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We experimentally determined the characteristics and Langmuir parameters of the binding of calcium ions to different polycarboxylates. By using potentiometric titrations and isothermal titration calorimetry, the effects of side chain chemistry, pH value, and chain length were systematically investigated using the linear polymers poly(aspartic acid), poly(glutamic acid), and poly(acrylic acid). We demonstrate that for polymers with high polymerization degrees, the binding process is governed by higher-order effects, such as the change of apparent p

Characterizing the structural dynamics of proteins with heterogeneous conformational landscapes is crucial to understanding complex biomolecular processes. To this end, dimensionality reduction algorithms are used to produce low-dimensional embeddings of the high-dimensional conformational phase space. However, identifying a compact and informative set of input features for the embedding remains an ongoing challenge. Here, we propose to harness the power of Residue Interaction Networks (RINs) and their centrality measures, established tools to provide a graph theoretical view on molecular structure. Specifically, we combine the closeness centrality, which captures global features of the protein conformation at residue-wise resolution, with EncoderMap, a hybrid neural-network autoencoder/multidimensional-scaling like dimensionality reduction algorithm. We find that the resulting low-dimensional embedding is a meaningful visualization of the residue interaction landscape that resolves structural details of the protein behavior while retaining global interpretability. This feature-based graph embedding of temporal protein graphs makes it possible to apply the general descriptive power of RIN formalisms to the analysis of protein simulations of complex processes such as protein folding and multi-domain interactions requiring no protein-specific input. We demonstrate this on simulations of the fast folding protein Trp-Cage and the multi-domain signalling protein FAT10. Due to its generality and modularity, the presented approach can easily be transferred to other protein systems.

Classical multiscale simulations are perfectly suited to investigate biological soft matter systems. Owing to the bridging between microscopically realistic and lower-resolution models or the integration of a hierarchy of subsystems, one gets access to biologically relevant system sizes and timescales. In recent years, increasingly complex systems and processes have come into focus such as multidomain proteins, phase separation processes in biopolymer solutions, multicomponent biomembranes, or multiprotein complexes up to entire viruses. The review shows factors that have contributed to this progress - from improved models to machine-learning-based analysis and scale-bridging methods.

O objeto do trabalho é a dogmática constitucional feminista. Não obstante a expressão “constitucionalismo feminista” já faça parte do léxico acadêmico internacional, ainda não há uma doutrina brasileira sistematizada sobre as suas diversas perspectivas, de forma que o presente trabalho objetiva apresentar a perspectiva dogmática do constitucionalismo feminista brasileiro. Por dogmática jurídica compreende-se a linha de pensamento voltada para a decidibilidade normativa dos conflitos, sendo a dogmática constitucional feminista uma proposta de releitura da dogmática constitucional pela voz, intelectualidade e experiência das mulheres. A partir de revisão bibliográfica e pesquisa documental, apresentam-se os pressupostos doutrinários e as normas constitucionais positivadas, que garantem direitos fundamentais para as mulheres e minorias de gênero, bem como os precedentes constitucionais do Supremo Tribunal Federal que evidenciam, nos anos de 2019 e 2020, discursos e argumentos com influência das premissas da dogmática constitucional feminista.

