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.

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. METHODS: The computational model consists of a network of cellular bodies of neurons and glial cells connected to a three-dimensional (3D) network of juxtaposed extracellular compartments. The extracellular electrodiffusion calculation was used to simulate the extracellular potential. Each cellular body was represented in terms of the transmembrane ionic transports (Na(+)/K(+) pumps, ionic channels, and cotransport mechanisms), the intercellular electrodiffusion through gap-junctions, and the neuronal interaction by electric field and the variation of cellular volume. RESULTS: The computational model allows simulating the nonsynaptic epileptiform activity and the extracellular potential captured the main feature of the experimental measurements. The simulations of the concomitant ionic fluxes and concentrations can be used to propose the basic mechanisms involved in the induction and sustaining of the activities. DISCUSSION: The simulations suggest: The bursting induction is mediated by the Cl(-) Nernst potential overcoming the transmembrane potential in response to the extracellular [K(+)] increase. The burst onset is characterized by a critical point defined by the instant when the Na(+) influx through its permeable ionic channels overcomes the Na(+)/K(+) pump electrogenic current. The burst finalization is defined by another critical point, when the electrogenic current of the Na(+)/K(+) pump overcomes its influx through the channels.

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 Leão's 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.

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.