A Modern Approach to Stability Studies via Bayesian Linear Mixed Models Incorporating Auxiliary Effects.

In preparation to the launch of a pharmaceutical product, an estimate of its shelf life via stability testing is required by regulatory agencies. The ICH-Q1E guidance has been the worldwide reference to reach this objective, but in recent years several authors have criticized many of its aspects. To that end we discuss a complete Bayesian transcript of the ICH-Q1E, treating all the apparent shortcomings, while also addressing the presence of multiple batches using a linear mixed model (LMM) for proper shelf life prediction by explicitly modelling the batch-to-batch variability. This comprises a redefinition of the linear models proposed in the ICH-Q1E by suitable LMM counterparts, and a Bayesian analogue for model selection, which is more intuitive and remedies detrimental features of the ICH approach. In that context, a proper mathematical foundation of shelf life is provided that we use to investigate and mathematically compare the two available approaches to shelf life determination via shelf life distribution and batch distribution. The discussed method is then tested and evaluated using real data in comparison with the ICH-Q1E approach demonstrating their approximate equivalency for 6 batches. As a major objective, we extended the LMM with auxiliary fixed effects, here the concentration, which interconnect data sets allowing a prediction of shelf lives for concentrations lacking a sufficient number of batches. This establishes a novel approach to accelerate the speed to submission while retaining the patients' safety. Both case studies underline the inherent superiority of LMMs within a Bayesian framework regarding predictability and interpretability, and we hope that the relevant authorities will accept this approach in the future.

Structural dynamics of DNA strand break sensing by PARP-1 at a single-molecule level.

Single-stranded breaks (SSBs) are the most frequent DNA lesions threatening genomic integrity. A highly kinked DNA structure in complex with human PARP-1 domains led to the proposal that SSB sensing in Eukaryotes relies on dynamics of both the broken DNA double helix and PARP-1's multi-domain organization. Here, we directly probe this process at the single-molecule level. Quantitative smFRET and structural ensemble calculations reveal how PARP-1's N-terminal zinc fingers convert DNA SSBs from a largely unperturbed conformation, via an intermediate state into the highly kinked DNA conformation. Our data suggest an induced fit mechanism via a multi-domain assembly cascade that drives SSB sensing and stimulates an interplay with the scaffold protein XRCC1 orchestrating subsequent DNA repair events. Interestingly, a clinically used PARP-1 inhibitor Niraparib shifts the equilibrium towards the unkinked DNA conformation, whereas the inhibitor EB47 stabilizes the kinked state.

Determination of the Three-Dimensional Magnetic Field Vector Orientation with Nitrogen Vacany Centers in Diamond.

Absolute knowledge about the magnetic field orientation plays a crucial role in single spin-based quantum magnetometry and the application toward spin-based quantum computation. In this paper, we reconstruct the three-dimensional orientation of an arbitrary static magnetic field with individual nitrogen vacancy (NV) centers in diamond. We determine the polar and the azimuthal angle of the magnetic field orientation relative to the diamond lattice. Therefore, we use information from the photoluminescence anisotropy of the NV, together with a simple pulsed optically detected magnetic resonance experiment. Our nanoscopic magnetic field determination is generally applicable and does not rely on special prerequisites such as strongly coupled nuclear spins or particular controllable fields. Hence, our presented results open up new paths for precise NMR reconstructions and the modulation of the electron-electron spin interaction in EPR measurements by specifically tailored magnetic fields.

Publisher Correction: Precision and accuracy of single-molecule FRET measurements-a multi-laboratory benchmark study.

This paper was originally published under standard Springer Nature copyright. As of the date of this correction, the Analysis is available online as an open-access paper with a CC-BY license. No other part of the paper has been changed.

Complete Kinetic Theory of FRET.

Förster resonance energy transfer (FRET) can be used to measure distances and infer structures at the molecular level. However, the flexible linkers with which the fluorophores are attached to a macromolecule introduce a lack of knowledge. Both the dye's geometry and kinetics give rise to uncertainties. Whereas the impact of the geometry is already well understood, the real extent of the kinetics has not been investigated thoroughly. Here, we present a single-molecule (sm)FRET theory that defines the kinetics of dye movements in a complete form. We introduce a formal nomenclature and provide a recipe for the calculation of the corresponding FRET efficiency. We further analyze experimental data in order to obtain parameters characterizing the geometry and kinetics of the FRET dyes and use them to resimulate the FRET efficiencies by diffusion of fluorophore and linker movement. We show in a real case scenario of dye molecules attached to dsDNA that when making geometrical and kinetic assumptions commonly used in the FRET community one obtains results differing from the experimental data. In contrast, our stochastic simulations taking kinetic parameters from experiments into account reproduce the correct FRET efficiencies. Furthermore, we present a method enabling us to classify the kinetics of the dyes by investigating single realizations of the simulated transfer process. The results support our notion that the common kinetic assumptions are not appropriate over the whole range of distances inferred by FRET even for the simple situation of dyes attached to DNA where few interactions occur.

