Bounds for the Minimum Distance and Covering Radius of Orthogonal Arrays via Their Distance Distributions

We propose two methods for obtaining estimations on the minimum distance and covering radius of orthogonal arrays. Both methods are based on knowledge about the (feasible) sets of distance distributions of orthogonal arrays with given length, cardinality, factors and strength. New bounds are presented either in analytic form and as products of an ongoing project for computation and investigation of the possible distance distributions of orthogonal arrays with parameters in doable ranges.

A Comparison of Cysteine-Conjugated Nitroxide Spin Labels for Pulse Dipolar EPR Spectroscopy

The structure-function and materials paradigms drive research on the understanding of structures and structural heterogeneity of molecules and solids from materials science to structural biology. Functional insights into complex architectures are often gained from a suite of complementary physicochemical methods. In the context of biomacromolecular structures, the use of pulse dipolar electron paramagnetic resonance spectroscopy (PDS) has become increasingly popular. The main interest in PDS is providing long-range nanometre distance distributions that allow for identifying macromolecular topologies, validating structural models and conformational transitions as well as docking of quaternary complexes. Most commonly, cysteines are introduced into protein structures by site-directed mutagenesis and modified site-specifically to a spin-labelled side-chain such as a stable nitroxide radical. In this contribution, we investigate labelling by four different commercial labelling agents that react through different sulfur-specific reactions. Further, the distance distributions obtained are between spin-bearing moieties and need to be related to the protein structure via modelling approaches. Here, we compare two different approaches to modelling these distributions for all four side-chains. The results indicate that there are significant differences in the optimum labelling procedure. All four spin-labels show differences in the ease of labelling and purification. Further challenges arise from the different tether lengths and rotamers of spin-labelled side-chains; both influence the modelling and translation into structures. Our comparison indicates that the spin-label with the shortest tether in the spin-labelled side-group, (bis-(2,2,5,5-Tetramethyl-3-imidazoline-1-oxyl-4-yl) disulfide, may be underappreciated and could increase the resolution of structural studies by PDS if labelling conditions are optimised accordingly.

The Exploitation of Distance Distributions for Clustering

Although distance measures are used in many machine learning algorithms, the literature on the context-independent selection and evaluation of distance measures is limited in the sense that prior knowledge is used. In cluster analysis, current studies evaluate the choice of distance measure after applying unsupervised methods based on error probabilities, implicitly setting the goal of reproducing predefined partitions in data. Such studies use clusters of data that are often based on the context of the data as well as the custom goal of the specific study. Depending on the data context, different properties for distance distributions are judged to be relevant for appropriate distance selection. However, if cluster analysis is based on the task of finding similar partitions of data, then the intrapartition distances should be smaller than the interpartition distances. By systematically investigating this specification using distribution analysis through the mirrored-density (MD plot), it is shown that multimodal distance distributions are preferable in cluster analysis. As a consequence, it is advantageous to model distance distributions with Gaussian mixtures prior to the evaluation phase of unsupervised methods. Experiments are performed on several artificial datasets and natural datasets for the task of clustering.

Methodology for rigorous modeling of protein conformational changes by Rosetta using DEER Distance Restraints

We describe an approach for integrating distance restraints from Double Electron-Electron Resonance (DEER) spectroscopy into Rosetta with the purpose of modeling alternative protein conformations from an initial experimental structure. Fundamental to this approach is a multilateration algorithm that harnesses sets of interconnected spin label pairs to identify optimal rotamer ensembles at each residue that fit the DEER decay in the time domain. Benchmarked relative to data analysis packages, the algorithm yields comparable distance distributions with the advantage that fitting the DEER decay and rotamer ensemble optimization are coupled. We demonstrate this approach by modeling the protonation-dependent transition of the multidrug transporter PfMATE to an inward facing conformation with a deviation to the experimental structure of less than 2Å Cα RMSD. By decreasing spin label rotamer entropy, this approach engenders more accurate Rosetta models that are also more closely clustered, thus setting the stage for more robust modeling of protein conformational changes.

