Enhancing LC×LC separations through multi-task Bayesian optimization.

Method development in comprehensive two-dimensional liquid chromatography (LC×LC) is a challenging process. The interdependencies between the two dimensions and the possibility of incorporating complex gradient profiles, such as multi-segmented gradients or shifting gradients, make trial-and-error method development time-consuming and highly dependent on user experience. Retention modeling and Bayesian optimization (BO) have been proposed as solutions to mitigate these issues. However, both approaches have their strengths and weaknesses. On the one hand, retention modeling, which approximates true retention behavior, depends on effective peak tracking and accurate retention time and width predictions, which are increasingly challenging for complex samples and advanced gradient assemblies. On the other hand, Bayesian optimization may require many experiments when dealing with many adjustable parameters, as in LC×LC. Therefore, in this work, we investigate the use of multi-task Bayesian optimization (MTBO), a method that can combine information from both retention modeling and experimental measurements. The algorithm was first tested and compared with BO using a synthetic retention modeling test case, where it was shown that MTBO finds better optima with fewer method-development iterations than conventional BO. Next, the algorithm was tested on the optimization of a method for a pesticide sample and we found that the algorithm was able to improve upon the initial scanning experiments. Multi-task Bayesian optimization is a promising technique in situations where modeling retention is challenging, and the high number of adjustable parameters and/or limited optimization budget makes traditional Bayesian optimization impractical.

Redox Properties of Flavin in BLUF and LOV Photoreceptor Proteins from Hybrid QM/MM Molecular Dynamics Simulation.

Flavins play an important role in many oxidation and reduction processes in biological systems. For example, flavin adenine dinucleotide (FAD) and flavin mononucleotide (FMN) are common cofactors found in enzymatic proteins that use the special redox properties of these flavin molecules for their catalytic or photoactive functions. The redox potential of the flavin is strongly affected by its (protein) environment; however, the underlying molecular interactions of this effect are still unknown. Using hybrid quantum mechanics/molecular mechanics (QM/MM) simulation techniques, we have studied the redox properties of flavin in the gas phase, aqueous solution, and two different protein environments, in particular, a BLUF and a LOV photoreceptor domain. By mapping the changes in electrostatic potential and solvent structure, we gain insight into how specific polarization of the flavin by its environment tunes the reduction potential. We find also that accurate calculation of the reduction potentials of these systems by using the hybrid QM/MM approach is hampered by a too limited sampling of the counterion configurations and by artifacts at the QM/MM boundary. We make suggestions for how these issues can be overcome.

Predicting RP-LC retention indices of structurally unknown chemicals from mass spectrometry data.

Non-target analysis combined with liquid chromatography high resolution mass spectrometry is considered one of the most comprehensive strategies for the detection and identification of known and unknown chemicals in complex samples. However, many compounds remain unidentified due to data complexity and limited number structures in chemical databases. In this work, we have developed and validated a novel machine learning algorithm to predict the retention index (r[Formula: see text]) values for structurally (un)known chemicals based on their measured fragmentation pattern. The developed model, for the first time, enabled the predication of r[Formula: see text] values without the need for the exact structure of the chemicals, with an [Formula: see text] of 0.91 and 0.77 and root mean squared error (RMSE) of 47 and 67 r[Formula: see text] units for the NORMAN ([Formula: see text]) and amide ([Formula: see text]) test sets, respectively. This fragment based model showed comparable accuracy in r[Formula: see text] prediction compared to conventional descriptor-based models that rely on known chemical structure, which obtained an [Formula: see text] of 0.85 with an RMSE of 67.

Closed-loop automatic gradient design for liquid chromatography using Bayesian optimization.

