Smoothing of, and Parameter Estimation from, Noisy Biophysical Recordings

Biophysically detailed models of single cells are difficult to fit to real data. Recent advances in imaging techniques allow simultaneous access to various intracellular variables, and these data can be used to significantly facilitate the modelling task. These data, however, are noisy, and current approaches to building biophysically detailed models are not designed to deal with this. We extend previous techniques to take the noisy nature of the measurements into account. Sequential Monte Carlo (“particle filtering”) methods, in combination with a detailed biophysical description of a cell, are used for principled, model-based smoothing of noisy recording data. We also provide an alternative formulation of smoothing where the neural nonlinearities are estimated in a non-parametric manner. Biophysically important parameters of detailed models (such as channel densities, intercompartmental conductances, input resistances, and observation noise) are inferred automatically from noisy data via expectation-maximisation. Overall, we find that model-based smoothing is a powerful, robust technique for smoothing of noisy biophysical data and for inference of biophysical parameters in the face of recording noise. Author Summary: Cellular imaging techniques are maturing at a great pace, but are still plagued by high levels of noise. Here, we present two methods for smoothing individual, noisy traces. The first method fits a full, biophysically accurate description of the cell under study to the noisy data. This allows both smoothing of the data and inference of biophysically relevant parameters such as the density of (active) channels, input resistance, intercompartmental conductances, and noise levels; it does, however, depend on knowledge of active channel kinetics. The second method achieves smoothing of noisy traces by fitting arbitrary kinetics in a non-parametric manner. Both techniques can additionally be used to infer unobserved variables, for instance voltage from calcium concentration. This paper gives a detailed account of the methods and should allow for straightforward modification and inclusion of additional measurements.