Mário A. Duarte

Mechanistic hypotheses for nonsynaptic epileptiform activity induction and its transition from the interictal to ictal state—Computational simulation

Purpose:  The aim of this work is to study, by means of computational simulations, the induction and sustaining of nonsynaptic epileptiform activity.

Model and simulation of Na+/K+ pump phosphorylation in the presence of palytoxin

The ATP hydrolysis reactions responsible for the Na(+)/K(+)-ATPase phosphorylation, according to recent experimental evidences, also occur for the PTX-Na(+)/K(+) pump complex. Moreover, it has been demonstrated that PTX interferes with the enzymes phosphorylation status. However, the reactions involved in the PTX-Na(+)/K(+) pump complex phosphorylation are not very well established yet. This work aims at proposing a reaction model for PTX-Na(+)/K(+) pump complex, with similar structure to the Albers-Post model, to contribute to elucidate the PTX effect over Na(+)/K(+)-ATPase phosphorylation and dephosphorylation. Computational simulations with the proposed model support several hypotheses and also suggest: (i) phosphorylation promotes an increase of the open probability of induced channels; (ii) PTX reduces the Na(+)/K(+) pump phosphorylation rate; (iii) PTX may cause conformational changes to substates where the Na(+)/K(+)-ATPase may not be phosphorylated; (iv) PTX can bind to substates of the two principal states E1 and E2, with highest affinity to phosphorylated enzymes and with ATP bound to its low-affinity sites. The proposed model also allows previewing the behavior of the PTX-pump complex substates for different levels of intracellular ATP concentrations.

Alcohol Abuse Promotes Changes in Non-Synaptic Epileptiform Activity with Concomitant Expression Changes in Cotransporters and Glial Cells

Non-synaptic mechanisms are being considered the common factor of brain damage in status epilepticus and alcohol intoxication. The present work reports the influence of the chronic use of ethanol on epileptic processes sustained by non-synaptic mechanisms. Adult male Wistar rats administered with ethanol (1, 2 e 3 g/kg/d) during 28 days were compared with Control. Non-synaptic epileptiform activities (NEAs) were induced by means of the zero-calcium and high-potassium model using hippocampal slices. The observed involvement of the dentate gyrus (DG) on the neurodegeneration promoted by ethanol motivated the monitoring of the electrophysiological activity in this region. The DG regions were analyzed for the presence of NKCC1, KCC2, GFAP and CD11b immunoreactivity and cell density. The treated groups showed extracellular potential measured at the granular layer with increased DC shift and population spikes (PS), which was remarkable for the group E1. The latencies to the NEAs onset were more prominent also for the treated groups, being correlated with the neuronal loss. In line with these findings were the predispositions of the treated slices for neuronal edema after NEAs induction, suggesting that restrict inter-cell space counteracts the neuronal loss and subsists the hyper-synchronism. The significant increase of the expressions of NKCC1 and CD11b for the treated groups confirms the existence of conditions favorable to the observed edematous necrosis. The data suggest that the ethanol consumption promotes changes on the non-synaptic mechanisms modulating the NEAs. For the lower ethanol dosage the neurophysiological changes were more effective suggesting to be due to the less intense neurodegenertation.

Biophysical Aspects of the Nonsynaptic Epileptiform Activity

Since the demonstration that the hippocampus slice exposed to low calcium external solution is able to sustain nonsynaptic epileptiform activity, it has been accepted that nonsynaptic interactions may be sufficient, in some conditions, for generating seizure like activity in cortical network. Recently, evidences have suggested that the reductions in calcium are not essential for nonsynaptic mechanisms to contribute to epileptic activity. Therefore, evidences allow demonstrating that the conjoint actuation of nonsynaptic mechanisms and nonsynaptic connections are able to induce and sustain seizures. The nonsynaptic mechanisms considered in this context are all mechanisms which are not directly involved with synaptic transmission, but comprehending important action on the homeostasis equilibrium and, consequently, on the neuronal excitability. The non-synaptic connections are all types of neuronal coupling that are not mediated by synaptic transmission. The concomitant actuation of nonsynaptic mechanisms and connections seems to be a relevant process for the seizure intensity modulation. Therefore, it may be conjectured that the nonsynaptic mechanisms and connections could be considered a natural target for investigations aiming to control refractory seizures. Within this perspective, the scope of the present chapter will cover the following topics: • nonsynaptic events: experimental induction and electrophysiological characteristics; • nonsynaptic mechanisms; • nonsynaptic connections; • biophysical aspects of the nonsynaptic epileptiform activities; • possible targets for controlling refractory seizures.