Contemporary complex samples require sophisticated methods for full analysis. This work describes the development of a Bayesian optimization algorithm for automated and unsupervised development of gradient programs. The algorithm was tailored to LC using a Gaussian process model with a novel covariance kernel. To facilitate unsupervised learning, the algorithm was designed to interface directly with the chromatographic system. Single-objective and multi-objective Bayesian optimization strategies were investigated for the separation of two complex (n>18, and n>80) dye mixtures. Both approaches found satisfactory optima in under 35 measurements. The multi-objective strategy was found to be powerful and flexible in terms of exploring the Pareto front. The performance difference between the single-objective and multi-objective strategy was further investigated using a retention modeling example. One additional advantage of the multi-objective approach was that it allows for a trade-off to be made between multiple objectives without prior knowledge. In general, the Bayesian optimization strategy was found to be particularly suitable, but not limited to, cases where retention modelling is not possible, although its scalability might be limited in terms of the number of parameters that can be simultaneously optimized.

Chemometric Strategies for Fully Automated Interpretive Method Development in Liquid Chromatography.

The majority of liquid chromatography (LC) methods are still developed in a conventional manner, that is, by analysts who rely on their knowledge and experience to make method development decisions. In this work, a novel, open-source algorithm was developed for automated and interpretive method development of LC(-mass spectrometry) separations ("AutoLC"). A closed-loop workflow was constructed that interacted directly with the LC system and ran unsupervised in an automated fashion. To achieve this, several challenges related to peak tracking, retention modeling, the automated design of candidate gradient profiles, and the simulation of chromatograms were investigated. The algorithm was tested using two newly designed method development strategies. The first utilized retention modeling, whereas the second used a Bayesian-optimization machine learning approach. In both cases, the algorithm could arrive within 4-10 iterations (i.e., sets of method parameters) at an optimum of the objective function, which included resolution and analysis time as measures of performance. Retention modeling was found to be more efficient while depending on peak tracking, whereas Bayesian optimization was more flexible but limited in scalability. We have deliberately designed the algorithm to be modular to facilitate compatibility with previous and future work (e.g., previously published data handling algorithms).

Sequence dependence of transient Hoogsteen base pairing in DNA.

Hoogsteen (HG) base pairing is characterized by a 180° rotation of the purine base with respect to the Watson-Crick-Franklin (WCF) motif. Recently, it has been found that both conformations coexist in a dynamical equilibrium and that several biological functions require HG pairs. This relevance has motivated experimental and computational investigations of the base-pairing transition. However, a systematic simulation of sequence variations has remained out of reach. Here, we employ advanced path-based methods to perform unprecedented free-energy calculations. Our methodology enables us to study the different mechanisms of purine rotation, either remaining inside or after flipping outside of the double helix. We study seven different sequences, which are neighbor variations of a well-studied A⋅T pair in A6-DNA. We observe the known effect of A⋅T steps favoring HG stability, and find evidence of triple-hydrogen-bonded neighbors hindering the inside transition. More importantly, we identify a dominant factor: the direction of the A rotation, with the 6-ring pointing either towards the longer or shorter segment of the chain, respectively relating to a lower or higher barrier. This highlights the role of DNA's relative flexibility as a modulator of the WCF/HG dynamic equilibrium. Additionally, we provide a robust methodology for future HG proclivity studies.

Fast Proton Transport in FeFe Hydrogenase via a Flexible Channel and a Proton Hole Mechanism.

Di-iron hydrogenases are a class of enzymes that are capable of reducing protons to form molecular hydrogen with high efficiency. In addition to the catalytic site, these enzymes have evolved dedicated pathways to transport protons and electrons to the reaction center. Here, we present a detailed study of the most likely proton transfer pathway in such an enzyme using QM/MM molecular dynamics simulations. The protons are transported through a channel lined out from the protein exterior to the di-iron active site, by a series of hydrogen-bonded, weakly acidic or basic, amino acids and two incorporated water molecules. The channel shows remarkable flexibility, which is an essential feature to quickly reset the hydrogen-bond direction in the channel after each proton passing. Proton transport takes place via a "hole" mechanism, rather than an excess proton mechanism, the free energy landscape of which is remarkably flat, with a highest transition state barrier of only 5 kcal/mol. These results confirm our previous assumptions that proton transport is not rate limiting in the H2 formation activity and that cysteine C299 may be considered protonated at physiological pH conditions. Detailed understanding of this proton transport may aid in the ongoing attempts to design artificial biomimetic hydrogenases for hydrogen fuel production.

