Testing for dependence on tree structures.

Tree structures, showing hierarchical relationships and the latent structures between samples, are ubiquitous in genomic and biomedical sciences. A common question in many studies is whether there is an association between a response variable measured on each sample and the latent group structure represented by some given tree. Currently, this is addressed on an ad hoc basis, usually requiring the user to decide on an appropriate number of clusters to prune out of the tree to be tested against the response variable. Here, we present a statistical method with statistical guarantees that tests for association between the response variable and a fixed tree structure across all levels of the tree hierarchy with high power while accounting for the overall false positive error rate. This enhances the robustness and reproducibility of such findings.

Analysis of patchclamp recordings: model-free multiscale methods and software.

Analysis of patchclamp recordings is often a challenging issue. We give practical guidance how such recordings can be analyzed using the model-free multiscale idealization methodology JSMURF, JULES, and HILDE. We provide an operational manual how to use the accompanying software available as an R-package and as a graphical user interface. This includes selection of the right approach and tuning of parameters. We also discuss advantages and disadvantages of model-free approaches in comparison to hidden Markov model approaches and explain how they complement each other.

Molecular contribution function in RESOLFT nanoscopy.

The ultimate objective of a microscope of the highest resolution is to map the molecules of interest in the sample. Traditionally, linear imaging systems are characterized by their spatial frequency transfer function, which is given, in real space, by the point spread function (PSF). By extending the concept of the PSF towards the molecular contribution function (MCF), that quantifies the average contribution of a single fluorophore to the image, a straightforward concept for counting fluorophores is obtained. Using reversible saturable optical fluorescence transitions (RESOLFT), fluorophores are effectively activated only in a small, subdiffraction-sized volume before they are read out. During readout the signal exhibits an increased variance due to the stochastic nature of prior activation, which scales quadratically with the brightness of the active fluorophores while the mean of the signal scales only linearly with it. Using a two-state Markov model for the activation, showing comparable behavior to the switching kinetics of the switchable fluorescent protein rsEGFP2, we can approximate quantitatively the MCF of RESOLFT nanoscopy allowing to count the number of fluorophores within a subdiffraction-sized region of the sample. The method is validated on measurements of tubulin structures in Drosophila melagonaster larvae. Modeling and estimation of the MCF is a promising approach to quantitative microscopy.

Fluorescence nanoscopy by polarization modulation and polarization angle narrowing.

When excited with rotating linear polarized light, differently oriented fluorescent dyes emit periodic signals peaking at different times. We show that measurement of the average orientation of fluorescent dyes attached to rigid sample structures mapped to regularly defined (50 nm)(2) image nanoareas can provide subdiffraction resolution (super resolution by polarization demodulation, SPoD). Because the polarization angle range for effective excitation of an oriented molecule is rather broad and unspecific, we narrowed this range by simultaneous irradiation with a second, de-excitation, beam possessing a polarization perpendicular to the excitation beam (excitation polarization angle narrowing, ExPAN). This shortened the periodic emission flashes, allowing better discrimination between molecules or nanoareas. Our method requires neither the generation of nanometric interference structures nor the use of switchable or blinking fluorescent probes. We applied the method to standard wide-field microscopy with camera detection and to two-photon scanning microscopy, imaging the fine structural details of neuronal spines.

A studentized permutation test for three-arm trials in the 'gold standard' design.

The 'gold standard' design for three-arm trials refers to trials with an active control and a placebo control in addition to the experimental treatment group. This trial design is recommended when being ethically justifiable and it allows the simultaneous comparison of experimental treatment, active control, and placebo. Parametric testing methods have been studied plentifully over the past years. However, these methods often tend to be liberal or conservative when distributional assumptions are not met particularly with small sample sizes. In this article, we introduce a studentized permutation test for testing non-inferiority and superiority of the experimental treatment compared with the active control in three-arm trials in the 'gold standard' design. The performance of the studentized permutation test for finite sample sizes is assessed in a Monte Carlo simulation study under various parameter constellations. Emphasis is put on whether the studentized permutation test meets the target significance level. For comparison purposes, commonly used Wald-type tests, which do not make any distributional assumptions, are included in the simulation study. The simulation study shows that the presented studentized permutation test for assessing non-inferiority in three-arm trials in the 'gold standard' design outperforms its competitors, for instance the test based on a quasi-Poisson model, for count data. The methods discussed in this paper are implemented in the R package ThreeArmedTrials which is available on the comprehensive R archive network (CRAN). Copyright © 2016 John Wiley & Sons, Ltd.

Design and analysis of three-arm trials with negative binomially distributed endpoints.

