone to the appearance of irregular SD waves.

CONCLUSION

The gyrencephalic brain is capable of irregular SD propagation patterns. The irregularities of the gyrencephalic brain cortex may promote the presence of re-entrance waves, such as spirals and reverberating waves.

Electrochemical Failure of the Brain Cortex Is More Deleterious When it Is Accompanied by Low Perfusion

Background and Purpose—

Clinical and experimental evidence suggests that spreading depolarization facilitates neuronal injury when its duration exceeds a certain time point, termed commitment point. We here investigated whether this commitment point is shifted to an earlier period, when spreading depolarization is accompanied by a perfusion deficit.

Methods—

Electrophysiological and cerebral blood flow changes were studied in a rat cranial window model followed by histological and immunohistochemical analyses of cortical damage.

Results—

In group 1, brain topical application of artificial cerebrospinal fluid (ACSF) with high K + concentration ([K + ] ACSF ) for 1 hour allowed us to induce a depolarizing event of fixed duration with cerebral blood flow fluctuations around the baseline (short-lasting initial hypoperfusions followed by hyperemia). In group 2, coapplication of the NO-scavenger hemoglobin ([Hb] ACSF ) with high [K + ] ACSF caused a depolarizing event of similar duration, to which a severe perfusion deficit was coupled (=spreading ischemia). In group 3, intravenous coadministration of the L-type calcium channel antagonist nimodipine with brain topical application of high [K + ] ACSF /[Hb] ACSF caused spreading ischemia to revert to spreading hyperemia. Whereas scattered neuronal injury occurred in the superficial cortical layers in the window areas of groups 1 and 3, necrosis of all layers with partial loss of the tissue texture and microglial activation were observed in group 2.

Conclusions—

The results suggest that electrochemical failure of the cortex is more deleterious when it is accompanied by low perfusion. Thus, the commitment point of the cortex is not a universal value but depends on additional factors, such as the level of perfusion.

Effects of NMDA receptor antagonists with different subtype selectivities on retinal spreading depression

BACKGROUND AND PURPOSE

Spreading depression (SD) is a local, temporary disruption of cellular ionic homeostasis that propagates slowly across the cerebral cortex and other neural tissues such as the retina. Spreading depolarization associated with SD occurs in different types of stroke, and this phenomenon correlates also with the initiation of classical migraine aura. The aim of this study was to investigate how NMDA receptor antagonists with different subtype selectivity alter SD.

EXPERIMENTAL APPROACH

Immunoblotting was applied to the chick retina for NMDA receptor subunit protein analysis, and an efficient in vitro chick retinal model used with SD imaging for NMDA receptor pharmacology.

KEY RESULTS

The prominent NMDA receptor subtypes GluN1, GluN2A and GluN2B were found highly expressed in the chick retina. Nanomolar concentrations of NVP-AAM077 (GluN2A-preferring receptor antagonist) markedly suppressed high K(+) -induced SD; that is, ∼30 times more effectively than MK801. At sub-micromolar concentrations, Ro 25-6981 (GluN2B-preferring receptor antagonist) produced a moderate SD inhibition, whereas CP-101,606 (also GluN2B-preferring receptor antagonist) and UBP141 (GluN2C/2D-preferring receptor antagonist) had no effect.

CONCLUSIONS AND IMPLICATIONS

The expression of major NMDA receptor subtypes, GluN1, GluN2A and GluN2B in the chick retina makes them pertinent targets for pharmacological inhibition of SD. The high efficacy of NVP-AAM077 on SD inhibition suggests a critical role of GluN2A-containing receptors in SD genesis. Such high anti-SD potency suggests that NVP-AAM077, and other GluN2A-selective drug-like candidates, could be potential anti-migraine agents.

SPREADING DEPRESSION IN MAINLY LOCALLY CONNECTED CELLULAR AUTOMATON

A computational model based on cellular automaton (CA) is developed for studying the spreading depression (SD) phenomenon. CA cells correspond to neurons which are mainly locally connected. The influence of the parameter values in the spatiotemporal dynamics is investigated in order to obtain ways of reducing, or even preventing, occurrences of SD.