Linear Scaling Relationships to Predict pKa's and Reduction Potentials for Bioinspired Hydrogenase Catalysis.

Biomimetic catalysts inspired by the active site of the [FeFe] hydrogenase enzyme can convert protons into molecular hydrogen. Minimizing the overpotential of the electrocatalytic process remains a major challenge for practical application of the catalyst. The catalytic cycle of the hydrogen production follows an ECEC mechanism (E represents an electron transfer step, and C refers to a chemical step), in which the electron and proton transfer steps can be either sequential or coupled (PCET). In this study, we have calculated the pKa's and the reduction potentials for a series of commonly used ligands (80 different complexes) using density functional theory. We establish that the required acid strength for protonation at the Fe-Fe site correlates with the standard reduction potential of the di-iron complexes with a linear energy relationship. These linear relationships allow for fast screening of ligands and tuning of the properties of the catalyst. Our study also suggests that bridgehead ligand properties, such as bulkiness and aromaticity, can be exploited to alter or even break the linear scaling relationships.

Bayesian optimization of comprehensive two-dimensional liquid chromatography separations.

Comprehensive two-dimensional liquid chromatography (LC×LC), is a powerful, emerging separation technique in analytical chemistry. However, as many instrumental parameters need to be tuned, the technique is troubled by lengthy method development. To speed up this process, we applied a Bayesian optimization algorithm. The algorithm can optimize LC×LC method parameters by maximizing a novel chromatographic response function based on the concept of connected components of a graph. The algorithm was benchmarked against a grid search (11,664 experiments) and a random search algorithm on the optimization of eight gradient parameters for four different samples of 50 compounds. The worst-case performance of the algorithm was investigated by repeating the optimization loop for 100 experiments with random starting experiments and seeds. Given an optimization budget of 100 experiments, the Bayesian optimization algorithm generally outperformed the random search and often improved upon the grid search. Moreover, the Bayesian optimization algorithm offered a considerably more sample-efficient alternative to grid searches, as it found similar optima to the grid search in far fewer experiments (a factor of 16-100 times less). This could likely be further improved by a more informed choice of the initialization experiments, which could be provided by the analyst's experience or smarter selection procedures. The algorithm allows for expansion to other method parameters (e.g., temperature, flow rate, etc.) and unlocks closed-loop automated method development.

Discovering Collective Variables of Molecular Transitions via Genetic Algorithms and Neural Networks.

With the continual improvement of computing hardware and algorithms, simulations have become a powerful tool for understanding all sorts of (bio)molecular processes. To handle the large simulation data sets and to accelerate slow, activated transitions, a condensed set of descriptors, or collective variables (CVs), is needed to discern the relevant dynamics that describes the molecular process of interest. However, proposing an adequate set of CVs that can capture the intrinsic reaction coordinate of the molecular transition is often extremely difficult. Here, we present a framework to find an optimal set of CVs from a pool of candidates using a combination of artificial neural networks and genetic algorithms. The approach effectively replaces the encoder of an autoencoder network with genes to represent the latent space, i.e., the CVs. Given a selection of CVs as input, the network is trained to recover the atom coordinates underlying the CV values at points along the transition. The network performance is used as an estimator of the fitness of the input CVs. Two genetic algorithms optimize the CV selection and the neural network architecture. The successful retrieval of optimal CVs by this framework is illustrated at the hand of two case studies: the well-known conformational change in the alanine dipeptide molecule and the more intricate transition of a base pair in B-DNA from the classic Watson-Crick pairing to the alternative Hoogsteen pairing. Key advantages of our framework include the following: optimal interpretable CVs, avoiding costly calculation of committor or time-correlation functions, and automatic hyperparameter optimization. In addition, we show that applying a time-delay between the network input and output allows for enhanced selection of slow variables. Moreover, the network can also be used to generate molecular configurations of unexplored microstates, for example, for augmentation of the simulation data.

