Explainable Graph Neural Networks with Data Augmentation for Predicting pKa of C-H Acids.

The pKa of C-H acids is an important parameter in the fields of organic synthesis, drug discovery, and materials science. However, the prediction of pKa is still a great challenge due to the limit of experimental data and the lack of chemical insight. Here, a new model for predicting the pKa values of C-H acids is proposed on the basis of graph neural networks (GNNs) and data augmentation. A message passing unit (MPU) was used to extract the topological and target-related information from the molecular graph data, and a readout layer was utilized to retrieve the information on the ionization site C atom. The retrieved information then was adopted to predict pKa by a fully connected network. Furthermore, to increase the diversity of the training data, a knowledge-infused data augmentation technique was established by replacing the H atoms in a molecule with substituents exhibiting different electronic effects. The MPU was pretrained with the augmented data. The efficacy of data augmentation was confirmed by visualizing the distribution of compounds with different substituents and by classifying compounds. The explainability of the model was studied by examining the change of pKa values when a specific atom was masked. This explainability was used to identify the key substituents for pKa. The model was evaluated on two data sets from the iBonD database. Dataset1 includes the experimental pKa values of C-H acids measured in DMSO, while dataset2 comprises the pKa values measured in water. The results show that the knowledge-infused data augmentation technique greatly improves the predictive accuracy of the model, especially when the number of samples is small.

Interpretable Perturbator for Variable Selection in near-Infrared Spectral Analysis.

A perturbator was developed for variable selection in near-infrared (NIR) spectral analysis based on the perturbation strategy in deep learning for developing interpretation methods. A deep learning predictor was first constructed to predict the targets from the spectra in the training set. Then, taking the output of the predictor as a reference, the perturbator was trained to derive the perturbation-positive (P+) and perturbation-negative (P-) features from the spectra. Therefore, the weight (σ) of the perturbator layer can be a criterion to evaluate the importance of the variables in the spectra. Ranking the spectral variables by the criterion, the number of the variables used in the quantitative model can be obtained through cross-validation. Three NIR data sets were used to evaluate the proposed method. The root mean squared error was found to be comparable with or superior to that obtained by the commonly used methods. Moreover, the selected spectral variables are interpretable in identifying the key spectral features related to the prediction target. Therefore, the proposed method provides not only an effective tool for optimizing quantitative model, but also an efficient way for explaining spectra of multicomponent samples.

Aggregation, structure and water permeability of membrane-embedded helical Aß oligomers.

It is widely recognized that membranes can facilitate the aggregation of amyloid-ß (Aß) peptides, while Aß can in turn cause membrane damage. Many studies focus on the peptide-membrane interactions of Aß oligomers with ß-rich structures. However, the exact aggregation and toxicity mechanism of the membrane-embedded helical Aß oligomers remain ambiguous. Herein, the molecular dynamics simulations were performed on membrane-embedded helical Aß42 peptides. Initiated by eight Aß42 monomers embedded in a lipid bilayer, the monomers aggregate into oligomers with stable transmembrane helix structures. With the aggregation of peptides, the membrane perturbations caused by Aß aggregates decrease. The molecular architectures of oligomers were characterized and a helix-rich octamer stabilized by an annular network of hydrogen bonds was observed. The oligomers demonstrate the capability to assist transmembrane water transport. Our study may provide new insights for the investigation of transmembrane Aß oligomers.

Achieving Accurate Standard Protein-Protein Binding Free Energy Calculations through the Geometrical Route and Ergodic Sampling.

