Alain Destexhe

Synthesis of Models for Excitable Membranes, Synaptic Transmission and Neuromodulation Using a Common Kinetic Formalism

Markov kinetic models were used to synthesize a complete description of synaptic transmission, including opening of voltage-dependent channels in the presynaptic terminal, release of neurotransmitter, gating of postsynaptic receptors, and activation of second-messenger systems. These kinetic schemes provide a more general framework for modeling ion channels than the Hodgkin-Huxley formalism, supporting a continuous spectrum of descriptions ranging from the very simple and computationally efficient to the highly complex and biophysically precise. Examples are given of simple kinetic schemes based on fits to experimental data that capture the essential properties of voltage-gated, synaptic and neuromodulatory currents. The Markov formalism allows the dynamics of ionic currents to be considered naturally in the larger context of biochemical signal transduction. This framework can facilitate the integration of a wide range of experimental data and promote consistent theoretical analysis of neural mechanisms from molecular interactions to network computations.

An efficient method for computing synaptic conductances based on a kinetic model of receptor binding

where gsyn is the synaptic conductance and to is the time of transmitter release. This function peaks at a value of l / e at t = to + T , and decays exponentially with a time constant of T . When multiple events occur in succession at a single synapse, the total conductance at any time is a sum of such waveforms calculated over the individual event times. There are several drawbacks to this method. First, the relationship to actual synaptic conductances is based only on an approximate correspondence of the time-course of the waveform to physiological recordings of the postsynaptic response, rather than plausible biophysical mechanisms. Second, summation of multiple waveforms can be cumbersome, since each event time must be stored in a queue for the duration of the waveform and necessitates calculation of an additional exponential during this period (but see Srinivasan and Chiel 1993). Third, there is no natural provision for saturation of the conductance. An alternative to the use of stereotyped waveforms is to compute synaptic conductances directly using a kinetic model (Perkel eta! . 1981). This approach allows a more realistic biophysical representation and is consistent with the formalism used to describe the conductances of other ion channels. However, solution of the associated differential equations generally requires computationally expensive numerical integration. In this paper we show that reasonable biophysical assumptions about synaptic transmission allow the equations for a simple kinetic synapse model to be solved analytically. This yields a mechanism that preserves the advantages of kinetic models while being as fast to compute as a single tr-function. Moreover, this mechanism accounts implicitly for sat-

Handbook of neural activity measurement

Neuroscientists employ many different techniques to observe the activity of the brain, from single-channel recording to functional imaging (fMRI). Many practical books explain how to use these techniques, but in order to extract meaningful information from the results it is necessary to understand the physical and mathematical principles underlying each measurement. This book covers an exhaustive range of techniques, with each chapter focusing on one in particular. Each author, a leading expert, explains exactly which quantity is being measured, the underlying principles at work, and most importantly the precise relationship between the signals measured and neural activity. The book is an important reference for neuroscientists who use these techniques in their own experimental protocols and need to interpret their results precisely; for computational neuroscientists who use such experimental results in their models; and for scientists who want to develop new measurement techniques or enhance existing ones.

Fast Kinetic Models for Simulating AMPA, NMDA, GABA A and GABA B Receptors

Since the introduction of the alpha function by Rall in 1967 [12], there has been significant progress in our understanding of the molecular events underlying synaptic transmission. Particular receptor types have been identified and their activation kinetics characterized. It is now possible to develop models of these receptors, using a formalism similar to that introduced by Hodgkin and Huxley [9]. In this paper, we present recently-introduced models obtained by simplifying more detailed biophysical models of postsynaptic receptors [7]. The simplified models are fully compatible with the Hodgkin-Huxley formalism, are very efficient to simulate, and account for important phenomena such as synaptic summation and desensitization. These models should be useful in large-scale network simulations.

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.

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.

Dynamic Clamp with High-Resistance Electrodes Using Active Electrode Compensation In Vitro and In Vivo

The active electrode compensation (AEC) consists of an online correction of the recorded membrane potential based on a computational model of the electrode. This technique may be particularly useful for situations where high-frequency components (such as noise) must be injected. This is particularly important for dynamic-clamp applications because of the real-time feedback between injected current and recorded voltage, since any artifact is amplified and may cause instabilities. We show here that such problems are greatly limited by the AEC, and this technique enables dynamic-clamp injection at high feedback frequencies (>10 kHz) and in demanding conditions. We illustrate AEC with applications such as injection of conductance noise in vivo and in vitro.