Strong Reduction of the Chain Rigidity of Hyaluronan by Selective Binding of Ca2+ Ions.

The biological functions of natural polyelectrolytes are strongly influenced by the presence of ions, which bind to the polymer chains and thereby modify their properties. Although the biological impact of such modifications is well recognized, a detailed molecular picture of the binding process and of the mechanisms that drive the subsequent structural changes in the polymer is lacking. Here, we study the molecular mechanism of the condensation of calcium, a divalent cation, on hyaluronan, a ubiquitous polymer in human tissues. By combining two-dimensional infrared spectroscopy experiments with molecular dynamics simulations, we find that calcium specifically binds to hyaluronan at millimolar concentrations. Because of its large size and charge, the calcium cation can bind simultaneously to the negatively charged carboxylate group and the amide group of adjacent saccharide units. Molecular dynamics simulations and single-chain force spectroscopy measurements provide evidence that the binding of the calcium ions weakens the intramolecular hydrogen-bond network of hyaluronan, increasing the flexibility of the polymer chain. We also observe that the binding of calcium to hyaluronan saturates at a maximum binding fraction of ∼10-15 mol %. This saturation indicates that the binding of Ca2+ strongly reduces the probability of subsequent binding of Ca2+ at neighboring binding sites, possibly as a result of enhanced conformational fluctuations and/or electrostatic repulsion effects. Our findings provide a detailed molecular picture of ion condensation and reveal the severe effect of a few, selective and localized electrostatic interactions on the rigidity of a polyelectrolyte chain.

Frontiers in Multiscale Modeling of Photoreceptor Proteins.

This perspective article highlights the challenges in the theoretical description of photoreceptor proteins using multiscale modeling, as discussed at the CECAM workshop in Tel Aviv, Israel. The participants have identified grand challenges and discussed the development of new tools to address them. Recent progress in understanding representative proteins such as green fluorescent protein, photoactive yellow protein, phytochrome, and rhodopsin is presented, along with methodological developments.

Hydration interactions beyond the first solvation shell in aqueous phenolate solution.

We investigate the orientational dynamics of water molecules solvating phenolate ions using ultrafast vibrational spectroscopy and density functional theory-based molecular dynamics simulations. To assess the roles of the hydrophobic and hydrophilic parts of the anion, we also perform experiments and simulations on solutions of phenol. The experiments show that phenolate immobilizes (τor > 10 ps) 6.2 ± 0.5 water molecules beyond the first solvation shell of its oxygen atom, whereas phenol immobilizes only ∼2 water molecules, including the water molecules in its first solvation shell. The simulations reproduce the experiments very well, and show that phenolate causes a local ordering of the hydrogen-bond structure that extends beyond the first solvation shell, thus explaining the experimental observations. The comparison with phenol solution shows that the solvation interaction of phenolate beyond its first solvation shell is due to the high charge density of its negatively charged oxygen atom.

Optimizing the Energetics of FLP-Type H2 Activation by Modulating the Electronic and Structural Properties of the Lewis Acids: A DFT Study.