Self-terminating wave patterns and self-organized pacemakers in a phenomenological model of spreading depression

A simple reaction-diffusion model of spreading depression (SD) is presented. Its local dynamics are governed by two activator and two inhibitor variables that provide an extremely simplified description of the mutual interaction between the neurons and extracellular space. This interaction is realized by the substances in the extracellular space that are increasing excitability of the neurons that have released them and are diffusing to the neighboring neurons, thereby spreading this excitation. Typical dynamic patterns of simulated activity are presented. The focus is laid on the case where response of the extracellular medium is relatively fast, and retracting waves, spiral-shaped waves, and autonomous pacemakers are observed, which is in good agreement with experimental observations. The underlying mechanisms are found to be related to switching between the local bi-stable, excitable, and self-sustained dynamics in the simulated medium. This article is part of a Special Issue entitled: Neural Coding.

Dynamical structures in binary media of potassium-driven neurons

According to the conventional approach neural ensembles are modeled with fixed ionic concentrations in the extracellular environment. However, in some cases the extracellular concentration of potassium ions cannot be regarded as constant. Such cases represent specific chemical pathway for neurons to interact and can influence strongly the behavior of single neurons and of large ensembles. The released chemical agent diffuses in the external medium and lowers thresholds of individual excitable units. We address this problem by studying simplified excitable units given by a modified FitzHugh-Nagumo dynamics. In our model the neurons interact only chemically via the released and diffusing potassium in the surrounding nonactive medium and are permanently affected by noise. First, we study the dynamics of a single excitable unit embedded in the extracellular matter. That leads to a number of noise-induced effects such as self-modulation of firing rate in an individual neuron. After the consideration of two coupled neurons we consider the spatially extended situation. By holding parameters of the neuron fixed, various patterns appear ranging from spirals and traveling waves to oscillons and inverted structures depending on the parameters of the medium.

Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke

The stability of cortical function depends critically on proper regulation. Under conditions of migraine and stroke a breakdown of transmembrane chemical gradients can spread through cortical tissue. A concomitant component of this emergent spatio-temporal pattern is a depolarization of cells detected as slow voltage variations. The propagation velocity of approximately 3 mm/min indicates a contribution of diffusion. We propose a mechanism for spreading depolarizations (SD) that rests upon a nonlocal or noninstantaneous feedback in a reaction-diffusion system. Depending upon the characteristic space and time scales of the feedback, the propagation of cortical SD can be suppressed by shifting the bifurcation line, which separates the parameter regime of pulse propagation from the regime where a local disturbance dies out. The optimization of this feedback is elaborated for different control schemes and ranges of control parameters.

Alterations in the alpha2 isoform of Na,K-ATPase associated with familial hemiplegic migraine type 2

A number of missense mutations in the Na,K-ATPase alpha2 catalytic subunit have been identified in familial hemiplegic migraine with aura. Two alleles (L764P and W887R) showed loss-of-function, whereas a third (T345A) is fully functional but with altered Na,K-ATPase kinetics. This study describes two additional mutants, R689Q and M731T, originally identified by Vanmolkot et al. [Vanmolkot, K. R., et al. (2003) Ann. Neurol. 54, 360-366], which we show here to also be functional and kinetically altered. Both mutants have reduced catalytic turnover and increased apparent affinity for extracellular K(+). For both R689Q and M731T, sensitivity to vanadate inhibition is decreased, suggesting that the steady-state E(1) <==> E(2) poise of the enzyme is shifted toward E(1). Whereas the K'(ATP) is not affected by the R689Q replacement, the M731T mutant has an increase in apparent affinity for ATP. Analysis of the structural changes effected by T345A, R689Q, and M731T mutations, based on homologous replacements in the known crystal structure of the sarcoplasmic reticulum Ca-ATPase, provides insights into the molecular bases for the kinetic alterations. It is suggested that the disease phenotype is the consequence of lowered molecular activity of the alpha2 pump isoform due to either decreased K(+) affinity (T345A) or catalytic turnover (R689Q and M731T), thus causing a delay in extracellular K(+) clearance and/or altered localized Ca(2+) handling/signaling secondary to reduced activity in colocalized Na(+)/Ca(2+) exchange.

Intrinsic optical signal of retinal spreading depression: Second phase depends on energy metabolism and nitric oxide

Spreading depression (SD) is a wave-like phenomenon that spreads through the gray matter of central nervous tissue. The aim of this work is to investigate how cellular energy supply and nitric oxide (NO) influence the recovery period after SD wave propagation. We have examined the SD wave in chicken retina by registration of the intrinsic optical signal (IOS). The changes of the IOS were observed via a microscope, transferred to a photomultiplier and amplified. The IOS of the SD wave consists of two phases. The first phase of IOS coexists with cellular swelling induced by ion distribution; the second phase is thought to reflect metabolic changes and reflects the refractory (recovery) period. To analyze the IOS, the amplitude, the duration and the front and the back maximal slopes of the both phases were analyzed. To reduce the cellular level of ATP the blocker of glucose transport-dexamethasone (glucocorticoid hormone) and the blocker of the respiratory chain-potassium cyanide were used. Sodium nitroprusside and trinitroglycerine were chosen as NO-donors. Our results show that during and after SD wave propagation (i) increased NO concentration changes the first and the second phases of IOS (duration of both phases is NO independent), (ii) reduced glucose uptake leads to an increased second phase duration and (iii) block of the respiratory chain prolongs the first phase. According to the results here presented, we propose that glycogen synthesis is one of the mechanisms reflected by the second phase of the IOS.