Simulation of the effect of Na+ and Cl- on the velocity of a spreading depression wave using a simplified electrochemical model of synaptic terminals.

In the study of the spreading depression (SD) wave phenomenon and its dynamics, it is necessary to describe the ionic movements along the extracellular space, as well as between this and the intracellular space. In both cases, the ionic movement includes a double coupling involving the concentration and the potential gradients and hence must be described by electrodiffusion mechanisms. Based on this, the effects of the ionic composition on the characteristics of the wave propagation can be predicted. The influence of varying extracellular sodium and chloride concentrations on the velocity of propagation of the SD wave was investigated by simulation. The results achieved are close to the experimental measurement from the literature. These findings suggest the potentiality of the model proposed in supporting the interpretation of experimental data in neuronal tissues, particularly the SD.

Enhanced Synaptic Connectivity in the Dentate Gyrus during Epileptiform Activity: Network Simulation

Structural rearrangement of the dentate gyrus has been described as the underlying cause of many types of epilepsies, particularly temporal lobe epilepsy. It is said to occur when aberrant connections are established in the damaged hippocampus, as described in human epilepsy and experimental models. Computer modelling of the dentate gyrus circuitry and the corresponding structural changes has been used to understand how abnormal mossy fibre sprouting can subserve seizure generation observed in experimental models when epileptogenesis is induced by status epilepticus. The model follows the McCulloch-Pitts formalism including the representation of the nonsynaptic mechanisms. The neuronal network comprised granule cells, mossy cells, and interneurons. The compensation theory and the Hebbian and anti-Hebbian rules were used to describe the structural rearrangement including the effects of the nonsynaptic mechanisms on the neuronal activity. The simulations were based on neuroanatomic data and on the connectivity pattern between the cells represented. The results suggest that there is a joint action of the compensation theory and Hebbian rules during the inflammatory process that accompanies the status epilepticus. The structural rearrangement simulated for the dentate gyrus circuitry promotes speculation about the formation of the abnormal mossy fiber sprouting and its role in epileptic seizures.

Research Article: Investigating the potassium interactions with the palytoxin induced channels in Na+/K+ pump

K(+) has been appointed as the main physiological inhibitor of the palytoxin (PTX) effect on the Na(+)/K(+) pump. This toxin acts opening monovalent cationic channels through the Na(+)/K(+) pump. We investigate, by means of computational modeling, the kinetic mechanisms related with K(+) interacting with the complex PTX-Na(+)/K(+) pump. First, a reaction model, with structure similar to Albers-Post model, describing the functional cycle of the pump, was proposed for describing K(+) interference on the complex PTX-Na(+)/K(+) pump in the presence of intracellular ATP. A mathematic model was derived from the reaction model and it was possible to solve numerically the associated differential equations and to simulate experimental maneuvers about the PTX induced currents in the presence of K(+) in the intra- and extracellular space as well as ATP in the intracellular. After the model adjusting to the experimental data, a Monte Carlo method for sensitivity analysis was used to analyze how each reaction parameter acts during each experimental maneuver involving PTX. For ATP and K(+) concentrations conditions, the simulations suggest that the enzyme substate with ATP bound to its high-affinity sites is the main substate for the PTX binding. The activation rate of the induced current is limited by the K(+) deocclusion from the PTX-Na(+)/K(+) pump complex. The K(+) occlusion in the PTX induced channels in the enzymes with ATP bound to its low-affinity sites is the main mechanism responsible for the reduction of the enzyme affinity to PTX.

Research Article: Identifying essential conditions for refractoriness of Leão's spreading depression-Computational modeling