A new strategy for the prediction of binding free energies of protein-protein complexes is reported in the present article. By combining an ergodic-sampling algorithm with the so-called "geometrical route", which introduces a series of geometrical restraints as a preamble to the physical separation of the two partners, we achieve accurate binding free energy calculations for medium-sized protein-protein complexes within the microsecond timescale. The ergodic-sampling algorithm, namely, Gaussian-accelerated molecular dynamics (GaMD), implicitly helps explore the conformational change of the two binding partners as they associate reversibly by raising the energy wells. Therefore, independent simulations capturing the isomerization of proteins are no longer needed, reducing both the computational cost and human effort. Numerical applications indicate errors on the order of 0.1 kcal/mol for the Abl-SH3 domain binding a decapeptide, of 2.6 kcal/mol for the barnase-barstar complex, and of 0.2 kcal/mol for human leukocyte elastase binding the third domain of the turkey ovomucoid inhibitor. Compared with the classical geometrical route, which resorts to collective variables to describe the isomerization of proteins, our new strategy possesses remarkable convergence properties and robustness for protein-protein complexes owing to improved ergodic sampling. We are confident that the strategy presented in this study will have a broad range of applications, helping us understand recognition-association phenomena in the areas of physical, biological, and medicinal chemistry.

Binding Thermodynamics of Fourth-Generation EGFR Inhibitors Revealed by Absolute Binding Free Energy Calculations.

The overexpression or mutation of the kinase domain of the epidermal growth factor receptor (EGFR) is strongly associated with non-small-cell lung cancer (NSCLC). EGFR tyrosine kinase inhibitors (TKIs) have proven to be effective in treating NSCLC patients. However, EGFR mutations can result in drug resistance. To elucidate the mechanisms underlying this resistance and inform future drug development, we examined the binding affinities of BLU-945, a recently reported fourth-generation TKI, to wild-type EGFR (EGFRWT) and its double-mutant (L858R/T790M; EGFRDM) and triple-mutant (L858R/T790M/C797S; EGFRTM) forms. We compared the binding affinities of BLU-945, BLU-945 analogues, CH7233163 (another fourth-generation TKI), and erlotinib (a first-generation TKI) using absolute binding free energy calculations. Our findings reveal that BLU-945 and CH7233163 exhibit binding affinities to both EGFRDM and EGFRTM stronger than those of erlotinib, corroborating experimental data. We identified K745 and T854 as the key residues in the binding of fourth-generation EGFR TKIs. Electrostatic forces were the predominant driving force for the binding of fourth-generation TKIs to EGFR mutants. Furthermore, we discovered that the incorporation of piperidinol and sulfone groups in BLU-945 substantially enhanced its binding capacity to EGFR mutants. Our study offers valuable theoretical insights for optimizing fourth-generation EGFR TKIs.

Hyperactive Antifreeze Proteins Promote Ice Growth before Binding to It.

The antifreeze mechanism of antifreeze proteins (AFPs) evolved by organisms has been widely studied. However, detailed knowledge of the synergy between AFPs and ice crystals still remains fragmentary. In the present contribution, the cooperative effect of the hyperactive insect antifreeze protein TmAFP and ice crystals on the interfacial water during the entire process of inhibiting ice growth is systematically investigated at the atomic level and compared with its low activity mutant and a nonantifreeze protein. The results indicate a significant synergy between TmAFP and ice crystals, which enables the TmAFP to promote the ice growth before adsorbing on the surfaces of the ice crystals, while the mutant and the nonantifreeze protein cannot promote the ice growth due to the lack of this synergy. When TmAFP approaches the ice surface, the interfacial water is induced by both the AFP and the ice crystals to form the anchored clathrate motif, which binds TmAFP to the ice surface, resulting in a local increase in the curvature of the ice surface, thereby inhibiting the growth of ice. In this study, three stages, namely, promotion, adsorption, and inhibition, are observed in the complete process of TmAFP inhibiting ice growth, and the synergistic mechanism between protein and ice crystals is revealed. The results are helpful for the design of antifreeze proteins and bioinspired antifreeze materials with superior performance.

Spectral Encoder to Extract the Features of Near-Infrared Spectra for Multivariate Calibration.