The chromatin in eukaryotic cells plays a fundamental role in all processes during a cell’s life cycle. This nucleoprotein is normally tightly packed but needs to be unpacked for expression and division. The linker histones are critical for such packaging processes and while most experimental and simulation works recognize their crucial importance, the focus is nearly always set on the nucleosome as the basic chromatin building block. Linker histones can undergo several modifications, but only few studies on their ubiquitylation have been conducted. Mono-ubiquitylated linker histones (HUb), while poorly understood, are expected to influence DNA compaction. The size of ubiquitin and the globular domain of the linker histone are comparable and one would expect an increased disorder upon ubiquitylation of the linker histone. However, the formation of higher order chromatin is not hindered and ubiquitylation of the linker histone may even promote gene expression. Structural data on chromatosomes is rare and HUb has never been modeled in a chromatosome so far. Descriptions of the chromatin complex with HUb would greatly benefit from computational structural data. In this study we generate molecular dynamics simulation data for six differently linked HUb variants with the help of a sampling scheme tailored to drive the exploration of phase space. We identify conformational sub-states of the six HUb variants using the sketch-map algorithm for dimensionality reduction and iterative HDBSCAN for clustering on the excessively sampled, shallow free energy landscapes. We present a highly efficient geometric scoring method to identify sub-states of HUb that fit into the nucleosome. We predict HUb conformations inside a nucleosome using on-dyad and off-dyad chromatosome structures as reference and show that unbiased simulations of HUb produce significantly more fitting than non-fitting HUb conformations. A tetranucleosome array is used to show that ubiquitylation can even occur in chromatin without too much steric clashes.Author summaryIn eukaryotic cells the linker histones play a crucial role in the formation of higher order nucleoprotein complex of DNA, especially for the arrangement of the nucleosomes. Histones can undergo several modifications, but modification of a linker histone with a single udiquitin (mono-ubiquitylation) remains one of the least understood epigenetic modifications. One reason is the inaccessibility of homogeneously modified linker histones for experimental methods, which are crucial for distinct studies. We combine molecular dynamics simulations with machine learning-based approaches to study the influence of mono-ubiquitylation in linker histones on DNA interaction and their ability to form higher order chromatin structures. We were able to determine the probable states in six differently linked histone-ubiquitin complexes via accelerating classical molecular dynamics simulations and using advanced state characterization techniques. As it is computationally unfeasible to simulate the whole chromatosome with different modified histones we developed efficient geometric scoring technique to select biologically relevant structures of all six mono-ubiquitylated linker histone that can bound to nucleosome.

Aktivitätsbasierte Sonden sind wertvolle Werkzeuge in der chemischen Biologie. Nach wie vor ist es jedoch eine Herausforderung, molekulare Sonden zu entwickeln, die spezifisch an das aktive Zentrum eines bestimmten Enzyms binden. Wir stellen hier eine Strategie zur Ligandenselektion vor, die es ermöglicht, rasch elektrophile Sonden auf ausgewählte Enzyme zuzuschneiden, und zeigen in einer Machbarkeitsstudie ihre Anwendung für die beiden Cysteinproteasen von SARS‐CoV‐2. Die resultierenden Sonden markieren spezifisch die aktiven Zentren von 3CLpro und PLpro mit hinreichender Selektivität sowohl in einem lebenden Zellmodell als auch vor dem Hintergrund eines nativen menschlichen Proteoms. Durch die Nutzung der Sonden als Werkzeuge für das kompetitive Screening einer Bibliothek von Naturstoffen wurden Salvianolsäurederivate als vielversprechende 3CLpro‐Inhibitoren identifiziert. Unsere Strategie zur Ligandenselektion wird für die schnelle Entwicklung von maßgeschneiderten Sonden von großem Nutzen sein und die Entdeckung von Inhibitoren für eine Vielzahl von Zielproteinen ermöglichen, die auch über Coronavirus‐Proteasen hinausgehen. published

In experimental studies, heavy water (D

Understanding the role of polymers rich in aspartic acid (Asp) and glutamic acid (Glu) is the key to gaining precise control over mineralization processes. Despite their chemical similarity, experiments revealed a surprisingly different influence of Asp and Glu sequences. We conducted molecular dynamics simulations of Asp and Glu peptides in the presence of calcium and chloride ions to elucidate the underlying phenomena. In line with experimental differences, in our simulations, we indeed find strong differences in the way the peptides interact with ions in solution. The investigated Asp pentapeptide tends to pull a lot of ions into its vicinity, and many structures with clusters of calcium and chloride ions on the surface of the peptide can be observed. Under the same conditions, comparatively fewer ions can be found in proximity of the investigated Glu pentapeptide, and the structures are characterized by single calcium ions bound to multiple carboxylate groups. Based on our simulation data, we identified three reasons contributing to these differences, leading to a new level of understanding additive-ion interactions. published

