Biophysical models of synaptic transmission
In collaboration with Zach Mainen and Terrence Sejnowski (Salk Institute, USA), we have developed biophysical models of synaptic transmission on the main receptor types (glutamatergic and GABAergic receptors). The aim of these models was (1) to represent synaptic interactions using the same formalism (Hodgkin-Huxley) as used to represent voltage-dependent conductances; (2) to provide a simple kinetic description that captures the summated behavior of high-frequency presynaptic stimuli; (3) to provide models that are fast to simulate and adequate to be used in network simulations. We proposed a unified description of voltage-dependent and ligand-dependent channels using the same kinetic formalism . From this, we derived simplified models of synaptic conductances based on the kinetics of postsynaptic receptors [1,2]. This method proved useful in modeling various types of glutamatergic and GABAergic synaptic receptors (AMPA, NMDA, GABAA) and is used by many other researchers. It is now incorporated into the widely-used NEURON simulator.
Metabotropic receptors (GABAB and neuromodulators) were also modeled based on kinetic models of K+ channel activation or inactivation by G-proteins [2,3,5]. These relatively detailed models were simplified to yield two-variable representations of GABAB currents that showed correct stimulus/response relations . With Terrence Sejnowski, we also designed a model of GABAergic transmission that incorporated the diffusion of GABA extracellularly and its binding on GABAA and GABAB receptors, possibly located outside the synaptic cleft . This model established that the particular stimulus/response properties of GABAB receptors were best reproduced by assuming that 4 G-proteins are needed to activate the K+ channels associated to these receptors, consistent with the tetrameric structure of K+ channels. These nonlinear properties were characterized more recently, in collaboration with Alex Thomson (University of London, UK), by combining dual intracellular recordings and computational models . The recordings realized by Alex Thomson directly demonstrated the sensitivity to number of presynaptic spikes predicted by models . This property has important consequences for understanding some types of pathological behavior such as absence seizures (see Section 3.4).
Recently, in collaboration with different members of UNIC, we have investigated models of spike-timing dependent plasticity (STDP) [6,7,8]. This form of associative synaptic modification depends on the respective timing of pre- and post-synaptic spikes, but the underlying biophysical mechanisms are unknown. We have proposed a biophysical model of STDP based on enzymatic cascades underlying the activity-dependent regulation of AMPA receptors. One of the successes of this model is that it reproduces the complex spike interactions in STDP (such as triplet interactions and frequency dependence), without any built-in mechanism. A simplified model was also derived, which is computationally efficient, and aimed at being used in network simulations. The most recent "metaplastic STDP" (mSTDP) model  proposes a solution to a well-known caveat of STDP, its sensitivity to spontaneous activity. The mSTDP model includes slower time scale regulations found experimentally and is robust to spontaneous activity. This model was tested in networks of IF neurons displaying self-generated stochastic states .
 Destexhe, A., Mainen, Z.F. and Sejnowski, T.J. An efficient method for computing synaptic conductances based on a kinetic model of receptor binding. Neural Computation 6: 14-18, 1994. (see abstract)
 Destexhe, A., Mainen, Z.F. and Sejnowski, T.J. Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. J. Computational Neuroscience 1: 195-230, 1994. (see abstract)
 Destexhe, A. and Sejnowski, T.J. G-protein activation kinetics and spill-over of GABA may account for differences between inhibitory responses in the hippocampus and thalamus. Proc. Natl. Acad. Sci. USA 92: 9515-9519, 1995. (see abstract)
 Destexhe, A., Mainen, Z.F. and Sejnowski, T.J. Kinetic models of synaptic transmission. In: Methods in Neuronal Modeling (2nd edition), Edited by Koch, C. and Segev, I. MIT Press, Cambridge, MA, pp. 1-26, 1998. (see abstract)
 Thomson, A.M. and Destexhe, A. Dual intracellular recordings and computational models of slow inhibitory postsynaptic potentials in rat neocortical and hippocampal slices. Neuroscience 92: 1193-1215, 1999 (see abstract)
 Badoual, M., Zou, Q., Davison, A.P., Rudolph, M., Bal, T. and Frégnac, Y. and Destexhe, A. Biophysical and phenomenological models of multiple spike interactions in spike-timing dependent plasticity. International Journal of Neural Systems 16: 1-19, 2006 (see abstract)
 Zou, Q. and Destexhe, A. Kinetic models of spike-timing dependent plasticity and their functional consequences in detecting correlations. Biological Cybernetics 97: 81-97, 2007 (see abstract)
 El Boustani S, Yger P, Frégnac Y and Destexhe, A. Stable learning in stochastic network states. Journal of Neuroscience 32: 194-214, 2012. (see abstract)
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