An autoencoder architecture was adopted for near-infrared (NIR) spectral analysis by extracting the common features in the spectra. Three autoencoder-based networks with different purposes were constructed. First, a spectral encoder was established by training the network with a set of spectra as the input. The features of the spectra can be encoded by the nodes in the bottleneck layer, which in turn can be used to build a sparse and robust model. Second, taking the spectra of one instrument as the input and that of another instrument as the reference output, the common features in both spectra can be obtained in the bottleneck layer. Therefore, in the prediction step, the spectral features of the second can be predicted by taking the reverse of the decoder as the encoder. Furthermore, transfer learning was used to build the model for the spectra of more instruments by fine-tuning the trained network. NIR datasets of plant, wheat, and pharmaceutical tablets measured on multiple instruments were used to test the method. The multi-linear regression (MLR) model with the encoded features was found to have a similar or slightly better performance in prediction compared with the partial least-squares (PLS) model.

Binding Models of Aß42 Peptide with Membranes Explored by Molecular Simulations.

One of the factors contributing to the toxicity of amyloid-ß (Aß) peptides is the destruction of membrane integrity through Aß peptide-membrane interactions. The binding of Aß peptides to membranes has been studied by experiments and theoretical simulations extensively. The exact binding mechanism, however, still remains elusive. In the present study, the molecular basis of the peptide-bilayer binding mechanism of the full-length Aß42 monomer with POPC/POPS/CHOL bilayers is investigated by all-atom (AA) simulations. Three main binding models in coil, bend, and turn structures are obtained. Model 1 of the three models with the central hydrophobic core (CHC) buried inside the membrane is the dominant binding model. The structural features of the peptide, the peptide-bilayer interacting regions, the intrapeptide interactions, and peptide-water interactions are studied. The binding of the Aß42 monomer to the POPC/POPS/CHOL bilayer is also explored by coarse-grained (CG) simulations as a complement. Both the AA and CG simulations show that residues in CHC prefer forming interactions with the bilayer, indicating the crucial role of CHC in peptide-bilayer binding. Our results can provide new insights for the investigation of the peptide-bilayer binding mechanism of the Aß peptide.

Accurate Description of Solvent-Exposed Salt Bridges with a Non-polarizable Force Field Incorporating Solvent Effects.

The strength of salt bridges resulting from the interaction of cations and anions is modulated by their environment. However, polarization of the solvent molecules by the charged moieties makes the accurate description of cation-anion interactions in an aqueous solution by means of a pairwise additive potential energy function and classical combination rules particularly challenging. In this contribution, aiming at improving the representation of solvent-exposed salt-bridge interactions with an all-atom non-polarizable force field, we put forth here a parametrization strategy. First, the interaction of a cation and an anion is characterized by hybrid quantum mechanical/molecular mechanics (QM/MM) potential of mean force (PMF) calculations, whereby constantly exchanging solvent molecules around the ions are treated at the quantum mechanical level. The Lennard-Jones (LJ) parameters describing the salt-bridge ion pairs are then optimized to match the reference QM/MM PMFs through the so-called nonbonded FIX, or NBFIX, feature of the CHARMM force field. We apply the new set of parameters, coined CHARMM36m-SBFIX, to the calculation of association constants for the ammonium-acetate and guanidinium-acetate complexes, the osmotic pressures for glycine zwitterions, guanidinium, and acetate ions, and to the simulation of both folded and intrinsically disordered proteins. Our findings indicate that CHARMM36m-SBFIX improves the description of solvent-exposed salt-bridge interactions, both structurally and thermodynamically. However, application of this force field to the standard binding free-energy calculation of a protein-ligand complex featuring solvent-excluded salt-bridge interactions leads to a poor reproduction of the experimental value, suggesting that the parameters optimized in an aqueous solution cannot be readily transferred to describe solvent-excluded salt-bridge interactions. Put together, owing to their sensitivity to the environment, modeling salt-bridge interactions by means of a single, universal set of LJ parameters remains a daunting theoretical challenge.

MLCV: Bridging Machine-Learning-Based Dimensionality Reduction and Free-Energy Calculation.