The great potential of frustrated Lewis pairs (FLPs) as metal-free catalysts for activation of molecular hydrogen has attracted increasing interest as an alternative to transition-metal catalysts. However, the complexity of FLP systems, involving the simultaneous interaction of three molecules, impedes a detailed understanding of the activation mechanism and the individual roles of the Lewis acid (LA) and Lewis base (LB). In the present work, using density functional theory (DFT) calculations, we examine the reactivity of 75 FLPs for the H2 splitting reaction, including a series of experimentally investigated LAs combined with conventional phosphine-based (tBu3P) and oxygen-based (i.e., ethereal solvent) Lewis bases. We find that the catalytic activity of the FLP is the result of a delicate balance of the LA and LB strengths and their bulkiness. The H2 splitting reaction can be changed from endergonic to exergonic by tuning the electrophilicity of the LA. Also, a more nucleophilic LB results in a more stable ion pair product and a lower barrier for the hydrogen splitting. The bulkiness of the LB leads to an early transition state to reduce steric hindrance and lower the barrier height. The bulkiness of the fragments determines the cavity size in the FLP complex, and a large cavity allows for a larger charge separation in the ion pair configuration. A shorter proton-hydride distance in this product complex correlates with a stronger attraction between the fragments, which forms more reactive ion pairs and facilitates the proton and hydride donations in the subsequent hydrogenation process. These insights may help with rationalizing the experimentally observed reactivities of FLPs and with designing better FLP systems for hydrogenation catalysis and hydrogen storage.

Peptide Side-COOH Groups Have Two Distinct Conformations under Biorelevant Conditions.

The carboxyl (COOH) side chain groups of amino acids, such as aspartic acid, play an important role in biochemical processes, including enzymatic proton transport. In many theoretical studies, it was found that the (bio)chemical reactivity of the carboxyl group strongly depends on the conformation of this group. Interestingly, up to now there has been no experimental investigation of the geometry and the stability of different COOH conformers under biorelevant conditions. Here, we investigate the conformational isomerism of the side chain COOH group of N-acetyl aspartic acid amide using polarization-resolved two-dimensional infrared spectroscopy. We find that the carboxyl group shows two distinct near-planar conformers (syn and anti) when dissolved in water at room temperature. Both conformers are significantly populated in aqueous solution (75 ± 10% and 25 ± 10% for syn and anti, respectively). Molecular dynamics simulations show that the anti conformer interacts more strongly with water molecules than the syn conformer, explaining why this conformer is significantly present in aqueous solution.

Unraveling the mechanism of biomimetic hydrogen fuel production - a first principles molecular dynamics study.

The Fe2(bdt)(CO)6 [bdt = benzenedithiolato] complex, a synthetic mimic of the [FeFe] hydrogenase enzyme can electrochemically convert protons into molecular hydrogen. Molecular understanding of the cascade of reaction steps is important for the design of more efficient catalysts. In this study, we investigate the reaction mechanism of the hydrogen production catalysis in explicit solution of acetonitrile using first principles molecular dynamics simulations. We have characterized all reduction and protonation intermediates taking part in the catalytic cycle. Free energy surfaces of the activated reaction steps are calculated using metadynamics. We find that the second protonation leading to molecular hydrogen formation is the rate limiting step. Direct protonation of the bridging hydride by a proton from the solution to form H2 is the most favorable reaction pathway. However, also a bdt sulfur atom can become protonated, leading to a possible proton trap state that reduces the catalytic efficiency. Our calculations validate the ECEC mechanism proposed using cyclic voltammetry.

Microscopic Picture of the Solvent Reorganization During Electron Transfer to Flavin in Water.

The redox potential of molecular species is largely modulated by its molecular environment so that a change of the environment will lead to a different redox potential. However, a detailed molecular picture of reorganization of the environment upon reduction is still unclear. To unravel the details of the solvent reorganization during electron transfer, we have performed density functional theory-based molecular dynamics (DFT-MD) and hybrid quantum mechanics/molecular mechanics (QM/MM) simulations of the reduction of lumiflavin. Previously, we have calculated the reduction free energy curves of the redox half reactions of lumiflavin in water as a function of the instantaneous gap energy (ΔE) ( J. Chem. Theory Comput. 2013 , 9 , 3889 - 3899 ). In this work, we focus on finding the changes in the solvent environment that correlate with this ΔE reaction coordinate. Comparing the QM/MM simulations, in which the solvent is modeled with an empirical force field, with the (full) DFT-MD simulations, we find that the response through electronic polarization plays a significant role in the latter case. Also a small charge transfer between flavin and solvent is observed in the full DFT treatment. As a result, we find only in the case of the QM/MM model a strong correlation between ΔE and the (pairwise computed) electrostatic potential (ESP) at the flavin due to the solvent. By analyzing the contribution of the ESP at the flavin per solvent molecule, we cannot only distinguish between the different modes of hydration by solvent molecules that coordinate at the hydrophilic and hydrophobic sides of the flavin molecule but also quantify their contribution to the reorganization free energy by measuring the ESP fluctuations per solvent molecule.

