Tensor-SqRA: Modeling the transition rates of interacting molecular systems in terms of potential energies.

Estimating the rate of rare conformational changes in molecular systems is one of the goals of molecular dynamics simulations. In the past few decades, a lot of progress has been done in data-based approaches toward this problem. In contrast, model-based methods, such as the Square Root Approximation (SqRA), directly derive these quantities from the potential energy functions. In this article, we demonstrate how the SqRA formalism naturally blends with the tensor structure obtained by coupling multiple systems, resulting in the tensor-based Square Root Approximation (tSqRA). It enables efficient treatment of high-dimensional systems using the SqRA and provides an algebraic expression of the impact of coupling energies between molecular subsystems. Based on the tSqRA, we also develop the projected rate estimation, a hybrid data-model-based algorithm that efficiently estimates the slowest rates for coupled systems. In addition, we investigate the possibility of integrating low-rank approximations within this framework to maximize the potential of the tSqRA.

Polymorphism and Visible-Light-Driven Photocatalysis of Doped Bi2O3:M (M = S, Se, and Re).

δ-Bi2O3:M (M = S, Se, and Re) with an oxygen-defective fluorite-type structure is obtained by a coprecipitation method starting from the bismuth oxido cluster [Bi38O45(OMc)24(dmso)9]·2dmso·7H2O (A) in the presence of additives such as Na2SO4, Na2SeO4, NH4ReO4, Na2SeO3·5H2O, and Na2SO3. The coprecipitation of the starting materials with aqueous NaOH results in the formation of alkaline reaction mixtures, and the cubic bismuth(III)-based oxides Bi14O20(SO4) (1c), Bi14O20(SeO4) (2c), Bi14O20(ReO4.5) (3c), Bi12.25O16.625(SeO3)1.75 (4c), and Bi10.51O14.765(SO3)0.49(SO4)0.51 (5c) are obtained after microwave-assisted heating; formation of compound 5c is the result of partial oxidation of sulfur. The compounds 1c, 2c, 4c, and 5c absorb UV light only, whereas compound 3c absorbs in the visible-light region of the solar spectrum. Thermal treatment of the as-prepared metastable bismuth(III) oxide chalcogenates 1c and 2c at T = 600 °C provides a monotropic phase transition into their tetragonal polymorphs Bi14O20(SO4) (1t) and Bi14O20(SeO4) (2t), while compound 3c is transformed into the tetragonal modification of Bi14O20(ReO4.5) (3t) after calcination at T = 700 °C. Compounds of the systems Bi2O3-SOx (x = 2 and 3) and Bi2O3-Re2O7 are thermally stable up to T = 800 °C, whereas compounds of the system Bi2O3-SeO3 completely lose SeO3. Thermal treatment of 4c and 5c in air results in the oxidation of the tetravalent to hexavalent sulfur and selenium, respectively, upon heating to T = 400-500 °C. The as-prepared cubic bismuth(III)-based oxides 1c-5c were studied with regard to the photocatalytic decomposition of rhodamine B under visible-light irradiation with compound 3c showing the highest turnover and efficiency.

Assessing transition rates as functions of environmental variables.

We present a method to estimate the transition rates of molecular systems under different environmental conditions that cause the formation or the breaking of bonds and require the sampling of the Grand Canonical Ensemble. For this purpose, we model the molecular system in terms of probable "scenarios," governed by different potential energy functions, which are separately sampled by classical MD simulations. Reweighting the canonical distribution of each scenario according to specific environmental variables, we estimate the grand canonical distribution, then use the Square Root Approximation method to discretize the Fokker-Planck operator into a rate matrix and the robust Perron Cluster Cluster Analysis method to coarse-grain the kinetic model. This permits efficiently estimating the transition rates of conformational states as functions of environmental variables, for example, the local pH at a cell membrane. In this work, we formalize the theoretical framework of the procedure, and we present a numerical experiment comparing the results with those provided by a constant-pH method based on non-equilibrium Molecular Dynamics Monte Carlo simulations. The method is relevant for the development of new drug design strategies that take into account how the cellular environment influences biochemical processes.