Mechanisms of chloride influx during KCl-induced swelling in the chicken retina

An increase in extracellular KCl ([KCl]o) occurs under various pathological conditions in the retina, leading to retinal swelling and possible neuronal damage. The mechanisms of this KCl o-induced retinal swelling were investigated in the present study, with emphasis on the Cl- transport mechanisms. Increasing [KCl]o (from 5 to 70 mM) led to concentration-dependent swelling in chicken retinas. The curve relating the degree of swelling to [KCl]o was biphasic, with one component from 5 to 35 mM [KCl]o and another from 35 to 100 mM. As Cl- omission prevented swelling in all conditions, the effect of cotransporter or Cl- channel blockers was examined to investigate the mechanisms of Cl- influx. The cotransporter blockers bumetanide and DIOA reduced swelling by 68% and 76%, respectively at [KCl]o 25 mM (K25), and by 14-17% at [KCl]o 54 mM (K54). The Cl- channel blockers NPPB and niflumic acid did not affect swelling at K25 but reduced it by 90-95% at K54 (NPPB IC50 60.7 microM). Furosemide showed an atypical effect, decreasing swelling by 14% at K25 and by 95% at K54 (IC50 173.9 microM). Na+ omission decreased swelling at K25 but not at K54. These results suggest the contribution of cotransporters to Cl- influx at K25 and of Cl- channels at K54. At K25, swelling was found in the ganglion cell layer and in the lower half of the inner nuclear layer. With K54, swelling occurred in all inner retinal layers. The ganglion cell layer swelling was due to both Muller cell end-foot and ganglion cell soma swelling. K54 also induced ganglion cell damage as shown by disorganized, pyknotic and refringent nuclei.

A computational perspective on migraine aura

The classical visual aura of migraine is characterized by a unilateral hallucination, composed of a zigzag fortification pattern followed by a trailing scotoma. This pattern usually starts in central vision, expands and spreads to the periphery, and then disappears. We review a number of historical attempts to explain the migraine aura in terms of brain events, then summarize recent theories of the pathophysiology of the aura. We describe an approach to the computational modeling of migraine aura, based on the principles of (a) cortical organization, and (b) active wave propagation in an excitable medium. We demonstrate correspondences between properties of the model system and aspects of the pathophysiology of the aura. The simulations produced by the model are in agreement with descriptions and drawings of visual aura from migraine patients. We outline several testable predictions stemming from the implementation of the model, and explain how model-based empirical research has the capacity to (a) improve recording of the phenomena of the visual aura, (b) improve understanding of the spatio-temporal dynamics of other types of aura, in particular somatosensory and dysphasic aurae, and (c) clarify the theoretical requirements for the initiation of aura in the brain.

Inhomogeneous propagation of cortical spreading depression—detection by electro- and magnetoencephalography in rats

Spreading depression (SD) propagates in cortical regions that are different in their morphological and functional characteristics. We tested whether the propagation pattern of spreading depression was different between parts of the cortex. In six adult rats, we recorded the ECoG by a 4 x 4 electrode array that covered parts of the frontal, parietal cortex and the cingulate cortex. Simultaneously a 16-channel magnetoencephalogram was recorded to characterize the development and direction of intracortical ion movements accompanying this phenomenon. Spreading depression was initiated by occipital application of 0.3 molar KCl solution. Depolarization was observed, at first, at lateral cortical regions and then at medial cortical regions. Thereafter, the propagation velocity increased in medial cortical regions and was faster than in lateral regions. Negative potential shifts were detected by all electrodes, but the depolarization reached a maximum over lateral and caudal cortical regions. The recorded magnetic fields indicated the same orientation of currents underlying these fields, which was perpendicular to the wave front and points away from the depolarization region. Overall, the data indicated that propagation patterns of spreading depression differed between parts of the cortex and, thus, propagation was inhomogeneous. This propagation was accompanied by strong currents parallel to the cortical surface.