The Adaptive Path Collective Variable: A Versatile Biasing Approach to Compute the Average Transition Path and Free Energy of Molecular Transitions.

In the past decade, great progress has been made in the development of enhanced sampling methods, aimed at overcoming the time-scale limitations of molecular dynamics (MD) simulations. Many sampling schemes rely on adding an external bias to favor the sampling of transitions and to estimate the underlying free energy landscape. Nevertheless, sampling molecular processes described by many order parameters, or collective variables (CVs), such as complex biomolecular transitions, remains often very challenging. The computational cost has a prohibitive scaling with the dimensionality of the CV-space. Inspiration can be taken from methods that focus on localizing transition pathways: the CV-space can be projected onto a path-CV that connects two stable states, and a bias can be exerted onto a one-dimensional parameter that captures the progress of the transition along the path-CV. In principle, such a sampling scheme can handle an arbitrarily large number of CVs. A standard enhanced sampling technique combined with an adaptive path-CV can then locate the mean transition pathway and obtain the free energy profile along the path. In this chapter, we discuss the adaptive path-CV formalism and its numerical implementation. We apply the path-CV with several enhanced sampling methods-steered MD, metadynamics, and umbrella sampling-to a biologically relevant process: the Watson-Crick to Hoogsteen base-pairing transition in double-stranded DNA. A practical guide is provided on how to recognize and circumvent possible pitfalls during the calculation of a free energy landscape that contains multiple pathways. Examples are presented on how to perform enhanced sampling simulations using PLUMED, a versatile plugin that can work with many popular MD engines.

On the origin of the extremely different solubilities of polyethers in water.

The solubilities of polyethers are surprisingly counter-intuitive. The best-known example is the difference between polyethylene glycol ([-CH2-CH2-O-]n) which is infinitely soluble, and polyoxymethylene ([-CH2-O-]n) which is completely insoluble in water, exactly the opposite of what one expects from the C/O ratios of these molecules. Similar anomalies exist for oligomeric and cyclic polyethers. To solve this apparent mystery, we use femtosecond vibrational and GHz dielectric spectroscopy with complementary ab initio calculations and molecular dynamics simulations. We find that the dynamics of water molecules solvating polyethers is fundamentally different depending on their C/O composition. The ab initio calculations and simulations show that this is not because of steric effects (as is commonly believed), but because the partial charge on the O atoms depends on the number of C atoms by which they are separated. Our results thus show that inductive effects can have a major impact on aqueous solubilities.

Double helical conformation and extreme rigidity in a rodlike polyelectrolyte.

The ubiquitous biomacromolecule DNA has an axial rigidity persistence length of ~50 nm, driven by its elegant double helical structure. While double and multiple helix structures appear widely in nature, only rarely are these found in synthetic non-chiral macromolecules. Here we report a double helical conformation in the densely charged aromatic polyamide poly(2,2'-disulfonyl-4,4'-benzidine terephthalamide) or PBDT. This double helix macromolecule represents one of the most rigid simple molecular structures known, exhibiting an extremely high axial persistence length (~1 micrometer). We present X-ray diffraction, NMR spectroscopy, and molecular dynamics (MD) simulations that reveal and confirm the double helical conformation. The discovery of this extreme rigidity in combination with high charge density gives insight into the self-assembly of molecular ionic composites with high mechanical modulus (~ 1 GPa) yet with liquid-like ion motions inside, and provides fodder for formation of other 1D-reinforced composites.