Importance-sampling algorithms leaning on the definition of a model reaction coordinate (RC) are widely employed to probe processes relevant to chemistry and biology alike, spanning time scales not amenable to common, brute-force molecular dynamics (MD) simulations. In practice, the model RC often consists of a handful of collective variables (CVs) chosen on the basis of chemical intuition. However, constructing manually a low-dimensional RC model to describe an intricate geometrical transformation for the purpose of free-energy calculations and analyses remains a daunting challenge due to the inherent complexity of the conformational transitions at play. To solve this issue, remarkable progress has been made in employing machine-learning techniques, such as autoencoders, to extract the low-dimensional RC model from a large set of CVs. Implementation of the differentiable, nonlinear machine-learned CVs in common MD engines to perform free-energy calculations is, however, particularly cumbersome. To address this issue, we present here a user-friendly tool (called MLCV) that facilitates the use of machine-learned CVs in importance-sampling simulations through the popular Colvars module. Our approach is critically probed with three case examples consisting of small peptides, showcasing that through hard-coded neural network in Colvars, deep-learning and enhanced-sampling can be effectively bridged with MD simulations. The MLCV code is versatile, applicable to all the CVs available in Colvars, and can be connected to any kind of dense neural networks. We believe that MLCV provides an effective, powerful, and user-friendly platform accessible to experts and nonexperts alike for machine-learning (ML)-guided CV discovery and enhanced-sampling simulations to unveil the molecular mechanisms underlying complex biochemical processes.

Do antifreeze proteins generally possess the potential to promote ice growth?

The binding of antifreeze proteins (AFPs) to ice needs to be mediated by interfacial water molecules. Our previous study of the effect of AFPs on the dynamics of the interfacial water of freezing at its initial stage has shown that AFPs can promote the growth of ice before binding to it. However, whether different AFPs can promote the freezing of water molecules on the basal and the prismatic surfaces of ice still needs further study. In the present contribution, five representative natural AFPs with different structures and different activities that can be adsorbed on the basal and/or prismatic surfaces of ice are investigated at the atomic level. Our results show that the phenomenon of promoting the growth of ice crystals is not universal. Only hyperactive AFPs (hypAFPs) can promote the growth of the basal plane of ice, while moderately active AFPs cannot. Moreover, this significant promotion is not observed on the prismatic plane regardless of their activity. Further analysis indicates that this promotion may result from the thicker ice/water interface of the basal plane, and the synergy of hypAFPs with ice crystals.

Computer-aided design of molecular machines: techniques, paradigms and difficulties.

With their development in the past decade, molecular machines, which achieve specific tasks by responding to external stimuli, have gradually come to be regarded as powerful tools for a wide range of applications, rather than interesting molecular toys. This conceptual change in turn motivates scientists to design molecular machines with complex architectures. Due to the lack of general principles bridging the functions and the chemical structures of molecular machines, experience-based design becomes difficult with the increase of size and complexity of the architectures. Computer-aided molecular-machine design, therefore, has attracted widespread attention on account of its ability to model and investigate complex molecular architectures without too much time and expense required for synthetic experiments. Using leading-edge numerical-simulation techniques, the mechanisms underlying achieving tasks through response to external stimuli of a large number of existing molecular machines have been successfully explored. Based on the experience of studying existing molecular machines, generalized methodologies of predicting the properties and working principles of molecular candidates have been established, paving the way for de novo computer-aided design of molecular machines. In this perspective, we introduce cutting-edge techniques that have been applied for investigating and designing molecular machines. We show paradigms of computer-aided design of molecular machines, which can serve as guidelines for the investigation of new supramolecular architectures. Moreover, we discuss the limitations and possible future developments of current techniques and methodologies in the field of computer-aided design of molecular machines.

Metabolic Engineering of the Isopentenol Utilization Pathway Enhanced the Production of Terpenoids in Chlamydomonas reinhardtii.