A three-arm clinical trial design with an experimental treatment, an active control, and a placebo control, commonly referred to as the gold standard design, enables testing of non-inferiority or superiority of the experimental treatment compared with the active control. In this paper, we propose methods for designing and analyzing three-arm trials with negative binomially distributed endpoints. In particular, we develop a Wald-type test with a restricted maximum-likelihood variance estimator for testing non-inferiority or superiority. For this test, sample size and power formulas as well as optimal sample size allocations will be derived. The performance of the proposed test will be assessed in an extensive simulation study with regard to type I error rate, power, sample size, and sample size allocation. For the purpose of comparison, Wald-type statistics with a sample variance estimator and an unrestricted maximum-likelihood estimator are included in the simulation study. We found that the proposed Wald-type test with a restricted variance estimator performed well across the considered scenarios and is therefore recommended for application in clinical trials. The methods proposed are motivated and illustrated by a recent clinical trial in multiple sclerosis. The R package ThreeArmedTrials, which implements the methods discussed in this paper, is available on CRAN.

Multiscale DNA partitioning: statistical evidence for segments.

MOTIVATION: DNA segmentation, i.e. the partitioning of DNA in compositionally homogeneous segments, is a basic task in bioinformatics. Different algorithms have been proposed for various partitioning criteria such as Guanine/Cytosine (GC) content, local ancestry in population genetics or copy number variation. A critical component of any such method is the choice of an appropriate number of segments. Some methods use model selection criteria and do not provide a suitable error control. Other methods that are based on simulating a statistic under a null model provide suitable error control only if the correct null model is chosen. RESULTS: Here, we focus on partitioning with respect to GC content and propose a new approach that provides statistical error control: as in statistical hypothesis testing, it guarantees with a user-specified probability [Formula: see text] that the number of identified segments does not exceed the number of actually present segments. The method is based on a statistical multiscale criterion, rendering this as a segmentation method that searches segments of any length (on all scales) simultaneously. It is also accurate in localizing segments: under benchmark scenarios, our approach leads to a segmentation that is more accurate than the approaches discussed in the comparative review of Elhaik et al. In our real data examples, we find segments that often correspond well to features taken from standard University of California at Santa Cruz (UCSC) genome annotation tracks. AVAILABILITY AND IMPLEMENTATION: Our method is implemented in function smuceR of the R-package stepR available at http://www.stochastik.math.uni-goettingen.de/smuce.

Aggregated motion estimation for real-time MRI reconstruction.

PURPOSE: In real-time MRI serial images are generally reconstructed from highly undersampled datasets as the iterative solutions of an inverse problem. While practical realizations based on regularized nonlinear inversion (NLINV) have hitherto been surprisingly successful, strong assumptions about the continuity of image features may affect the temporal fidelity of the estimated reconstructions. THEORY AND METHODS: The proposed method for real-time image reconstruction integrates the deformations between nearby frames into the data consistency term of the inverse problem. The aggregated motion estimation (AME) is not required to be affine or rigid and does not need additional measurements. Moreover, it handles multi-channel MRI data by simultaneously determining the image and its coil sensitivity profiles in a nonlinear formulation which also adapts to non-Cartesian (e.g., radial) sampling schemes. The new method was evaluated for real-time MRI studies using highly undersampled radial gradient-echo sequences. RESULTS: AME reconstructions for a motion phantom with controlled speed as well as for measurements of human heart and tongue movements demonstrate improved temporal fidelity and reduced residual undersampling artifacts when compared with NLINV reconstructions without motion estimation. CONCLUSION: Nonlinear inverse reconstructions with aggregated motion estimation offer improved image quality and temporal acuity for visualizing rapid dynamic processes by real-time MRI.

Design and semiparametric analysis of non-inferiority trials with active and placebo control for censored time-to-event data.

The clinical trial design including a test treatment, an active control and a placebo is called the gold standard design. In this paper, we develop a statistical method for planning and evaluating non-inferiority trials with gold standard design for right-censored time-to-event data. We consider both lost to follow-up and administrative censoring. We present a semiparametric approach that only assumes the proportionality of the hazard functions. In particular, we develop an algorithm for calculating the minimal total sample size and its optimal allocation to treatment groups such that a desired power can be attained for a specific parameter constellation under the alternative. For the purpose of sample size calculation, we assume the endpoints to be Weibull distributed. By means of simulations, we investigate the actual type I error rate, power and the accuracy of the calculated sample sizes. Finally, we compare our procedure with a previously proposed procedure assuming exponentially distributed event times. To illustrate our method, we consider a double-blinded, randomized, active and placebo controlled trial in major depression.

