Zuzanna Piwkowska

Minimal Hodgkin–Huxley type models for different classes of cortical and thalamic neurons

We review here the development of Hodgkin–Huxley (HH) type models of cerebral cortex and thalamic neurons for network simulations. The intrinsic electrophysiological properties of cortical neurons were analyzed from several preparations, and we selected the four most prominent electrophysiological classes of neurons. These four classes are “fast spiking” “regular spiking” “intrinsically bursting” and “low-threshold spike” cells. For each class, we fit “minimal” HH type models to experimental data. The models contain the minimal set of voltage-dependent currents to account for the data. To obtain models as generic as possible, we used data from different preparations in vivo and in vitro, such as rat somatosensory cortex and thalamus, guinea-pig visual and frontal cortex, ferret visual cortex, cat visual cortex and cat association cortex. For two cell classes, we used automatic fitting procedures applied to several cells, which revealed substantial cell-to-cell variability within each class. The selection of such cellular models constitutes a necessary step towards building network simulations of the thalamocortical system with realistic cellular dynamical properties.

High-Resolution Intracellular Recordings Using a Real-Time Computational Model of the Electrode

Intracellular recordings of neuronal membrane potential are a central tool in neurophysiology. In many situations, especially in vivo, the traditional limitation of such recordings is the high electrode resistance and capacitance, which may cause significant measurement errors during current injection. We introduce a computer-aided technique, Active Electrode Compensation (AEC), based on a digital model of the electrode interfaced in real time with the electrophysiological setup. The characteristics of this model are first estimated using white noise current injection. The electrode and membrane contribution are digitally separated, and the recording is then made by online subtraction of the electrode contribution. Tests performed in vitro and in vivo demonstrate that AEC enables high-frequency recordings in demanding conditions, such as injection of conductance noise in dynamic-clamp mode, not feasible with a single high-resistance electrode until now. AEC should be particularly useful to characterize fast neuronal phenomena intracellularly in vivo.

A non-parametric electrode model for intracellular recording

We present a new way to model the response of an electrode to an injected current. The electrode is represented by an unknown complex linear circuit, characterized by a kernel which we determine by injecting a noisy current. We show both in simulations and experiments that, when applied to a full recording setup (including acquisition board and amplifier), the method captures not only the characteristics of the electrode, but also those of all the devices between the computer and the tip of the electrode, including filters and the capacitance neutralization circuit on the amplifier. Simulations show that the method allows correct predictions of the response of complex electrode models. Finally, we successfully apply the technique to challenging intracellular recording situations in which the voltage across the electrode during injection needs to be subtracted from the recording, in particular conductance injection with the dynamic clamp protocol. We show in numerical simulations and confirm with experiments that the method performs well in cases when both bridge recording and recording in discontinuous mode (DCC) exhibit artefacts. (This work was supported by: CNRS, INRIA, European Commission (FACETS, FP6-2004-IST-FET), Action Concertee Incitative (NIC0005).)

A novel method for characterizing synaptic noise in cortical neurons

Cortical neurons in vivo are subjected to intense synaptic noise that has a significant impact on various electrophysiological properties. Here we characterize the subthreshold activity of cortical neurons using an explicit solution of the passive membrane equation subject to independent inhibitory and excitatory conductance noise sources described by stochastic random-walk processes. The analytic expression for the membrane potential distribution can be used to estimate the average and variance of synaptic conductances from intracellular recordings obtained under current clamp. We demonstrate the application of this method to neuronal models of various complexity as well as to in vitro intracellular recordings.

High discharge variability in neurons driven by current noise

Cortical neurons in vivo show a highly irregular spontaneous discharge activity, characterized by a gamma statistics and coefficient of variation around unity. Modelling studies showed that this irregularity is a consequence of the high-conductance state caused by the ongoing activity in the cortical network. Here, we investigate to which extent this high discharge variability can be reproduced in vitro using current noise injection. In agreement with numerical studies, we found that equalizing the time constant of the noisy input with the membrane time constant may lead to an irregular discharge activity which, however, departs from a gamma statistics.