Regulation of gene expression via riboswitches is a widespread mechanism in bacteria. Here, we investigate ligand binding of a member of the guanidine sensing riboswitch family, the guanidine-II riboswitch (Gd-II). It consists of two stem–loops forming a dimer upon ligand binding. Using extensive molecular dynamics simulations we have identified conformational states corresponding to ligand-bound and unbound states in a monomeric stem–loop of Gd-II and studied the selectivity of this binding. To characterize these states and ligand-dependent conformational changes we applied a combination of dimensionality reduction, clustering, and feature selection methods. In absence of a ligand, the shape of the binding pocket alternates between the conformation observed in presence of guanidinium and a collapsed conformation, which is associated with a deformation of the dimerization interface. Furthermore, the structural features responsible for the ability to discriminate against closely related analogs of guanidine are resolved. Based on these insights, we propose a mechanism that couples ligand binding to aptamer dimerization in the Gd-II system, demonstrating the value of computational methods in the field of nucleic acids research.

Striated muscle undergoes remodelling in response to mechanical and physiological stress, but little is known about the integration of such varied signals in the myofibril. The interaction of the elastic kinase region from sarcomeric titin (A168‐M1) with the autophagy receptors Nbr1/p62 and MuRF E3 ubiquitin ligases is well suited to link mechanosensing with the trophic response of the myofibril. To investigate the mechanisms of signal cross‐talk at this titin node, we elucidated its 3D structure, analysed its response to stretch using steered molecular dynamics simulations and explored its functional relation to MuRF1 and Nbr1/p62 using cellular assays. We found that MuRF1‐mediated ubiquitination of titin kinase promotes its scaffolding of Nbr1/p62 and that the process can be dynamically down‐regulated by the mechanical unfolding of a linker sequence joining titin kinase with the MuRF1 receptor site in titin. We propose that titin ubiquitination is sensitive to the mechanical state of the sarcomere, the regulation of sarcomere targeting by Nbr1/p62 being a functional outcome. We conclude that MuRF1/Titin Kinase/Nbr1/p62 constitutes a distinct assembly that predictably promotes sarcomere breakdown in inactive muscle., The pseudokinase domain of the titin myofilament is a node for the cross‐talk of mechanical signals and turn‐over pathways in the sarcomere, contributing to a coordinated response to cellular stress.

Dimensionality reduction can be used to project high-dimensional molecular data into a simplified, low-dimensional map. One feature of our recently introduced dimensionality reduction technique EncoderMap, which relies on the combination of an autoencoder with multidimensional scaling, is its ability to do the reverse. It is able to generate conformations for any selected points in the low-dimensional map. This transfers the simplified, low-dimensional map back into the high-dimensional conformational space. Although the output is again high-dimensional, certain aspects of the simplification are preserved. The generated conformations only mirror the most dominant conformational differences that determine the positions of conformational states in the low-dimensional map. This allows depicting such differences and-in consequence-visualizing molecular motions and gives a unique perspective on high-dimensional conformational data. In our previous work, protein conformations described in backbone dihedral angle space were used as the input for EncoderMap, and conformations were also generated in this space. For large proteins, however, the generation of conformations is inaccurate with this approach due to the local character of backbone dihedral angles. Here, we present an improved variant of EncoderMap which is able to generate large protein conformations that are accurate in short-range and long-range orders. This is achieved by differentiable reconstruction of Cartesian coordinates from the generated dihedrals, which allows adding a contribution to the cost function that monitors the accuracy of all pairwise distances between the C

As a concept for distinct shape polymer nanoparticles, nanoscale single crystals composed of a crystallizable chain with lyophilic end groups are explored. This differs from much studied block copolymer nanoparticles and nanostructures, in which the second (noncrystalline) blocks’ spacial demand impacts the overall structure and blurs the cores’ anisotropic shape. For precise C48 polyethylene telechelics X(CH2)46X (X = COO–M+ or CH2SO3–M+, with M+ = Na+, K+, or Cs+) as a relevant model system, a combined experimental and atomistic-level simulation study reveals them to form extended-chain, single-crystalline nanoparticles sandwiched by a layer of head groups. Their microscopic structure, order, and the resulting overall shape are decisively impacted by the mutual repulsion of the head groups, itself determined by the degree of ion pairing with the counterions and the size of the head groups. This leads to the bending of the chains at the lateral side of the crystal, preventing the particles from agglomera...