Precision and accuracy of single-molecule FRET measurements-a multi-laboratory benchmark study.

Single-molecule Förster resonance energy transfer (smFRET) is increasingly being used to determine distances, structures, and dynamics of biomolecules in vitro and in vivo. However, generalized protocols and FRET standards to ensure the reproducibility and accuracy of measurements of FRET efficiencies are currently lacking. Here we report the results of a comparative blind study in which 20 labs determined the FRET efficiencies (E) of several dye-labeled DNA duplexes. Using a unified, straightforward method, we obtained FRET efficiencies with s.d. between ±0.02 and ±0.05. We suggest experimental and computational procedures for converting FRET efficiencies into accurate distances, and discuss potential uncertainties in the experiment and the modeling. Our quantitative assessment of the reproducibility of intensity-based smFRET measurements and a unified correction procedure represents an important step toward the validation of distance networks, with the ultimate aim of achieving reliable structural models of biomolecular systems by smFRET-based hybrid methods.

Precision and accuracy in smFRET based structural studies-A benchmark study of the Fast-Nano-Positioning System.

Modern hybrid structural analysis methods have opened new possibilities to analyze and resolve flexible protein complexes where conventional crystallographic methods have reached their limits. Here, the Fast-Nano-Positioning System (Fast-NPS), a Bayesian parameter estimation-based analysis method and software, is an interesting method since it allows for the localization of unknown fluorescent dye molecules attached to macromolecular complexes based on single-molecule Förster resonance energy transfer (smFRET) measurements. However, the precision, accuracy, and reliability of structural models derived from results based on such complex calculation schemes are oftentimes difficult to evaluate. Therefore, we present two proof-of-principle benchmark studies where we use smFRET data to localize supposedly unknown positions on a DNA as well as on a protein-nucleic acid complex. Since we use complexes where structural information is available, we can compare Fast-NPS localization to the existing structural data. In particular, we compare different dye models and discuss how both accuracy and precision can be optimized.

smFRET experiments of the RNA polymerase II transcription initiation complex.

Single-molecule fluorescence and in particular single-molecule Förster Resonance Energy Transfer (smFRET) is a powerful tool to provide real-time information on the dynamic architecture of large macromolecular structures such as eukaryotic transcription initiation complexes. In contrast to other structural biology methods, not only structural details, but dynamics transitions are revealed thus closing in on the underlying molecular mechanisms. Here, we describe a comprehensive quantitative biophysical toolbox which can be used for rigorous analysis of dynamic protein-nucleic acid complexes and is applied to the study of eukaryotic transcription initiation. We present detailed protocols for the purification of all essential protein components of the minimal eukaryotic transcription initiation complex. Moreover, we demonstrate how elaborate strategies for site-specific protein labeling can be used to produce complexes with dye molecules attached to arbitrary desired positions. These complexes are then used for smFRET measurements. Moreover, we describe the Nano-Positioning System (NPS) which allows us to quantitatively use the results from a network of smFRET measurements to obtain structural information. With this we provide a toolbox to answer open questions which could not be addressed using methods like X-ray crystallography or cryo-electron microscopy.

Structural Information from Single-molecule FRET Experiments Using the Fast Nano-positioning System.

Single-molecule Förster Resonance Energy Transfer (smFRET) can be used to obtain structural information on biomolecular complexes in real-time. Thereby, multiple smFRET measurements are used to localize an unknown dye position inside a protein complex by means of trilateration. In order to obtain quantitative information, the Nano-Positioning System (NPS) uses probabilistic data analysis to combine structural information from X-ray crystallography with single-molecule fluorescence data to calculate not only the most probable position but the complete three-dimensional probability distribution, termed posterior, which indicates the experimental uncertainty. The concept was generalized for the analysis of smFRET networks containing numerous dye molecules. The latest version of NPS, Fast-NPS, features a new algorithm using Bayesian parameter estimation based on Markov Chain Monte Carlo sampling and parallel tempering that allows for the analysis of large smFRET networks in a comparably short time. Moreover, Fast-NPS allows the calculation of the posterior by choosing one of five different models for each dye, that account for the different spatial and orientational behavior exhibited by the dye molecules due to their local environment. Here we present a detailed protocol for obtaining smFRET data and applying the Fast-NPS. We provide detailed instructions for the acquisition of the three input parameters of Fast-NPS: the smFRET values, as well as the quantum yield and anisotropy of the dye molecules. Recently, the NPS has been used to elucidate the architecture of an archaeal open promotor complex. This data is used to demonstrate the influence of the five different dye models on the posterior distribution.