Heterogeneous Multiscale Change-Point Inference and its Application to Ion Channel Recordings
von Florian Pein
Datum der mündl. Prüfung:2017-10-20
Betreuer:Prof. Dr. Axel Munk
Gutachter:Prof. Dr. Axel Munk
Gutachter:Prof. Dr. Andrea Krajina
EnglischIon channel recordings by the patch clamp technique are a major tool to quantify the electrophysiological dynamics of ion channels in the cell membrane, which is for instance important in medicine for the development of new drugs. In this work, we model these recordings as a time series which is equidistantly sampled from the convolution of a piecewise constant signal disturbed by white noise with a lowpass filter. We focus on nonparametric estimation of the underlying signal, but also discuss how to use these estimations to analyze the recordings. Estimating the underlying signal requires to detect multiple change-points in noisy and filtered Gaussian observations. The variance can be constant in time, but also a varying variance is observed in some measurements. Since this change-point regression problem is very difficult, we start with independent Gaussian observations but with heterogeneous noise. Such a model is of its own interest and has further applications for instance in genetics. For this model, we propose the heterogeneous simultaneous multiscale change-point estimator, H-SMUCE. It estimates the piecewise constant function by minimizing the number of change-points over the acceptance region of a multiscale test which locally adapts to changes in the variance. The multiscale test is a combination of local likelihood ratio tests which are properly calibrated by scale dependent critical values in order to keep a global nominal level alpha, even for finite samples. We show that H-SMUCE controls over- and underestimation of the number of change-points at a given probability for finitely many observations. To this end, new deviation bounds for F-type statistics are derived. We also bound the implicitly defined critical values. By combining these bounds, we obtain simultaneous confidence intervals for the change-point locations and a confidence band for the whole signal. Moreover, it allows us to show that H-SMUCE achieves the optimal detection rate and estimates the number of change-points consistently for vanishing signals, even when the number of change-points is unbounded. The only extra assumption we have to suppose is that the length of the constant segments does not vanished too fast. We compare the performance of H-SMUCE with several state of the art methods in simulations and show how it can be computed efficiently by a pruned dynamic program. An R-package is provided. In a second step we combine these multiscale regression techniques with deconvolution to obtain non-parametric estimators for the ion channel recordings. Truncating the filter kernel and pre-estimating the function values on longer constant segments enable us to perform the deconvolution locally which allows fast computation. Simulations and real data applications confirm that the proposed segmentation methods, JULES and JILTAD, estimate the underlying signal very accurately, even when events occur on small temporal scales, where the smoothing effect of the filter hinders estimation by common methods. Moreover, JILTAD shows still good results when the noise is heterogeneous, a situation for which previously no non-parametric estimation method existed. Also these methods are implemented in R. The usage of these methods is demonstrated in a biochemical study against the context of multidrug-resistant bacteria. We showed statistically significant differences for the interaction of the antibiotic ampicillin with the wild type and with the mutant G103K of the outer membrane channel PorB. These results improves the understanding of potential sources for bacterial resistance and might help to develop new drugs against it to alleviate the severe consequences of multidrug-resistant bacteria.
Keywords: change-point regression; deconvolution; deviation bounds; dynamic programming; flickering event detection; heterogeneous noise; honest confidence sets; inverse problems; multidrug-resistant bacteria; multiscale methods; planar patch clamp; robustness; scale dependent critical values