Calcium-containing minerals are key model systems for investigating fundamental principles of nucleation and mineral formation both experimentally and by simulation. Due to the rare event character of nucleation, the different dimensions of pre- and postnucleation stages and the possible relevance of nonclassical nucleation pathways, such investigations require advanced sampling techniques and simulation models on a range of resolution levels. To this end, we have developed coarse-grained (CG) models for calcium carbonate. We present a strategy to devise CG parameters, including nonbonded angular-dependent terms such that the model correctly represents the calcite phase along with properties of the constituents in solution. We show how the CG interactions affect the crystallization pathways by stabilizing different intermediates, spanning a wide range of degrees of crystallinity and water content. This will allow us to investigate contributions to crystallization transitions and link them to experimentall...

Molecular simulation is one example where large amounts of high-dimensional (high-d) data are generated. To extract useful information e.g. about relevant states and important conformational transitions, a form of dimensionality reduction is required. Dimensionality reduction algorithms differ in their ability to efficiently project large amounts of data to an informative low-dimensional (low-d) representation and the way the low and high-d representations are linked. We propose a dimensionality reduction algorithm called encoder-map which is based on a neural network autoencoder in combination with a non-linear distance metric. A key advantage of this method is that it establishes a functional link from the high-d to the low-d representation and vice versa. This allows not only to efficiently project data points to the low-d representation but also to generate high-d representatives for any point in the low-d map. The potential of the algorithm is demonstrated for molecular simulation data of a small, highly-flexible peptide as well as for folding simulations of the 20-residue Trp-cage protein. We demonstrate that the algorithm is able to efficiently project the ensemble of high-d structures to a low-d map where major states can be identified and important conformational transitions are revealed. We also show that molecular conformations can be generated for any point or any connecting line between points on the low-d map. This ability of inverse mapping from the low-d to the high-d representation is particularly relevant for the use in algorithms that enhance the exploration of conformational space or the sampling of transitions between conformational states. published

Activity‐based probes are valuable tools for chemical biology. However, finding probes that specifically target the active site of an enzyme remains a challenging task. Herein, we present a ligand selection strategy that allows to rapidly tailor electrophilic probes to a target of choice and showcase its application for the two cysteine proteases of SARS‐CoV‐2 as proof of concept. The resulting probes were specific for the active site labeling of 3CLpro and PLpro with sufficient selectivity in a live cell model as well as in the background of a native human proteome. Exploiting the probes as tools for competitive profiling of a natural product library identified salvianolic acid derivatives as promising 3CLpro inhibitors. We anticipate that our ligand selection strategy will be useful to rapidly develop customized probes and discover inhibitors for a wide range of target proteins also beyond corona virus proteases., Tuning the ligand space allows to rapidly customize chemical probes for efficacy and active site specificity for a protease of interest. The application of this ligand selection approach is exemplified by generating probes for the two non‐homologous yet essential proteases of the new corona virus SARS‐CoV‐2 providing complementary chemical tools for proteomic labeling and inhibitor discovery.