Cyanine Dye Coupling Mediates Self-assembly of a pH Sensitive Peptide into Novel 3D Architectures.

Synthetic multichromophore systems are of great importance in artificial light harvesting devices, organic optoelectronics, tumor imaging and therapy. Here, we introduce a promising strategy for the construction of self-assembled peptide templated dye stacks based on coupling of a de novo designed pH sensitive peptide with a cyanine dye Cy5 at its N-terminus. Microscopic techniques, in particular cryogenic TEM (cryo-TEM) and cryo-electron tomography technique (cryo-ET), reveal two types of highly ordered three-dimensional assembly structures on the micrometer scale. Unbranched compact layered rods are observed at pH 7.4 and two-dimensional membrane-like assemblies at pH 3.4, both species displaying spectral features of H-aggregates. Molecular dynamics simulations reveal that the coupling of Cy5 moieties promotes the formation of both ultrastructures, whereas the protonation states of acidic and basic amino acid side chains dictates their ultimate three-dimensional organization.

Structural Changes during the Growth of Atomically Precise Metal Oxido Nanoclusters from Combined Pair Distribution Function and Small-Angle X-ray Scattering Analysis.

The combination of in situ pair distribution function (PDF) analysis and small-angle X-ray scattering (SAXS) enables analysis of the formation mechanism of metal oxido nanoclusters and cluster-solvent interactions as they take place. Herein, we demonstrate the method for the formation of clusters with a [Bi38 O45 ] core. Upon dissolution of crystalline [Bi6 O5 (OH)3 (NO3 )5 ]⋅3 H2 O in DMSO, an intermediate rapidly forms, which slowly grows to stable [Bi38 O45 ] clusters. To identify the intermediate, we developed an automated modeling method, where smaller [Bix Oy ] structures based on the [Bi38 O45 ] framework are tested against the data. [Bi22 O26 ] was identified as the main intermediate species, illustrating how combined PDF and SAXS analysis is a powerful tool to gain insight into nucleation on an atomic scale. PDF also provides information on the interaction between nanoclusters and solvent, which is shown to depend on the nature of the ligands on the cluster surface.

From a Cerium-Doped Polynuclear Bismuth Oxido Cluster to ß-Bi2O3:Ce.

The simultaneous hydrolysis of Bi(NO3)3·5H2O and Ce(NO3)3·6H2O results in the formation of novel heterometallic bismuth oxido clusters with the general formula [Bi38O45(NO3)24(DMSO)28+δ]:Ce (DMSO = dimethyl sulfoxide; cerium content <1.50%), which is demonstrated by single-crystal X-ray diffraction analysis. The incorporation of cerium into the cluster core is a result of the interplay of hydrolysis and condensation of the metal nitrates in the presence of oxygen. Diffuse-reflectance UV-vis and X-ray photoelectron spectroscopy reveal the presence of CeIV in the final bismuth oxido clusters as a result of oxidation of the cerium source. The cerium atoms are statistically distributed mainly on the bismuth atom positions of the central [Bi6O9] motif of the [Bi38O45] cluster core. Hydrolysis and subsequent annealing of the bismuth oxido clusters in the temperature range of 300-400 °C provides ß-Bi2O3:Ce samples with slightly lowered band gaps of approximately 2.3 eV compared to the undoped ß-Bi2O3 (approximately 2.4 eV). The sintering behavior of ß-Bi2O3 is significantly affected by the cerium dopant. Finally, differences in the efficiency of the as-prepared ß-Bi2O3:Ce and undoped ß-Bi2O3 samples in the photocatalytic decomposition of the biocide triclosan in an aqueous solution under visible-light irradiation are demonstrated.

Sub-ambient pressure IR-MALDI ion mobility spectrometer for the determination of low and high field mobilities.

