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

Single-compartment model of a pyramidal neuron, fitted to recordings with current and conductance injection

For single neuron models, reproducing characteristics of neuronal activity such as the firing rate, amplitude of spikes, and threshold potentials as functions of both synaptic current and conductance is a challenging task. In the present work, we measure these characteristics of regular spiking cortical neurons using the dynamic patch-clamp technique, compare the data with predictions from the standard Hodgkin-Huxley and Izhikevich models, and propose a relatively simple five-dimensional dynamical system model, based on threshold criteria. The model contains a single sodium channel with slow inactivation, fast activation and moderate deactivation, as well as, two fast repolarizing and slow shunting potassium channels. The model quantitatively reproduces characteristics of steady-state activity that are typical for a cortical pyramidal neuron, namely firing rate not exceeding 30 Hz; critical values of the stimulating current and conductance which induce the depolarization block not exceeding 80 mV and 3, respectively (both values are scaled by the resting input conductance); extremum of hyperpolarization close to the midpoint between spikes. The analysis of the model reveals that the spiking regime appears through a saddle-node-on-invariant-circle bifurcation, and the depolarization block is reached through a saddle-node bifurcation of cycles. The model can be used for realistic network simulations, and it can also be implemented within the so-called mean-field, refractory density framework.

Increased noise relates to abnormal excitation-inhibition balance in schizophrenia: a combined empirical and computational study

Electroencephalography studies link sensory processing issues in schizophrenia to increased noise level-noise here is background spontaneous activity-as measured by the signal-to-noise ratio. The mechanism, however, of such increased noise is unknown. We investigate if this relates to changes in cortical excitation-inhibition balance, which has been observed to be atypical in schizophrenia, by combining electroencephalography and computational modeling. Our electroencephalography task results, for which the local field potentials can be used as a proxy, show lower signal-to-noise ratio due to higher noise in schizophrenia. Both electroencephalography rest and task states exhibit higher levels of excitation in the functional excitation-inhibition (as a proxy of excitation-inhibition balance). This suggests a relationship between increased noise and atypical excitation in schizophrenia, which was addressed by using computational modeling. A Leaky Integrate-and-Fire model was used to simulate the effects of varying degrees of noise on excitation-inhibition balance, local field potential, NMDA current, and . Results show a noise-related increase in the local field potential, excitation in excitation-inhibition balance, pyramidal NMDA current, and spike rate. Mutual information and mediation analysis were used to explore a cross-level relationship, showing that the cortical local field potential plays a key role in transferring the effect of noise to the cellular population level of NMDA.

Photostimulation activates fast-spiking interneurons and pyramidal cells in the entorhinal cortex of Thy1-ChR2-YFP line 18 mice

The application of optogenetics in animals has provided new insights into both fundamental neuroscience and diseases of the nervous system. This is primarily due to the fact that optogenetics allows selectively activating or inhibiting particular types of neurons. One of the first transgenic mouse lines developed for the optogenetic experiment was Thy1-ChR2-YFP. Thy1 is an immunoglobulin superfamily member expressing in projection neurons, so it was assumed that channelrhodopsin-2 (ChR2) would be primarily expressed in projection neurons. However, the specificity of ChR2 expression under promoter Thy1 in different lines has to be clarified yet. Therefore, we aimed to determine the cell specificity of ChR2 expression in the entorhinal cortex of Thy1-ChR2-YFP line 18 mice. We have found that both pyramidal cells and fast-spiking interneurons in deep layers of the entorhinal cortex depolarized and fired in response to 470-nm photostimulation. To exclude the effect of synaptic activation of interneurons by pyramidal cells, we used a selective antagonist of AMPA receptors. Under these conditions, inhibitory postsynaptic currents decreased but did not disappear completely. Furthermore, gabazine inhibited these postsynaptic currents entirely, thus confirming the direct activation of interneurons by light. These data demonstrate that ChR2 is expressed in both pyramidal neurons and fast-spiking interneurons of the entorhinal cortex in Thy1-ChR2-YFP mice.

Conductance-Based Refractory Density Approach for a Population of Bursting Neurons

The conductance-based refractory density (CBRD) approach is a parsimonious mathematical-computational framework for modelling interacting populations of regular spiking neurons, which, however, has not been yet extended for a population of bursting neurons. The canonical CBRD method allows to describe the firing activity of a statistical ensemble of uncoupled Hodgkin-Huxley-like neurons (differentiated by noise) and has demonstrated its validity against experimental data. The present manuscript generalises the CBRD for a population of bursting neurons; however, in this pilot computational study, we consider the simplest setting in which each individual neuron is governed by a piecewise linear bursting dynamics. The resulting population model makes use of slow-fast analysis, which leads to a novel methodology that combines CBRD with the theory of multiple timescale dynamics. The main prospect is that it opens novel avenues for mathematical explorations, as well as, the derivation of more sophisticated population activity from Hodgkin-Huxley-like bursting neurons, which will allow to capture the activity of synchronised bursting activity in hyper-excitable brain states (e.g. onset of epilepsy).

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 GABA_A 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 GABA_A 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 GABA_A 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.