Anton V. Chizhov

Reduced efficacy of the KCC2 cotransporter promotes epileptic oscillations in a subiculum network model

Pharmacoresistant epilepsy is a chronic neurological condition in which a basal brain hyperexcitability results in paroxysmal hypersynchronous neuronal discharges. Human temporal lobe epilepsy has been associated with dysfunction or loss of the potassium-chloride cotransporter KCC2 in a subset of pyramidal cells in the subiculum, a key structure generating epileptic activities. KCC2 regulates intraneuronal chloride and extracellular potassium levels by extruding both ions. Absence of effective KCC2 may alter the dynamics of chloride and potassium levels during repeated activation of GABAergic synapses due to interneuron activity. In turn, such GABAergic stress may itself affect Cl− regulation. Such changes in ionic homeostasis may switch GABAergic signaling from inhibitory to excitatory in affected pyramidal cells and also increase neuronal excitability. Possibly these changes contribute to periodic bursting in pyramidal cells, an essential component in the onset of ictal epileptic events. We tested this hypothesis with a computational model of a subicular network with realistic connectivity. The pyramidal cell model explicitly incorporated the cotransporter KCC2 and its effects on the internal/external chloride and potassium levels. Our network model suggested the loss of KCC2 in a critical number of pyramidal cells increased external potassium and intracellular chloride concentrations leading to seizure-like field potential oscillations. These oscillations included transient discharges leading to ictal-like field events with frequency spectra as in vitro. Restoration of KCC2 function suppressed seizure activity and thus may present a useful therapeutic option. These simulations therefore suggest that reduced KCC2 cotransporter activity alone may underlie the generation of ictal discharges. SIGNIFICANCE STATEMENT Ion regulation in the brain is a major determinant of neural excitability. Intracellular chloride in neurons, a partial determinant of the resting potential and the inhibitory reversal potentials, is regulated together with extracellular potassium via kation chloride cotransporters. During temporal lobe epilepsy, the homeostatic regulation of intracellular chloride is impaired in pyramidal cells, yet how this dysregulation may lead to seizures has not been explored. Using a realistic neural network model describing ion mechanisms, we show that chloride homeostasis pathology provokes seizure activity analogous to recordings from epileptogenic brain tissue. We show that there is a critical percentage of pathological cells required for seizure initiation. Our model predicts that restoration of the chloride homeostasis in pyramidal cells could be a viable antiepileptic strategy.

Synaptic Conductances during Interictal Discharges in Pyramidal Neurons of Rat Entorhinal Cortex

In epilepsy, the balance of excitation and inhibition underlying the basis of neural network activity shifts, resulting in neuronal network hyperexcitability and recurrent seizure-associated discharges. Mechanisms involved in ictal and interictal events are not fully understood, in particular, because of controversial data regarding the dynamics of excitatory and inhibitory synaptic conductances. In the present study, we estimated AMPAR-, NMDAR-, and GABAA R-mediated conductances during two distinct types of interictal discharge (IID) in pyramidal neurons of rat entorhinal cortex in cortico-hippocampal slices. Repetitively emerging seizure-like events and IIDs were recorded in high extracellular potassium, 4-aminopyridine, and reduced magnesium-containing solution. An original procedure for estimating synaptic conductance during IIDs was based on the differences among the current-voltage characteristics of the synaptic components. The synaptic conductance dynamics obtained revealed that the first type of IID is determined by activity of GABAA R channels with depolarized reversal potential. The second type of IID is determined by the interplay between excitation and inhibition, with early AMPAR and prolonged depolarized GABAA R and NMDAR-mediated components. The study then validated the contribution of these components to IIDs by intracellular pharmacological isolation. These data provide new insights into the mechanisms of seizures generation, development, and cessation.

Mappings between a macroscopic neural-mass model and a reduced conductance-based model

We present two alternative mappings between macroscopic neuronal models and a reduction of a conductance-based model. These provide possible explanations of the relationship between parameters of these two different approaches to modelling neuronal activity. Obtaining a physical interpretation of neural-mass models is of fundamental importance as they could provide direct and accessible tools for use in diagnosing neurological conditions. Detailed consideration of the assumptions required for the validity of each mapping elucidates strengths and weaknesses of each macroscopic model and suggests improvements for future development.

Simulation of neural population dynamics with a refractory density approach and a conductance-based threshold neuron model

We propose a macroscopic approach towards realistic simulations of population activity of cortical neurons, based on the known refractory density equation and a new threshold model of neuronal firing. The threshold model is a Hodgkin–Huxley model that is reduced by omitting the fast sodium current and instead using an explicit threshold criterion for action potential events based on the derivative of the membrane potential. The membrane potential of the model realistically describes postspike refractory states and postsynaptic current integration. The dynamics of a neural continuum are thus described by a partial differential equation in terms of the distributions of the refractory density, where the refractory state is defined by the time elapsed since the last action potential, the membrane potential and the potassium conductance, across the entire population. As a source term in the density equation, a probability density of firing, or a hazard function, is derived from the equation assuming a Gaussian distribution of spike thresholds over the population. Responses of an ensemble of unconnected neurons to stimulation by current step and sinusoidal inputs are simulated and compared with simulations of discrete individual neurons. A synaptically connected population model is also evaluated and compared with a model network of discrete neurons. r 2006 Elsevier B.V. All rights reserved.