A new ion mobility (IM) spectrometer, enabling mobility measurements in the pressure range between 5 and 500 mbar and in the reduced field strength range E/N of 5-90 Td, was developed and characterized. Reduced mobility (K0) values were studied under low E/N (constant value) as well as high E/N (deviation from low field K0) for a series of molecular ions in nitrogen. Infrared matrix-assisted laser desorption ionization (IR-MALDI) was used in two configurations: a source working at atmospheric pressure (AP) and, for the first time, an IR-MALDI source working with a liquid (aqueous) matrix at sub-ambient/reduced pressure (RP). The influence of RP on IR-MALDI was examined and new insights into the dispersion process were gained. This enabled the optimization of the IM spectrometer for best analytical performance. While ion desolvation is less efficient at RP, the transport of ions is more efficient, leading to intensity enhancement and an increased number of oligomer ions. When deciding between AP and RP IR-MALDI, a trade-off between intensity and resolving power has to be considered. Here, the low field mobility of peptide ions was first measured and compared with reference values from ESI-IM spectrometry (at AP) as well as collision cross sections obtained from molecular dynamics simulations. The second application was the determination of the reduced mobility of various substituted ammonium ions as a function of E/N in nitrogen. The mobility is constant up to a threshold at high E/N. Beyond this threshold, mobility increases were observed. This behavior can be explained by the loss of hydrated water molecules.

ISOKANN: Invariant subspaces of Koopman operators learned by a neural network.

The problem of determining the rate of rare events in dynamical systems is quite well-known but still difficult to solve. Recent attempts to overcome this problem exploit the fact that dynamic systems can be represented by a linear operator, such as the Koopman operator. Mathematically, the rare event problem comes down to the difficulty in finding invariant subspaces of these Koopman operators K. In this article, we describe a method to learn basis functions of invariant subspaces using an artificial neural network.

Generalized Markov modeling of nonreversible molecular kinetics.

Markov state models are to date the gold standard for modeling molecular kinetics since they enable the identification and analysis of metastable states and related kinetics in a very instructive manner. The state-of-the-art Markov state modeling methods and tools are very well developed for the modeling of reversible processes in closed equilibrium systems. On the contrary, they are largely not well suited to deal with nonreversible or even nonautonomous processes of nonequilibrium systems. Thus, we generalized the common Robust Perron Cluster Cluster Analysis (PCCA+) method to enable straightforward modeling of nonequilibrium systems as well. The resulting Generalized PCCA (G-PCCA) method readily handles equilibrium as well as nonequilibrium data by utilizing real Schur vectors instead of eigenvectors. This is implemented in the G-PCCA algorithm that enables the semiautomatic coarse graining of molecular kinetics. G-PCCA is not limited to the detection of metastable states but also enables the identification and modeling of cyclic processes. This is demonstrated by three typical examples of nonreversible systems.

From metastable to coherent sets- Time-discretization schemes.

Given a time-dependent stochastic process with trajectories x(t) in a space Ω, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable setsM are defined in space M⊂Ω, and coherent setsM(t)âŠ‚Ω are defined in space and time. Hence, if we extend the space Ω by the time-variable t, coherent sets are metastable sets in Ω×[0,∞) of an appropriate space-time process. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article, we show that these well-established spectral algorithms (like PCCA+, Perron Cluster Cluster Analysis) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-time-discretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.

Role of Counterions in Molecularly Imprinted Polymers for Anionic Species.

Small-molecule oxoanions are often imprinted noncovalently as carboxylates into molecularly imprinted polymers (MIPs), requiring the use of an organic counterion. Popular species are either pentamethylpiperidine (PMP) as a protonatable cation or tetraalkylammonium (TXA) ions as permanent cations. The present work explores the influence of the TXA as a function of their alkyl chain length, from methyl to octyl, using UV/vis absorption, fluorescence titrations, and HPLC as well as MD simulations. Protected phenylalanines (Z-l/d-Phe) served as templates/analytes. While the influence of the counterion on the complex stability constants and anion-induced spectral changes shows a monotonous trend with increasing alkyl chain length at the prepolymerization stage, the cross-imprinting/rebinding studies showed a unique pattern that suggested the presence of adaptive cavities in the MIP matrix, related to the concept of induced fit of enzyme-substrate interaction. Larger cavities formed in the presence of larger counterions can take up pairs of Z-x-Phe and smaller TXA, eventually escaping spectroscopic detection. Correlation of the experimental data with the MD simulations revealed that counterion mobility, the relative distances between the three partners, and the hydrogen bond lifetimes are more decisive for the response features observed than actual distances between interacting atoms in a complex or the orientation of binding moieties. TBA has been found to yield the highest imprinting factor, also showing a unique dual behavior regarding the interaction with template and fluorescent monomer. Finally, interesting differences between both enantiomers have been observed in both theory and experiment, suggesting true control of enantioselectivity. The contribution concludes with suggestions for translating the findings into actual MIP development.

