Bilayer Lipid Membrane as Memcapacitance: Capacitance-Voltage Pinched Hysteresis and Negative Insertion Conductance.

Inelastic (dissipative) effects of different natures in lipid bilayer membranes can lead to hysteresis phenomena. Early, it was shown that lipid bilayer membranes, under the action of a periodic sinusoidal voltage, demonstrate pinched-hysteresis loops in the experimental capacitance-voltage dependences and are almost the only example of the physical implementation of memcapacitance. Here, we propose an equivalent circuit and mathematical framework for analyzing the dynamic nonlinear current response of a lipid bilayer membrane as an externally controlled memcapacitance. Solving a nonlinear differential equation for the equivalent circuit of a membrane in the form of a parallel connection of a nonlinear viscoelastic capacitor and an active resistance using the small parameter method, we obtain explicit analytical dependences for the current response of the membrane and pinched-hysteresis loops. The explicit solutions and their comparison with experimental data allow us to identify the lumped equivalent circuit parameters that govern the memcapacitor behavior of the membrane and hence the magnitude of the hysteresis. We quantify the memcapacitance hysteresis in terms of negative work done by the control signal. An analysis of the formulas leads to the conclusion that the determining factor for the appearance of pinched hysteresis is the type of nonlinear dependence of the device capacitance on voltage.

Ictal wavefront propagation in slices and simulations with conductance-based refractory density model.

The mechanisms determining ictal discharge (ID) propagation are still not clear. In the present study, we aimed to examine these mechanisms in animal and mathematical models of epileptiform activity. Using double-patch and extracellular potassium ion concentration recordings in rat hippocampal-cortical slices, we observed that IDs moved at a speed of about 1 mm/s or less. The mechanisms of such slow propagation have been studied with a mathematical, conductance-based refractory density (CBRD) model that describes the GABA- and glutamatergic neuronal populations' interactions and ion dynamics in brain tissue. The modeling study reveals two main factors triggerring IDs: (i) increased interneuronal activity leading to chloride ion accumulation and a consequent depolarizing GABAergic effect and (ii) the elevation of extracellular potassium ion concentration. The local synaptic transmission followed by local potassium ion extrusion and GABA receptor-mediated chloride ion accumulation underlies the ID wavefront's propagation. In contrast, potassium ion diffusion in the extracellular space is slower and does not affect ID's speed. The short discharges, constituting the ID, propagate much faster than the ID front. The accumulation of sodium ions inside neurons due to their hyperactivity and glutamatergic currents boosts the Na+/K+ pump, which terminates the ID. Knowledge of the mechanism of ID generation and propagation contributes to the development of new treatments against epilepsy.

Correction: Minimal model of interictal and ictal discharges "Epileptor-2".

[This corrects the article DOI: 10.1371/journal.pcbi.1006186.].

Minimal model of interictal and ictal discharges "Epileptor-2".

Seizures occur in a recurrent manner with intermittent states of interictal and ictal discharges (IIDs and IDs). The transitions to and from IDs are determined by a set of processes, including synaptic interaction and ionic dynamics. Although mathematical models of separate types of epileptic discharges have been developed, modeling the transitions between states remains a challenge. A simple generic mathematical model of seizure dynamics (Epileptor) has recently been proposed by Jirsa et al. (2014); however, it is formulated in terms of abstract variables. In this paper, a minimal population-type model of IIDs and IDs is proposed that is as simple to use as the Epileptor, but the suggested model attributes physical meaning to the variables. The model is expressed in ordinary differential equations for extracellular potassium and intracellular sodium concentrations, membrane potential, and short-term synaptic depression variables. A quadratic integrate-and-fire model driven by the population input current is used to reproduce spike trains in a representative neuron. In simulations, potassium accumulation governs the transition from the silent state to the state of an ID. Each ID is composed of clustered IID-like events. The sodium accumulates during discharge and activates the sodium-potassium pump, which terminates the ID by restoring the potassium gradient and thus polarizing the neuronal membranes. The whole-cell and cell-attached recordings of a 4-AP-based in vitro model of epilepsy confirmed the primary model assumptions and predictions. The mathematical analysis revealed that the IID-like events are large-amplitude stochastic oscillations, which in the case of ID generation are controlled by slow oscillations of ionic concentrations. The IDs originate in the conditions of elevated potassium concentrations in a bath solution via a saddle-node-on-invariant-circle-like bifurcation for a non-smooth dynamical system. By providing a minimal biophysical description of ionic dynamics and network interactions, the model may serve as a hierarchical base from a simple to more complex modeling of seizures.

Soft perforation of planar bilayer lipid membranes of dipalmitoylphosphatidylcholine at the temperature of the phase transition from the liquid crystalline to the gel state.

In contrast to the widely used method of electroporation, the method of soft perforation of lipid bilayers is proposed. It is based on the structural rearrangement of the lipid bilayer formed from disaturated phospholipids at the temperature of the phase transition from the liquid crystalline state to the gel state. This allows us to obtain a lipid pore population without the use of a strong electric field. It is shown that the planar lipid bilayer membrane (pBLM) formed from dipalmitoylphosphatidylcholine in 1 M LiCl aqueous solution exhibits the appearance of up to 50 lipid pores per 1 mm(2) of membrane surface, with an average single pore conductivity of 31 +/- 13 nS. The estimation of a single pore radius carried out with water-soluble poly(ethylene glycol)s (PEGs) showed that the average pore radius ranged between 1.0-1.7 nm. It was found experimentally that PEG-1450, PEG-2000, and PEG-3350 should be in a position to block the single pore conductivity completely, while PEG-6000 fully restored the ionic conductivity. The similarity of these PEG effects to ionic conductivity in protein pores makes it possible to suggest that the partition of the PEG molecules between the pore and the bulk solution does not depend on the nature of the chemical groups located in the pore wall.