The structural basis for the stability of the trimeric form of the light harvesting complex (LHCII), a pigmented protein from green plants pivotal for photosynthesis, remains elusive till date. The protein embedded in a dipalmitoylphosphatidylcholine (DPPC) lipid membrane is investigated using all-atom molecular dynamics simulations to find out the interactions responsible for the structural integrity of the trimer and its relation to antenna function. Central association of chlorophyll a (CLA) molecules near the LHCII chains is attributed to a conserved coordination between the Mg of CLA and the oxygen of a specific residue of the first helix of a chain. The residue forms a salt-bridge with the fourth helix of the same chain of the trimer, not of the monomer. In an earlier experiment, three residues (WYR) at each chain of the trimer have been found indispensable for the trimerization and referred to as trimerization motif. We find that the residues of the trimerization motif are connected to the lipids or pigments by a chain of interactions rather than a direct contact. Synergistic effects of sequentially located hydrogen bonds and salt-bridges within monomers of the trimer keep the trimer conformation stable in association with the pigments or the lipids. These interactions are exclusively present in the pigmented trimer and not present in the monomer or in the unpigmented trimer. Thus, our results provide a molecular basis for the inherent stability of the LHCII trimer in a lipid membrane and explain many pre-existing experimental data. published

Polyethylene (PE) telechelics with carboxylate functional groups at both ends have been shown to assemble into hexagonal nanocrystal platelets with a height defined by their chain length in basic CsOH-solution. In this coarse grained (CG) simulation study we show how properties of the functional groups alter the aggregation and crystallization behavior of those telechelics. Systematic variation of the parameters of the CG model showed that important factors which control nanoparticle stability and structure are the PE chain length and the hydrophilicity and the steric demand of the head groups. To characterize the aggregation process we analyzed the number and size of the obtained aggregates as well as intramolecular order and intermolecular alignment of the polymer chains. By comparison of CG and atomistic simulation data, it could be shown that atomistic simulations representing different chemical systems can be emulated with specific, different CG parameter sets. Thus, the results from the (generic) CG simulation models can be used to explain the effect of different head groups and different counterions on the aggregation of PE telechelics and the order of the obtained nanocrystals.

Understanding the conformational characteristics of protein complexes in solution is crucial for a deeper insight in their biological function. Molecular dynamics simulations performed on high performance computing plants and with modern simulation techniques can be used to obtain large data sets that contain conformational and thermodynamic information about biomolecular systems. While this can in principle give a detailed picture of protein-protein interactions in solution and therefore complement experimental data, it also raises the challenge of processing exceedingly large high-dimensional data sets with several million samples. Here we present a novel method for the characterization of protein-protein interactions, which combines a neural network based dimensionality reduction technique to obtain a two-dimensional representation of the conformational space with a density based clustering algorithm for state detection and a metric which assesses the (dis)similarity between different conformational spaces. This method is highly scalable and therefore makes the analysis of massive data sets computationally tractable. We demonstrate the power of this approach to large scale data analysis by characterizing highly dynamic conformational phase spaces of differently linked ubiquitin (Ub) oligomers from coarse-grained simulations. We are able to extract a protein-protein interaction model for two unlinked Ub proteins which is then used to determine how the Ub-Ub interaction pattern is altered in Ub oligomers by the introduction of a covalent linkage. We find that the Ub chain conformational ensemble depends highly on the linkage type and for some cases also on the Ub chain length. By this, we obtain insight into the conformational characteristics of different Ub chains and how this may contribute to linkage type and chain length specific recognition.

For reproducing the behavior of water molecules adsorbed on gold surfaces in terms of density of both bulk and interfacial water and in terms of structuring of water on top of gold atoms, the implementation of a multibody potential is necessary, thus the Stillinger–Weber potential was tested. The goal is using a single nonbonded potential for coarse-grained models, without the usage of explicit charges. In order to modify the angular part of the Stillinger–Weber potential from a single cosine to a piecewise function accounting for multiple equilibrium angles, employed for Au–Au–Au and Au–Au–water triplets, it is necessary to create a version of the simulation package LAMMPS that supports the assignment of multiple favored angles. This novel approach is able to reproduce the data obtained using quantum mechanical calculations and density profiles of both bulk and adsorbed water molecules obtained using classical polarizable force fields. published

This work came out of a CECAM discussion meeting.; International audience; Machine learning encompasses a set of tools and algorithms which are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab-initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.