γ-Bi2O3 - To Be or Not To Be? Comparison of the Sillenite γ-Bi2O3 and Isomorphous Sillenite-Type Bi12SiO20.

The "controlled" synthesis of metastable γ-Bi2O3 by solution based approaches was reported several times recently, but the formation of Bi12SiO20 in the presence of trace amounts of silicates renders the results to be questionable. Here, the preparation of the Sillenite γ-Bi2O3 and the Sillenite-type Bi12SiO20 starting from the polynuclear bismuth oxido cluster [Bi38O45(O2CC3H5)24(DMSO)9] is reported. γ-Bi2O3 crystallizes after calcination at 800 °C of the silicate-free hydrolysis product "[Bi38O45(OH)24]" on a silver sheet. Corrosion of the substrate causes contamination with silver, which is not incorporated into the Bi-O lattice, and was removed by treatment with an aqueous KCN-solution. Bi12SiO20 was obtained after hydrothermal treatment of the bismuth oxido cluster in the presence of NaOH in glass vessels or Na2SiO3 in a Teflon-lined reactor vessel followed by calcination at 600 °C. PXRD studies, scanning electron microscopy, nitrogen adsorption measurements, IR- and Raman spectroscopy, diffuse UV-vis spectroscopy, and DSC were used for characterization. The phase transition of γ-Bi2O3 to give α-Bi2O3 occurred slowly in the temperature range of 348-510 °C ( Δ Hγ→α = 6.57 kJ·mol-1). The silver-containing γ-Bi2O3 exhibits slightly increased Raman modes compared to the silver-free sample due to the SERS effect. In the diffuse UV-vis spectrum γ-Bi2O3 exhibits an absorption edge at λ = 485 nm ( E g = 2.76 eV), and the contamination with silver results in an additional absorption edge at λ = 572 nm. Silver-free γ-Bi2O3 exhibits an absorption edge at λ = 460 nm ( E g = 2.83 eV) and Bi12SiO20 at λ = 422 nm ( E g = 3.16 eV). The photocatalytic activity of the compounds was investigated in the decomposition of aqueous rhodamine B under visible light irradiation, showing silver-containing γ-Bi2O3 to be slightly more effective compared to Bi12SiO20 and significantly more effective than the silver-free γ-Bi2O3.

Thermal analysis of ultrasound-powered miniaturized implants: A tissue-phantom study.

Neurological implants that harvest ultrasound power have the potential to provide long-term stimulation without complications associated with battery power. An important safety question associated with long-term operation of the implant involves the heat generated by the interaction of the device with the ultrasound field. A study was performed in which the temperature rise generated by this interaction was measured. Informed by temperature data from thermocouples outside the ultrasound beam, a mathematical inverse method was used to determine the volume heat source generated by ultrasound absorption within the implant as well as the surface heat source generated within the viscous boundary layer on the surface of the implant. For the test implant used, it was determined that most of the heat was generated in the boundary layer, giving a maximum temperature rise ∼5 times that for absorption in an equivalent volume of soft tissue. This result illustrates that thermal safety guidelines based solely on ultrasound absorption of tissue alone are not sufficient. The method presented represents an alternative approach for quantifying ultrasound thermal effects in the presence of implants. The analysis shows a steady temperature rise of about 0.2 °C for every 100 mW/cm2 for the presented test implant.

Set-free Markov state model building.