A mathematical description of the restoring ionic mechanisms in a compartmentalized electrochemical model of neuronal tissues was developed aiming at studying the essential conditions for refractoriness of Leãos spreading depression (SD). The model comprehends the representation of a plexiform layer, composed by synaptic terminals and glial process immersed in an extracellular space where the space-temporal variations of the ionic concentrations were described by electrodiffusion equations. The synaptic transmission was described by differential equations representing the corresponding chemical reactions associated with the neurotransmitter release, diffusion, binding to its receptor in the postsynaptic membrane and the uptake by the presynaptic terminals. The effect of the neurotransmitter binding to the receptor induces changes in the permeability of the postsynaptic membrane and the corresponding transmembrane fluxes were calculated. The fluxes promote changes in the external ionic concentrations, changing the ionic electrodiffusion through the extracellular space. The description of these mechanisms provides the reaction-diffusion structure of the model and allows simulating the wave propagation. The simulations of experimental maneuvers of application of two consecutive stimuli for inducing SD suggest: (i) the extracellular space acts coupling the postsynaptic terminals and glial cells recovery mechanisms in such a way that the extracellular ionic concentrations change only during the wave front; (ii) the potassium removed from the extracellular by the glial cells, originated from the depolarization of the synaptic terminals returns slowly limited by the glial release, contributing for the refractoriness of the tissue; (iii) critical points for sodium and potassium transmembrane fluxes could be identified, allowing proposing specific conditions for the interplay between channels and pumps fluxes for determining the absolute and relative refractory periods.

Effect of co-transporter blockers on non-synaptic epileptiform activity—computational simulation

The important role of cation-chloride co-transporters in epilepsy is being supported by an increasing number of investigations. However, enormous complexity is involved since the action of these co-transporters has effects on the ionic homeostasis influencing directly the neuronal excitability and the tissue propensity to sustain seizure. To unravel the complex mechanisms involving the co-transporters action during seizure, this paper shows simulations of non-synaptic epileptiform activity and the effect of the blockage of the two different types of cation-chloride co-transporters present in the brain: Na, K and 2Cl co-transporter (NKCC) and K and Cl co-transporter (KCC). The simulations were performed with an electrochemical model representing the non-synaptic structure of the granule cell layer of the dentate gyrus (DG) of the rat hippocampus. The simulations suggest: (i) the potassium clearance is based on the systemic interplay between the Na/K pump and the NKCC co-transporters; (ii) the simultaneous blockage of the NKCC of the neurons and KCC of glial cells acts efficiently suppressing the epileptiform activities; and (iii) the simulations show that depending on the combined blockage of the co-transporters, the epileptiform activities may be suppressed or enhanced.

Combined effect of bumetanide, bromide, and GABAergic agonists: an alternative treatment for intractable seizures.

The epilepsies constitute one of the most common serious brain disorders and know no geographic, social, or racial boundaries, occurring in men and women and affecting people of all ages, though more frequently affecting young people in the first two decades of life and people over the age of 60 [1,2]. Worldwide, there are at least 50 million people who have epilepsy, and many of these persons have seizures that are refractory to treatment with the currently available therapies [1,3,4]. The most common risk factors for epilepsy are cerebrovascular diseases, brain tumors, alcohol, traumatic head injuries, genetic inheritance, andmalformations of cortical development [5,6]. In resource-poor countries, endemic infections such as malaria and neurocysticercosis seem to be major risk factors [7]. The paradoxical excitatory action of GABAobserved in the immature brain plays a role in neonatal development [8,9], but also is responsible for the increased seizure propensity and lowered seizure threshold of neonates [10]. Differently frommature neurons of adults, the immature neurons of neonates exhibit amuch higher [Cl]i induced by higherNa, K,2Cl co-transporter type 1 (NKCC1) expression and lower K,Cl type 2 (KCC2) expression. In this circumstance, the activation of GABAA receptors is followed by an efflux of Cl, induced by the positivity of the Nernst potential for Cl with respect to the membrane potential, which accounts for the excitatory action of GABA. Almost all neurological insults (hypoxia–ischemia, metabolic derangement, hemorrhage, and infection) sustained during the neonatal period can trigger the synchronous firing of hyperexcitable neurons that underlie epileptogenesis [11]. Investigations conducted in human epileptogenic tissue have shown that dysplastic tissue may retain immature properties, exhibiting mechanisms of seizure generation resembling that observed during development in the immature brain [12,13]. To unravel the mechanisms involved in seizure initiation, epileptogenesis, and spontaneous recurrent seizures and to search for new treatment options, several experimental models mimicking different aspects of the epileptic process have been developed. Along with the seizure induction process, which leads to spontaneous seizures, many studies conducted with experimental models have identified activation of an inflammatory state [14]. Concomitantly with the inflammation, changes in expression of NKCC1 and KCC2 cotransporters have been observed that resemble the immature brain [15]. An increasing number of investigations suggest an important role for cation chloride co-transporters in controlling neuronal functions [6]. Deregulation of their expression may contribute to the mechanisms of hyperexcitability, which, in combination with neuronal coupling, may lead to synchronization and, therefore, to seizures. The hyperexcitability is attributed mainly to the accumulation of