Significance Despite being evolved to process the four canonical nucleotides, DNA polymerases are known to incorporate and extend from modified nucleotides, which is the key to numerous core biotechnology applications. The structural basis for postincorporation elongation remained elusive. We successfully crystallized KlenTaq DNA polymerase in six complexes, providing high-resolution snapshots of the modification “moving” from the 3′ terminus upstream to the sixth nucleotide in the primer strand. Combining these data with quantum mechanics/molecular mechanics calculations and biochemical studies elucidates how the enzyme and the modified substrate mutually modulate their conformations without compromising the enzyme’s activity. This highlights the unexpected plasticity of the system as origin of the broad substrate properties of the DNA polymerase and guide for the design of improved systems., DNA polymerases have evolved to process the four canonical nucleotides accurately. Nevertheless, these enzymes are also known to process modified nucleotides, which is the key to numerous core biotechnology applications. Processing of modified nucleotides includes incorporation of the modified nucleotide and postincorporation elongation to proceed with the synthesis of the nascent DNA strand. The structural basis for postincorporation elongation is currently unknown. We addressed this issue and successfully crystallized KlenTaq DNA polymerase in six closed ternary complexes containing the enzyme, the modified DNA substrate, and the incoming nucleotide. Each structure shows a high-resolution snapshot of the elongation of a modified primer, where the modification “moves” from the 3′-primer terminus upstream to the sixth nucleotide in the primer strand. Combining these data with quantum mechanics/molecular mechanics calculations and biochemical studies elucidates how the enzyme and the modified substrate mutually modulate their conformations without compromising the enzyme’s activity significantly. The study highlights the plasticity of the system as origin of the broad substrate properties of DNA polymerases and facilitates the design of improved systems.

Coarse-grained (CG) simulation models have become very popular tools to study complex molecular systems with great computational efficiency on length and time scales that are inaccessible to simulations at atomistic resolution. In so-called bottom-up coarse-graining strategies, the interactions in the CG model are devised such that an accurate representation of an atomistic sampling of configurational phase space is achieved. This means the coarse-graining methods use the underlying multibody potential of mean force (i.e., free-energy surface) derived from the atomistic simulation as parametrization target. Here, we present a new method where a neural network (NN) is used to extract high-dimensional free energy surfaces (FES) from molecular dynamics (MD) simulation trajectories. These FES are used for simulations on a CG level of resolution. The method is applied to simulating homo-oligo-peptides (oligo-glutamic-acid (oligo-glu) and oligo-aspartic-acid (oligo-asp)) of different lengths. We show that the NN not only is able to correctly describe the free-energy surface for oligomer lengths that it was trained on but also is able to predict the conformational sampling of longer chains.

Recent theories and simulations suggest that molecular additives can bind to the surfaces of nuclei, lower the surface energy, and accelerate nucleation. Experiments have shown that oligomeric and polymeric additives can also modify nucleation rates of proteins, ice, and minerals; however, general design principles for oligomeric or polymeric promoters do not yet exist. Here we investigate oligomeric additives for which each segment of the oligomer can bind to surfaces of nuclei. We use semigrand canonical Monte Carlo simulations in a Potts lattice gas model to study the effects of oligomer chain length, volume fraction, and binding strength. We find that increasing each of those parameters lowers the nucleation barrier. At extremely low oligomer concentrations, the nucleation kinetics can be modeled as though each oligomer is a heterogeneous nucleation site in solution.

A controlled route toward biocompatible nanostructures has immense relevance for drug delivery and tissue engineering. We present an experimental-computational study identifying factors that govern the formation of well-defined aggregates by self-assembled pentapeptides, using single amino acid substitution. A subtle interplay between peptide rigidity/flexibility, hydrogen-bonding capacity, partitioning of aromatic side chains, and influence of dimerization determines the formation of ordered and disordered aggregate structures, and shifts the balance between the emergence of spherical or ill-defined morphologies.