Molecular dynamics (MD) simulations face challenging problems since the time scales of interest often are much longer than what is possible to simulate; and even if sufficiently long simulations are possible the complex nature of the resulting simulation data makes interpretation difficult. Markov State Models (MSMs) help to overcome these problems by making experimentally relevant time scales accessible via coarse grained representations that also allow for convenient interpretation. However, standard set-based MSMs exhibit some caveats limiting their approximation quality and statistical significance. One of the main caveats results from the fact that typical MD trajectories repeatedly re-cross the boundary between the sets used to build the MSM which causes statistical bias in estimating the transition probabilities between these sets. In this article, we present a set-free approach to MSM building utilizing smooth overlapping ansatz functions instead of sets and an adaptive refinement approach. This kind of meshless discretization helps to overcome the recrossing problem and yields an adaptive refinement procedure that allows us to improve the quality of the model while exploring state space and inserting new ansatz functions into the MSM.

Allosteric and Chelate Cooperativity in Divalent Crown Ether/Ammonium Complexes with Strong Binding Enhancement.

A thorough thermodynamic analysis by isothermal titration calorimetry of allosteric and chelate cooperativity effects in divalent crown ether/ammonium complexes is combined with DFT calculations including implicit solvent on the one hand and large-scale molecular dynamics simulations with explicit solvent molecules on the other. The complexes studied exhibit binding constants up to 2×106 m-1 with large multivalent binding enhancements and thus strong chelate cooperativity effects. Slight structural changes in the spacers, that is, the exchange of two ether oxygen atoms by two isoelectronic methylene groups, cause significantly stronger binding and substantially increased chelate cooperativity. The analysis is complemented by the examination of solvent effects and allosteric cooperativity. Such a detailed understanding of the binding processes will help to efficiently design and construct larger supramolecular architectures with multiple multivalent building blocks.

Peptide-polymer ligands for a tandem WW-domain, an adaptive multivalent protein-protein interaction: lessons on the thermodynamic fitness of flexible ligands.

Three polymers, poly(N-(2-hydroxypropyl)methacrylamide) (pHPMA), hyperbranched polyglycerol (hPG), and dextran were investigated as carriers for multivalent ligands targeting the adaptive tandem WW-domain of formin-binding protein (FBP21). Polymer carriers were conjugated with 3-9 copies of the proline-rich decapeptide GPPPRGPPPR-NH2 (P1). Binding of the obtained peptide-polymer conjugates to the tandem WW-domain was investigated employing isothermal titration calorimetry (ITC) to determine the binding affinity, the enthalpic and entropic contributions to free binding energy, and the stoichiometry of binding for all peptide-polymer conjugates. Binding affinities of all multivalent ligands were in the µM range, strongly amplified compared to the monovalent ligand P1 with a K D > 1 mM. In addition, concise differences were observed, pHPMA and hPG carriers showed moderate affinity and bound 2.3-2.8 peptides per protein binding site resulting in the formation of aggregates. Dextran-based conjugates displayed affinities down to 1.2 µM, forming complexes with low stoichiometry, and no precipitation. Experimental results were compared with parameters obtained from molecular dynamics simulations in order to understand the observed differences between the three carrier materials. In summary, the more rigid and condensed peptide-polymer conjugates based on the dextran scaffold seem to be superior to induce multivalent binding and to increase affinity, while the more flexible and dendritic polymers, pHPMA and hPG are suitable to induce crosslinking upon binding.

Multi-Input data ASsembly for joint Analysis (MIASA): A framework for the joint analysis of disjoint sets of variables.

The joint analysis of two datasets [Formula: see text] and [Formula: see text] that describe the same phenomena (e.g. the cellular state), but measure disjoint sets of variables (e.g. mRNA vs. protein levels) is currently challenging. Traditional methods typically analyze single interaction patterns such as variance or covariance. However, problem-tailored external knowledge may contain multiple different information about the interaction between the measured variables. We introduce MIASA, a holistic framework for the joint analysis of multiple different variables. It consists of assembling multiple different information such as similarity vs. association, expressed in terms of interaction-scores or distances, for subsequent clustering/classification. In addition, our framework includes a novel qualitative Euclidean embedding method (qEE-Transition) which enables using Euclidean-distance/vector-based clustering/classification methods on datasets that have a non-Euclidean-based interaction structure. As an alternative to conventional optimization-based multidimensional scaling methods which are prone to uncertainties, our qEE-Transition generates a new vector representation for each element of the dataset union [Formula: see text] in a common Euclidean space while strictly preserving the original ordering of the assembled interaction-distances. To demonstrate our work, we applied the framework to three types of simulated datasets: samples from families of distributions, samples from correlated random variables, and time-courses of statistical moments for three different types of stochastic two-gene interaction models. We then compared different clustering methods with vs. without the qEE-Transition. For all examples, we found that the qEE-Transition followed by Ward clustering had superior performance compared to non-agglomerative clustering methods but had a varied performance against ultrametric-based agglomerative methods. We also tested the qEE-Transition followed by supervised and unsupervised machine learning methods and found promising results, however, more work is needed for optimal parametrization of these methods. As a future perspective, our framework points to the importance of more developments and validation of distance-distribution models aiming to capture multiple-complex interactions between different variables.