Towards Unbiased Fluorophore Counting in Superresolution Fluorescence Microscopy.

With the advent of fluorescence superresolution microscopy, nano-sized structures can be imaged with a previously unprecedented accuracy. Therefore, it is rapidly gaining importance as an analytical tool in the life sciences and beyond. However, the images obtained so far lack an absolute scale in terms of fluorophore numbers. Here, we use, for the first time, a detailed statistical model of the temporal imaging process which relies on a hidden Markov model operating on two timescales. This allows us to extract this information from the raw data without additional calibration measurements. We show this on the basis of added data from experiments on single Alexa 647 molecules as well as GSDIM/dSTORM measurements on DNA origami structures with a known number of labeling positions.

Toward quantitative super-resolution microscopy: molecular maps with statistical guarantees.

Quantifying the number of molecules from fluorescence microscopy measurements is an important topic in cell biology and medical research. In this work, we present a consecutive algorithm for super-resolution (stimulated emission depletion (STED)) scanning microscopy that provides molecule counts in automatically generated image segments and offers statistical guarantees in form of asymptotic confidence intervals. To this end, we first apply a multiscale scanning procedure on STED microscopy measurements of the sample to obtain a system of significant regions, each of which contains at least one molecule with prescribed uniform probability. This system of regions will typically be highly redundant and consists of rectangular building blocks. To choose an informative but non-redundant subset of more naturally shaped regions, we hybridize our system with the result of a generic segmentation algorithm. The diameter of the segments can be of the order of the resolution of the microscope. Using multiple photon coincidence measurements of the same sample in confocal mode, we are then able to estimate the brightness and number of molecules and give uniform confidence intervals on the molecule counts for each previously constructed segment. In other words, we establish a so-called molecular map with uniform error control. The performance of the algorithm is investigated on simulated and real data.

Partial least-squares functional mode analysis: application to the membrane proteins AQP1, Aqy1, and CLC-ec1.

We introduce an approach based on the recently introduced functional mode analysis to identify collective modes of internal dynamics that maximally correlate to an external order parameter of functional interest. Input structural data can be either experimentally determined structure ensembles or simulated ensembles, such as molecular dynamics trajectories. Partial least-squares regression is shown to yield a robust solution to the multidimensional optimization problem, with a minimal and controllable risk of overfitting, as shown by extensive cross-validation. Several examples illustrate that the partial least-squares-based functional mode analysis successfully reveals the collective dynamics underlying the fluctuations in selected functional order parameters. Applications to T4 lysozyme, the Trp-cage, the aquaporin channels Aqy1 and hAQP1, and the CLC-ec1 chloride antiporter are presented in which the active site geometry, the hydrophobic solvent-accessible surface, channel gating dynamics, water permeability (p(f)), and a dihedral angle are defined as functional order parameters. The Aqy1 case reveals a gating mechanism that connects the inner channel gating residues with the protein surface, thereby providing an explanation of how the membrane may affect the channel. hAQP1 shows how the p(f) correlates with structural changes around the aromatic/arginine region of the pore. The CLC-ec1 application shows how local motions of the gating Glu(148) couple to a collective motion that affects ion affinity in the pore.

Drift estimation for single marker switching based imaging schemes.

In recent years, the diffraction barrier in fluorescence imaging has been broken and optical nanoscopes now routinely image with resolutions of down to 20 nm, an improvement of more than 10 fold. Because this allows imaging much smaller features and because all super-resolution approaches trade off speed for spatial resolution, mechanical instabilities of the microscopes become a limiting factor. Here, we propose a fully data-driven statistical registration method for drift detection and drift correction for single marker switching (SMS) imaging schemes, including a guideline for parameter choice and quality checks of the drift analysis. The necessary assumptions about the drift are minimal, allowing a model-free approach, but more specific models can easily be integrated. We determine the resulting performance on standard SMS measurements and show that the drift determination can be routinely brought to the range of precision achievable by fiducial marker-tracking methods.

Heterogeneous Idealization of Ion Channel Recordings - Open Channel Noise.

We propose a new model-free segmentation method for idealizing ion channel recordings. This method is designed to deal with heterogeneity of measurement errors. This in particular applies to open channel noise which, in general, is particularly difficult to cope with for model-free approaches. Our methodology is able to deal with lowpass filtered data which provides a further computational challenge. To this end we propose a multiresolution testing approach, combined with local deconvolution to resolve the lowpass filter. Simulations and statistical theory confirm that the proposed idealization recovers the underlying signal very accurately at presence of heterogeneous noise, even when events are shorter than the filter length. The method is compared to existing approaches in computer experiments and on real data. We find that it is the only one which allows to identify openings of the PorB porine at two different temporal scales. An implementation is available as an R package.

