Electrogenic properties of the Na⁺/K⁺ATPase control transitions between normal and pathological brain states

Abstract

Ionic concentrations fluctuate significantly during epileptic seizures. In this study, using a combination of in vitro electrophysiology, computer modeling, and dynamical systems analysis, we demonstrate that changes in the potassium and sodium intra- and extracellular ion concentrations ([K(+)] and [Na(+)], respectively) during seizure affect the neuron dynamics by modulating the outward Na(+)/K(+) pump current. First, we show that an increase of the outward Na(+)/K(+) pump current mediates termination of seizures when there is a progressive increase in the intracellular [Na(+)]. Second, we show that the Na(+)/K(+) pump current is crucial in maintaining the stability of the physiological network state; a reduction of this current leads to the onset of seizures via a positive-feedback loop. We then present a novel dynamical mechanism for bursting in neurons with a reduced Na(+)/K(+) pump. Overall, our study demonstrates the profound role of the current mediated by Na(+)/K(+) ATPase on the stability of neuronal dynamics that was previously unknown.

Role of KCC2-Dependent Potassium Efflux in 4-Aminopyridine-Induced Epileptiform Synchronization

“…Principal or excitatory neurons (PNs) and inhibitory interneurons (INs) were both modeled as two compartment models as described previously in (Bazhenov et al, 2002, 2004; Houweling et al, 2005; Frohlich et al, 2008; Krishnan and Bazhenov, 2011; Volman et al, 2011b; Volman et al, 2011a; González et al, 2015; Krishnan et al, 2015). The membrane potential dynamics for each compartment were modeled by the following equations: where V D is the dendritic membrane potential, are the dendritic and axosomatic compartment coupling current conductance, are the sum total Na + /K + ATPase currents, are the sum of the ionic leak currents, and are the intrinsic currents for the dendritic and axosomatic compartments respectively.…”

“…The membrane potential dynamics for each compartment were modeled by the following equations: where V D is the dendritic membrane potential, are the dendritic and axosomatic compartment coupling current conductance, are the sum total Na + /K + ATPase currents, are the sum of the ionic leak currents, and are the intrinsic currents for the dendritic and axosomatic compartments respectively. The intrinsic currents for the dendritic and axosomatic compartments are have been previously described in (Krishnan and Bazhenov, 2011; González et al, 2015; Krishnan et al, 2015).…”

An electrodiffusive, ion conserving Pinsky-Rinzel model with homeostatic mechanisms

“…Intra-or extracellular electrodiffusion is not an issue in single-compartment models, 69 of which there are quite a few that incorporate ion concentration dynamics in a more or 70 less consistent way [28,29,[33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. There are also several morphologically explicit models 71 that have included homeostatic machinery and explicitly simulated ion concentration 72 dynamics (see e.g., [27,[48][49][50][51][52][53][54][55][56][57]). However, neither of these have accounted for the 73 electrodiffusive coupling between the movement of ions and electrical potentials (see 74 Results section titled Loss in accuracy when neglecting electrodiffusive effects on 75 concentration dynamics).…”

“…We, therefore, do not analyze it further here. e.g., [27,[48][49][50][51][52][53][54][55][56][57]). To specify, the change in the ion concentration in a given 363 compartment will, in reality, depend on (i) the transmembrane influx of ions into this 364 compartment, (ii) the diffusion of ions between this compartments and its neighboring 365 compartment(s), and (iii) the electrical drift of ions between this compartment and its 366 neighboring compartment(s).…”

“…To specify, the change in the ion concentration in a given 363 compartment will, in reality, depend on (i) the transmembrane influx of ions into this 364 compartment, (ii) the diffusion of ions between this compartments and its neighboring 365 compartment(s), and (iii) the electrical drift of ions between this compartment and its 366 neighboring compartment(s). Some of the cited models account for only (i) [27,49,51], 367 others account for (i) and (ii) [48,50,[52][53][54][55][56][57], but neither account for (iii). When (iii) is 368 not accounted for, electrical and diffusive processes are implicitly treated as independent 369 processes, a simplifying assumption which is also incorporated in the reaction-diffusion 370 module [72] in the NEURON simulation environment [73].…”