Hands-off linear interaction energy approach to binding mode and affinity estimation of estrogens.

With this work we target the development of a predictictive model for the identification of small molecules which bind to the estrogen receptor alpha and, thus, may act as endocrine disruptors. We propose a combined thermodynamic approach for the estimation of preferential binding modes along with corresponding free energy differences using a linear interaction energy (LIE) ansatz. The LIE model is extended by a Monte Carlo approach for the computation of conformational entropies as recently developed by our group. Incorporating the entropy contribution substantially increased the correlation with experimental affinity values. Both squared coefficients for the fitted data as well as the more meaningful leave-one-out cross-validation of predicted energies were elevated up to r(Fit)² = 0.87 and q(LOO)² = 0.82, respectively. All calculations have been performed on a set of 31 highly diverse ligands regarding their structural properties and affinities to the estrogen receptor alpha. Comparison of predicted ligand orientations with crystallographic data retrieved from the Protein database pdb.org revealed remarkable binding mode predictions.

Adaptive spectral clustering with application to tripeptide conformation analysis.

A decomposition of a molecular conformational space into sets or functions (states) allows for a reduced description of the dynamical behavior in terms of transition probabilities between these states. Spectral clustering of the corresponding transition probability matrix can then reveal metastabilities. The more states are used for the decomposition, the smaller the risk to cover multiple conformations with one state, which would make these conformations indistinguishable. However, since the computational complexity of the clustering algorithm increases quadratically with the number of states, it is desirable to have as few states as possible. To balance these two contradictory goals, we present an algorithm for an adaptive decomposition of the position space starting from a very coarse decomposition. The algorithm is applied to small data classification problems where it was shown to be superior to commonly used algorithms, e.g., k-means. We also applied this algorithm to the conformation analysis of a tripeptide molecule where six-dimensional time series are successfully analyzed.

Novel multi-objective affinity approach allows to identify pH-specific µ-opioid receptor agonists.

Opioids are essential pharmaceuticals due to their analgesic properties, however, lethal side effects, addiction, and opioid tolerance are extremely challenging. The development of novel molecules targeting the [Formula: see text]-opioid receptor (MOR) in inflamed, but not in healthy tissue, could significantly reduce these unwanted effects. Finding such novel molecules can be achieved by maximizing the binding affinity to the MOR at acidic pH while minimizing it at neutral pH, thus combining two conflicting objectives. Here, this multi-objective optimal affinity approach is presented, together with a virtual drug discovery pipeline for its practical implementation. When applied to finding pH-specific drug candidates, it combines protonation state-dependent structure and ligand preparation with high-throughput virtual screening. We employ this pipeline to characterize a set of MOR agonists identifying a morphine-like opioid derivative with higher predicted binding affinities to the MOR at low pH compared to neutral pH. Our results also confirm existing experimental evidence that NFEPP, a previously described fentanyl derivative with reduced side effects, and recently reported [Formula: see text]-fluorofentanyls and -morphines show an increased specificity for the MOR at acidic pH when compared to fentanyl and morphine. We further applied our approach to screen a >50K ligand library identifying novel molecules with pH-specific predicted binding affinities to the MOR. The presented differential docking pipeline can be applied to perform multi-objective affinity optimization to identify safer and more specific drug candidates at large scale.