Parameter estimation in neuronal stochastic differential equation models from intracellular recordings of membrane potentials in single neurons: a Review

Ditlevsen, Susanne; Samson, Adeline

Journal de la société française de statistique, Tome 157 (2016) no. 1, pp. 6-21.

On peut étudier la dynamique du potentiel de la membrane d’un neurone en estimant des paramètres biophysiques à partir d’enregistrement intracellulaire. Les processus de diffusion, définis comme solution à temps continu d’équations différentielles stochastiques ont été très utilisés pour modéliser l’évolution du potentiel membranaire. Parmi les processus de dimension un, les plus connus sont les modèles de diffusion intègre-et-tire. D’autres modèles neuronaux sont plus biophysiques et prennent en compte la dynamique des canaux ioniques ou de l’activité synaptique. Ce sont des processus de diffusion multidimensionnels. L’estimation des paramètres de ces modèles est difficile car seulement le potentiel membranaire peut être mesuré. Ce papier résume les techniques d’estimation qui ont été proposées pour ces modèles de diffusion de données intracellulaires.

Dynamics of the membrane potential in a single neuron can be studied by estimating biophysical parameters from intracellular recordings. Diffusion processes, given as continuous solutions to stochastic differential equations, are widely applied as models for the neuronal membrane potential evolution. One-dimensional models are the stochastic integrate-and-fire neuronal diffusion models. Biophysical neuronal models take into account the dynamics of ion channels or synaptic activity, leading to multidimensional diffusion models. Since only the membrane potential can be measured, this complicates the statistical inference and parameter estimation from these partially observed detailed models. This paper reviews parameter estimation techniques from intracellular recordings in these diffusion models.

Keywords: integrate-and-fire models, conductance based models, state space models, synaptic input estimation, maximum likelihood estimation, particle filter, estimating functions, MCMC methods, partial observations
Mot clés : modèles de diffusion intègre-et-tire, modèles de conductances, modèles à espace d’états, estimation synaptique, maximum de vraisemblance, filtre particulaire, fonctions estimantes, MCMC, observations partielles

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