Abstract or Additional Information
Abstract: A general challenge in neuroscience is to unveil the quantity of current that a neuron is receiving from other neurons and discerning between excitatory and inhibitory inputs. In particular, the goal is to estimate the time course of the synaptic conductances impinging on a cell. This quantity is experimentally inaccessible and instead requires inverse methods. A plethora of mathematical techniques exist in order to solve this inverse problem. Several methods are based on the assumption of membrane potential being driven only by linear terms, but there exist substantial misestimations in spiking regimes. Moreover, 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 non-linear contaminations. In this talk, we propose two methods to improve estimation methods aiming at incorporating nonlinear effects. The first includes quadratic-like stochastic methods to estimate conductances in the subthreshold activity. The second one uses slow-fast theory in piecewise linear systems to estimate conductances in the spiking regimes.