Comparison of different neuron models to conductance-based post-stimulus time histograms obtained in cortical pyramidal cells using dynamic-clamp in vitro

A wide diversity of models have been proposed to account for the spiking response of central neurons, from the integrate-and-fire (IF) model and its quadratic and exponential variants, to multiple-variable models such as the Izhikevich (IZ) model and the well-known Hodgkin–Huxley (HH) type models. Such models can capture different aspects of the spiking response of neurons, but there is few objective comparison of their performance. In this article, we provide such a comparison in the context of well-defined stimulation protocols, including, for each cell, DC stimulation, and a series of excitatory conductance injections, arising in the presence of synaptic background activity. We use the dynamic-clamp technique to characterize the response of regular-spiking neurons from guinea-pig visual cortex by computing families of post-stimulus time histograms (PSTH), for different stimulus intensities, and for two different background activities (low- and high-conductance states). The data obtained are then used to fit different classes of models such as the IF, IZ, or HH types, which are constrained by the whole data set. This analysis shows that HH models are generally more accurate to fit the series of experimental PSTH, but their performance is almost equaled by much simpler models, such as the exponential or pulse-based IF models. Similar conclusions were also reached by performing partial fitting of the data, and examining the ability of different models to predict responses that were not used for the fitting. Although such results must be qualified by using more sophisticated stimulation protocols, they suggest that nonlinear IF models can capture surprisingly well the response of cortical regular-spiking neurons and appear as useful candidates for network simulations with conductance-based synaptic interactions.

Re-Creating In Vivo-Like Activity and Investigating the Signal Transfer Capabilities of Neurons: Dynamic-Clamp Applications Using Real-Time Neuron

Understanding the input–output transfer properties of NEURONs is a complex problem which requires detailed knowledge of the intrinsic properties of neurons, and how these intrinsic properties influence signal integration. More recently, it became clear that the transfer function of neurons also highly depends on the activity of the surrounding network, and in particular on the presence of synaptic background activity. We review here different in vitro techniques to investigate such problems in cortex, thalamus, and spinal cord, along three examples: First, by constructing “hybrid” networks with real and artificial thalamic neurons using dynamic clamp, it was possible to study how the state of the circuit influences spike transfer through the thalamus. Second, the dynamic clamp was used to study how the state of discharge of spinal neurons influences their information processing capabilities. Third, the dynamic-clamp experiments could re-create “in vivo-like” background synaptic activity by injection of stochastic excitatory and inhibitory conductances, and we showed that this activity profoundly modifies the input–output transfer function of thalamic and cortical neurons. We also illustrate how such applications are greatly facilitated by the use of a neuronal simulator to run the dynamic-clamp experiments, as shown here for RT-NEURON.

Associating Living Cells and Computational Models: an Introduction to Dynamic Clamp Principles and its Applications

The dynamic-clamp electrophysiological technique allows the mimicking of the electrical effects of arbitrary ion channels, controlled by the experimentalist, activating and inactivating into the membrane of an intracellularly recorded biological cell. Dynamic clamp relies on the establishing of a loop between the injected current and the recorded membrane potential. In this introductory chapter, we first present the principles of the technique, starting by recalling the basis of the equivalent electrical circuit representation of a cellular membrane. We then briefly list some of the issues encountered in the practical implementation of the dynamic-clamp loop. Finally, we overview the numerous applications of the method to the study of neurons, other excitable cells and networks of cells: these include the manipulation of intrinsic ion channels and of single or multiple synaptic inputs to a cell, as well as the construction of whole hybrid networks in which the biological cell interacts with model cells simulated in real time using a digital or analog system. Many of the applications briefly presented here are the subject of the following chapters.

Re-creating active states in vitro with a dynamic-clamp protocol

In neocortical neurons, network activity is responsible for intense synaptic inputs, which maintain the membrane in a high-conductance state. Here, we propose a method for re-creating specific high-conductance states intracellularly. This method makes use of the estimation of the mean and variance of excitatory and inhibitory conductances based on intracellular recordings, and of the injection of appropriate stochastic conductances in in vitro slice preparations using a dynamic-clamp protocol. The approach could be used to evaluate the modulation of neuronal responses by specific network states.

Testing Methods for Synaptic Conductance Analysis Using Controlled Conductance Injection with Dynamic Clamp

In this chapter, we present different methods to analyze intracellular recordings and the testing of these methods using dynamic-clamp techniques. The methods are derived from a model of synaptic background activity where the synaptic membrane conductances are considered as stochastic processes. Because this fluctuating point-conductance model can be treated analytically, different methods can be outlined to estimate different characteristics of synaptic noise from the membrane potential (V m) activity, such as the mean and variance of the excitatory and inhibitory conductance distributions (the VmD method) or spike-triggered averages of conductances. These analysis methods can be validated in controlled conditions using dynamic-clamp injection of known synaptic conductance patterns, as we illustrate here. Our approach constitutes a novel application of the dynamic clamp, which could be extended to the testing of other methods for extracting conductance information from the recorded V m activity of neurons.