Efficient estimation of detailed single-neuron models

Quentin Huys, Misha Ahrens, Liam Paninski

Journal of Neurophysiology 96: 872-890.

Biophysically accurate multi-compartmental models of individual neurones have signi cantly advanced our understanding of the input-output function of single cells. These models depend on a large number of parameters which are dif cult to estimate. In practise, they are often hand tuned to match measured physiological behaviors, thus raising questions of identifiability and interpretability. We propose a statistical approach to the automatic estimation of various biologically relevant parameters, including 1) the distribution of channel densities; 2) the spatiotemporal pattern of synaptic input; and 3) axial resistances across extended dendrites. Recent experimental advances, notably in voltage-sensitive imaging, motivate us to assume access to: a) the spatiotemporal voltage signal in the dendrite, and b) an approximate description of the channel kinetics of interest. We show here that, given a) and b), the parameters 1)-3) can be inferred simultaneously by nonnegative linear regression; that this optimization problem possesses a unique solution and is guaranteed to converge despite the large number of parameters and their complex nonlinear interaction; and that standard optimization algorithms ef ciently reach this optimum with modest computational and data requirements. We demonstrate that the method leads to accurate estimations on a wide variety of challenging model data sets that include up to on the order of 10,000 parameters (roughly two orders of magnitude more than previously feasible), and describe how the method gives insights into the functional interaction of groups of channels.

A preliminary account of this work appeared as "Large-scale biophysical parameter estimation in single neurons via constrained linear regression," by Ahrens, Huys, and Paninski, in Advances in Neural Information Processing 2006.
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