Differences in nanoscale organization of DNase I hypersensitive and insensitive chromatin in single human cells

Methodological advances in conformation capture techniques have fundamentally changed our understanding of chromatin architecture. However, the nanoscale organization of chromatin and its cell-to-cell variance are less studied. By using a combination of high throughput super-resolution microscopy and coarse-grained modelling we investigated properties of active and inactive chromatin in interphase nuclei. Using DNase I hypersensitivity as a criterion, we have selected prototypic active and inactive regions from ENCODE data that are representative for K-562 and more than 150 other cell types. By using oligoFISH and automated STED microscopy we systematically measured physical distances of the endpoints of 5kb DNA segments in these regions. These measurements result in high-resolution distance distributions which are right-tailed and range from very compact to almost elongated configurations of more than 200 nm length for both the active and inactive regions. Coarse-grained modeling of the respective DNA segments suggests that in regions with high DNase I hypersensitivity cell-to-cell differences in nucleosome occupancy determine the histogram shape. Simulations of the inactive region cannot sufficiently describe the compaction measured by microscopy, although internucleosomal interactions were elevated and the linker histone H1 was included in the model. These findings hint at further organizational mechanisms while the microscopy-based distance distribution indicates high cell-to-cell differences also in inactive chromatin regions. The analysis of the distance distributions suggests that direct enhancer-promoter contacts, which most models of enhancer action assume, happen for proximal regulatory elements in a probabilistic manner due to chromatin flexibility.

Characterization of Weak Protein Domain Structure by Spin-Label Distance Distributions

Function of intrinsically disordered proteins may depend on deviation of their conformational ensemble from that of a random coil. Such deviation may be hard to characterize and quantify, if it is weak. We explored the potential of distance distributions between spin labels, as they can be measured by electron paramagnetic resonance techniques, for aiding such characterization. On the example of the intrinsically disordered N-terminal domain 1–267 of fused in sarcoma (FUS) we examined what such distance distributions can and cannot reveal on the random-coil reference state. On the example of the glycine-rich domain 188–320 of heterogeneous nuclear ribonucleoprotein A1 (hnRNP A1) we studied whether deviation from a random-coil ensemble can be robustly detected with 19 distance distribution restraints. We discuss limitations imposed by ill-posedness of the conversion of primary data to distance distributions and propose overlap of distance distributions as a fit criterion that can tackle this problem. For testing consistency and size sufficiency of the restraint set, we propose jack-knife resampling. At current desktop computers, our approach is expected to be viable for domains up to 150 residues and for between 10 and 50 distance distribution restraints.

Six-Pulse RIDME Sequence to Avoid Background Artifacts

Relaxation induced dipolar modulation enhancement (RIDME) is a valuable method for measuring nanometer-scale distances between electron spin centers. Such distances are widely used in structural biology to study biomolecular structures and track their conformational changes. Despite significant improvements of RIDME in recent years, the background analysis of primary RIDME signals remains to be challenging. In particular, it was recently shown that the five-pulse RIDME signals contain an artifact which can hinder the accurate extraction of distance distributions from RIDME time traces [as reported by Ritsch et al. (Phys Chem Chem Phys 21: 9810, 2019)]. Here, this artifact, as well as one additionally identified artifact, are systematically studied on several model compounds and the possible origins of both artifacts are discussed. In addition, a new six-pulse RIDME sequence is proposed that eliminates the artifact with the biggest impact on the extracted distance distributions. The efficiency of this pulse sequence is confirmed on several examples.

CellMixS: quantifying and visualizing batch effects in single-cell RNA-seq data

A key challenge in single-cell RNA-sequencing (scRNA-seq) data analysis is batch effects that can obscure the biological signal of interest. Although there are various tools and methods to correct for batch effects, their performance can vary. Therefore, it is important to understand how batch effects manifest to adjust for them. Here, we systematically explore batch effects across various scRNA-seq datasets according to magnitude, cell type specificity, and complexity. We developed a cell-specific mixing score (cms) that quantifies mixing of cells from multiple batches. By considering distance distributions, the score is able to detect local batch bias as well as differentiate between unbalanced batches and systematic differences between cells of the same cell type. We compare metrics in scRNA-seq data using real and synthetic datasets and whereas these metrics target the same question and are used interchangeably, we find differences in scalability, sensitivity, and ability to handle differentially abundant cell types. We find that cell-specific metrics outperform cell type–specific and global metrics and recommend them for both method benchmarks and batch exploration.