Nonlinear strategies to estimate synaptic conductances

A current challenge in neuroscience is to unveil the quantity of information that a neuron is receiving from other neurons and discerning between excitatory and inhibitory inputs. Concretely, the goal is to estimate the time course of the synaptic conductance impinging on a cell, a quantity that cannot be experimentally recorded and thus requiring inverse methods.

Nowadays, a plethora of mathematical techniques have been developed in order to solve this inverse problem. Seminal of this methods were based on the assumption of membrane potential being driven only by linear terms, but warning messages were thrown about huge misestimations in spiking regimes. Moreover, it has been also proven that ionic currents active in the subthreshold regime can also contaminate these estimations. Many recent methods, mostly based on observation of time constants and statistical inference tools, concentrate on the subthreshold activity without considering possible nonlinear contaminations.

In this talk, we will explain new proposals that we have recently developed to improve estimation methods aiming at incorporating nonlinear effects. These include a slow-fast dissection and quadratic-like stochastic methods for subthreshold activity, and the use of bifurcation theory in spiking regimes.