Ubiquitylation is an eminent posttranslational modification referring to the covalent attachment of single ubiquitin molecules or polyubiquitin chains to a target protein dictating the fate of such labeled polypeptide chains. Here, we have biochemically produced artificially Lys11-, and Lys27-, and Lys63-linked ubiquitin dimers based on click-chemistry generating milligram quantities in high purity. We show that the artificial linkage used for the conjugation of two ubiquitin moieties represents a fully reliable surrogate of the natural isopeptide bond by acquiring highly resolved nuclear magnetic resonance (NMR) spectroscopic data including ligand binding studies. Extensive coarse grained and atomistic molecular dynamics (MD) simulations allow to extract structures representing the ensemble of domain-domain conformations used to verify the experimental data. Advantageously, this methodology does not require individual isotopic labeling of both ubiquitin moieties as NMR data have been acquired on the isotopically labeled proximal moiety and complementary MD simulations have been used to fully interpret the experimental data in terms of domain-domain conformation. This combined approach intertwining NMR spectroscopy with MD simulations makes it possible to describe the conformational space non-canonically Lys11-, and Lys27-linked ubiquitin dimers occupy in a solution averaged ensemble by taking atomically resolved information representing all residues in ubiquitin dimers into account. published

One ongoing topic of research in MD simulations is how to enable sampling to chemically and biologically relevant time scales. We address this question by introducing a back-mapping based sampling (BMBS) that combines multiple aspects of different sampling techniques. BMBS uses coarse grained (CG) free energy surfaces (FESs) and dimensionality reduction to initiate new atomistic simulations. These new simulations are started from atomistic conformations that were back-mapped from CG points all over the FES in order to sample the entire accessible phase space as fast as possible. In the context of BMBS, we address relevant back-mapping related questions like where to start the back-mapping from and how to judge the atomistic ensemble that results from the BMBS. The latter is done with the use of the earth mover’s distance, which allows us to quantitatively compare distributions of CG and atomistic ensembles. By using this metric, we can also show that the BMBS is able to correct inaccuracies of the CG model. In this paper, BMBS is applied to a just recently introduced neural network (NN) based approach for a radical coarse graining to predict free energy surfaces for oligopeptides. The BMBS scheme back-maps these FESs to the atomistic scale, justifying and complementing the proposed NN based CG approach. The efficiency benefit of the algorithm scales with the length of the oligomer. Already for the heptamers, the algorithm is about one order of magnitude faster in sampling compared to a standard MD simulation. published

RNase H is a prototypical example for two metal ion catalysis in enzymes. An RNase H activity is present in the HIV-1 reverse transcriptase but also in many other nucleases such as Homo sapiens (Hs) or Escherichia coli (Ec) RNase H. The mechanism of the reaction has already been extensively studied based on the Bacillus halodurans (Bh) RNase H crystal structures, most recently using time-resolved X-Ray crystallography. However, kinetic and mutation experiments with HIV-1, Hs and Ec RNase H implicate a catalytic histidine in the reaction that is not present in Bh RNase H, and the protonation of the leaving group also remains poorly understood. We use quantum mechanics/molecular mechanics (QM/MM) calculations combining Hamiltonian replica exchange with a finite-temperature string method to study the cleavage of the ribonucleic acid (RNA) backbone of a DNA/RNA hybrid catalyzed by the HIV-1 RNase H with a focus on the proton transfer pathway and the role of the histidine. The reported pathway is consistent with kinetic data obtained with mutant HIV-1, Hs and Ec RNase H, the calculated pKa values of the DEDD residues and crystallographic studies. The overall reaction barrier of ∼18 kcal mol-1, encountered in the first step, matches the slow experimental rate of ∼1-100 min-1. Using Molecular dynamics (MD) calculations we are able to sample the recently identified binding site for a third transient divalent metal ion in the vicinity of the scissile phosphate in the product complex. Our results account for the experimental observation of a third metal ion facilitating product release in an Aquifex aeolicus RNase III crystal structure and the Bh RNase H in crystallo reaction. Based on our data we are able to show that the third ion and the histidine are key to product release as had been hypothesized.