Multiple haplotype reconstruction from allele frequency data.

Because haplotype information is of widespread interest in biomedical applications, effort has been put into their reconstruction. Here, we propose an efficient method, called haploSep, that is able to accurately infer major haplotypes and their frequencies just from multiple samples of allele frequency data. Even the accuracy of experimentally obtained allele frequencies can be improved by re-estimating them from our reconstructed haplotypes. From a methodological point of view, we model our problem as a multivariate regression problem where both the design matrix and the coefficient matrix are unknown. Compared to other methods, haploSep is very fast, with linear computational complexity in the haplotype length. We illustrate our method on simulated and real data focusing on experimental evolution and microbial data.

Colocalization for super-resolution microscopy via optimal transport.

Super-resolution fluorescence microscopy is a widely used technique in cell biology. Stimulated emission depletion (STED) microscopy enables the recording of multiple-color images with subdiffraction resolution. The enhanced resolution leads to new challenges regarding colocalization analysis of macromolecule distributions. We demonstrate that well-established methods for the analysis of colocalization in diffraction-limited datasets and for coordinate-stochastic nanoscopy are not equally well suited for the analysis of high-resolution STED images. We propose optimal transport colocalization, which measures the minimal transporting cost below a given spatial scale to match two protein intensity distributions. Its validity on simulated data as well as on dual-color STED recordings of yeast and mammalian cells is demonstrated. We also extend the optimal transport colocalization methodology to coordinate-stochastic nanoscopy.

An antibiotic-resistance conferring mutation in a neisserial porin: Structure, ion flux, and ampicillin binding.

Gram-negative bacteria cause the majority of highly drug-resistant bacterial infections. To cross the outer membrane of the complex Gram-negative cell envelope, antibiotics permeate through porins, trimeric channel proteins that enable the exchange of small polar molecules. Mutations in porins contribute to the development of drug-resistant phenotypes. In this work, we show that a single point mutation in the porin PorB from Neisseria meningitidis, the causative agent of bacterial meningitis, can strongly affect the binding and permeation of beta-lactam antibiotics. Using X-ray crystallography, high-resolution electrophysiology, atomistic biomolecular simulation, and liposome swelling experiments, we demonstrate differences in drug binding affinity, ion selectivity and drug permeability of PorB. Our work further reveals distinct interactions between the transversal electric field in the porin eyelet and the zwitterionic drugs, which manifest themselves under applied electric fields in electrophysiology and are altered by the mutation. These observations may apply more broadly to drug-porin interactions in other channels. Our results improve the molecular understanding of porin-based drug-resistance in Gram-negative bacteria.

High-resolution experimental and computational electrophysiology reveals weak ß-lactam binding events in the porin PorB.

The permeation of most antibiotics through the outer membrane of Gram-negative bacteria occurs through porin channels. To design drugs with increased activity against Gram-negative bacteria in the face of the antibiotic resistance crisis, the strict constraints on the physicochemical properties of the permeants imposed by these channels must be better understood. Here we show that a combination of high-resolution electrophysiology, new noise-filtering analysis protocols and atomistic biomolecular simulations reveals weak binding events between the ß-lactam antibiotic ampicillin and the porin PorB from the pathogenic bacterium Neisseria meningitidis. In particular, an asymmetry often seen in the electrophysiological characteristics of ligand-bound channels is utilised to characterise the binding site and molecular interactions in detail, based on the principles of electro-osmotic flow through the channel. Our results provide a rationale for the determinants that govern the binding and permeation of zwitterionic antibiotics in porin channels.

Global models for the orientation field of fingerprints: an approach based on quadratic differentials.

Quadratic differentials naturally define analytic orientation fields on planar surfaces. We propose to model orientation fields of fingerprints by specifying quadratic differentials. Models for all fingerprint classes such as arches, loops and whorls are laid out. These models are parametrised by few, geometrically interpretable parameters which are invariant under Euclidean motions. We demonstrate their ability in adapting to given, observed orientation fields, and we compare them to existing models using the fingerprint images of the NIST Special Database 4. We also illustrate that these model allow for extrapolation into unobserved regions. This goes beyond the scope of earlier models for the orientation field as those are restricted to the observed planar fingerprint region. Within the framework of quadratic differentials we are able to verify analytically Penrose's formula for the singularities on a palm. Potential applications of these models are the use of their parameters as indices of large fingerprint databases, as well as the definition of intrinsic coordinates for single fingerprint images.