Conductance-based refractory density model of primary visual cortex

A layered continual population model of primary visual cortex has been constructed, which reproduces a set of experimental data, including postsynaptic responses of single neurons on extracellular electric stimulation and spatially distributed activity patterns in response to visual stimulation. In the model, synaptically interacting excitatory and inhibitory neuronal populations are described by a conductance-based refractory density approach. Populations of two-compartment excitatory and inhibitory neurons in cortical layers 2/3 and 4 are distributed in the 2-d cortical space and connected by AMPA, NMDA and GABA type synapses. The external connections are pinwheel-like, according to the orientation of a stimulus. Intracortical connections are isotropic local and patchy between neurons with similar orientations. The model proposes better temporal resolution and more detailed elaboration than conventional mean-field models. In comparison to large network simulations, it excludes a posteriori statistical data manipulation and provides better computational efficiency and minimal parametrization.

The domain of neuronal firing on a plane of input current and conductance

The activation of neurotransmitter receptors increases the current flow and membrane conductance and thus controls the firing rate of a neuron. In the present work, we justified the two-dimensional representation of a neuronal input by voltage-independent current and conductance and obtained experimentally and numerically a complete input-output (I/O) function. The dependence of the steady-state firing rate on the input current and conductance was studied as a two-parameter I/O function. We employed the dynamic patch clamp technique in slices to get this dependence for the whole domain of two input signals that evoke stationary spike trains in a single neuron (Ω-domain). As found, the Ω-domain is finite and an additional conductance decreases the range of spike-evoking currents. The I/O function has been reproduced in a Hodgkin-Huxley-like model. Among the simulated effects of different factors on the I/O function, including passive and active membrane properties, external conditions and input signal properties, the most interesting were: the shift of the right boundary of the Ω-domain (corresponding to the exCitation block) leftwards due to the decrease of the maximal potassium conductance; and the reduction of the Ω-domain by the decrease of the maximal sodium concentration. As found in experiments and simulations, the Ω-domain is reduced by the decrease of extracellular sodium concentration, by cooling, and by adding slow potassium currents providing interspike interval adaptation; the Ω-domain height is increased by adding color noise. Our modeling data provided a generalization of I/O dependencies that is consistent with previous studies and our experiments. Our results suggest that both current flow and membrane conductance should be taken into account when determining neuronal firing activity.

A simple Markov model of sodium channels with a dynamic threshold

Characteristics of action potential generation are important to understanding brain functioning and, thus, must be understood and modeled. It is still an open question what model can describe concurrently the phenomena of sharp spike shape, the spike threshold variability, and the divisive effect of shunting on the gain of frequency-current dependence. We reproduced these three effects experimentally by patch-clamp recordings in cortical slices, but we failed to simulate them by any of 11 known neuron models, including one- and multi-compartment, with Hodgkin-Huxley and Markov equation-based sodium channel approximations, and those taking into account sodium channel subtype heterogeneity. Basing on our voltage-clamp data characterizing the dependence of sodium channel activation threshold on history of depolarization, we propose a 3-state Markov model with a closed-to-open state transition threshold dependent on slow inactivation. This model reproduces the all three phenomena. As a reduction of this model, a leaky integrate-and-fire model with a dynamic threshold also shows the effect of gain reduction by shunt. These results argue for the mechanism of gain reduction through threshold dynamics determined by the slow inactivation of sodium channels.

Firing-rate model of a population of adaptive neurons

A firing rate (FR) model for a population of adaptive leaky integrate-and-fire neurons has been proposed. Unlike known FR models, it describes more precisely the unsteady firing regimes and takes into account the effect of slow potassium currents of spike adaptation. Approximations of the adaptive channel conductances are rewritten from voltage-dependent to spike-dependent and then to rate-dependent ones. The proposed FR model is compared with a very detailed population model, namely, the conductance-based Refractory Density model. This comparison shows the coincidence of the first peak of activity after the start of stimulation as well as of the stationary state. As an example of simulation of coupled adaptive neuronal populations, a ring model has been constructed, which reproduces a visual illusion known as tilt after-effect. The FR model is recommended for mathematical analysis of neuronal population activity as well as for computationally expensive large-scale network simulations.

Simplest relationship between local field potential and intracellular signals in layered neural tissue

The relationship between the extracellularly measured electric field potential resulting from synaptic activity in an ensemble of neurons and intracellular signals in these neurons is an important but still open question. Based on a model neuron with a cylindrical dendrite and lumped soma, we derive a formula that substantiates a proportionality between the local field potential and the total somatic transmembrane current that emerges from the difference between the somatic and dendritic membrane potentials. The formula is tested by intra- and extracellular recordings of evoked synaptic responses in hippocampal slices. Additionally, the contribution of different membrane currents to the field potential is demonstrated in a two-population mean-field model. Our formalism, which allows for a simple estimation of unknown dendritic currents directly from somatic measurements, provides an interpretation of the local field potential in terms of intracellularly measurable synaptic signals. It is also applicable to the study of cortical activity using two-compartment neuronal population models.

Orientation hypercolumns of the visual cortex: Ring model

A hypercolumn of the visual cortex is a functional unit formed of neighboring columns whose neurons respond to a stimulus of particular orientation. The function of the hypercolumn is to amplify the orientation tuning of visually evoked responses. According to the conventional simple model of a hypercolumn, neuronal populations with different orientation preferences are distributed on a ring. Every population is described by a firing rate (FR) model. To determine the limitations of the FR-ring model, it was compared with a more detailed ring model, which takes into account the distribution of neurons of each population according to their voltage values. In the case of leaky integrate-and-fire neurons, every neuronal population is described by the Fokker-Planck equation (FPE). The mapping of parameters was obtained. The simulations revealed differences in the behavior of the two models. The FPE-based model reacts faster to a change in stimulus orientation. The FPE ring model gives a steady-state solution in the form of waves of activity traveling on the ring, whereas the FR ring model presents amplitude instability for the same parameter set. The FPE ring model reproduces the characteristic effects of the FR ring model: virtual rotation and symmetry breaking.