Eukaryotic green microalgae show considerable promise for the sustainable light-driven biosynthesis of high-value fine chemicals, especially terpenoids because of their fast and inexpensive phototrophic growth. Here, the novel isopentenol utilization pathway (IUP) was introduced into Chlamydomonas reinhardtii to enhance the hemiterpene (isopentenyl pyrophosphate, IPP) titers. Then, diphosphate isomerase (IDI) and limonene synthase (MsLS) were further inserted for limonene production. Transgenic algae showed 8.6-fold increase in IPP compared with the wild type, and 23-fold increase in limonene production compared with a single MsLS expressing strain. Following the culture optimization, the highest limonene production reached 117 µg/L, when the strain was cultured in a opt2 medium supplemented with 10 mM isoprenol under a light: dark regimen. This demonstrates that transgenic algae expressing the IUP represent an ideal chassis for the high-value terpenoid production. The IUP will facilitate further the metabolic and enzyme engineering to enhance the terpenoid titers by significantly reducing the number of enzyme steps required for an optimal biosynthesis.

Chemometrics: An Excavator in Temperature-Dependent Near-Infrared Spectroscopy.

Temperature-dependent near-infrared (NIR) spectroscopy has been developed and taken as a powerful technique for analyzing the structure of water and the interactions in aqueous systems. Due to the overlapping of the peaks in NIR spectra, it is difficult to obtain the spectral features showing the structures and interactions. Chemometrics, therefore, is adopted to improve the spectral resolution and extract spectral information from the temperature-dependent NIR spectra for structural and quantitative analysis. In this review, works on chemometric studies for analyzing temperature-dependent NIR spectra were summarized. The temperature-induced spectral features of water structures can be extracted from the spectra with the help of chemometrics. Using the spectral variation of water with the temperature, the structural changes of small molecules, proteins, thermo-responsive polymers, and their interactions with water in aqueous solutions can be demonstrated. Furthermore, quantitative models between the spectra and the temperature or concentration can be established using the spectral variations of water and applied to determine the compositions in aqueous mixtures.

BFEE2: Automated, Streamlined, and Accurate Absolute Binding Free-Energy Calculations.

Accurate absolute binding free-energy estimation in silico, following either an alchemical or a geometrical route, involves several subprocesses and requires the introduction of geometric restraints. Human intervention, for instance, to define the necessary collective variables, prepare the input files, monitor the simulation, and perform post-treatments is, however, tedious, cumbersome, and prone to errors. With the aim of automating and streamlining free-energy calculations, especially for nonexperts, version 2.0 of the binding free energy estimator (BFEE2) provides both standardized alchemical and geometrical workflows and obviates the need for extensive human intervention to guarantee complete reproducibility of the results. To achieve the largest gamut of protein-ligand and, more generally, of host-guest complexes, BFEE2 supports most academic force fields, such as CHARMM, Amber, OPLS, and GROMOS. Configurational files are generated in the NAMD and Gromacs formats, and all the post-treatments are performed in an automated fashion. Moreover, convergence of the free-energy calculation can be monitored from the intermediate files generated during the simulation. All in all, BFEE2 is a foolproof, versatile tool for accurate absolute binding free-energy calculations, assisting the end-user over a broad range of applications.

Regulation of aquaporin-3 water permeability by hyaluronan.

Hyaluronan (HA) is a major component in the extracellular matrix and is responsible for maintaining the water content of the skin. However, the function and moisturizing mechanism at the atomic level of HA remain only partially understood. Investigating the interactions of HA and other skin components can help us understand how the former moisturizes the skin. Considering that aquaporin-3 (AQP3) is a protein responsible for transmembrane water transport in the human skin, we have, therefore, investigated the interactions of AQP3 and HA with different molecular weights using molecular dynamics simulations in the present work. Our results indicate that HA can adsorb onto AQP3 and decrease water mobility around the latter. In addition, the permeation rate of water through AQP3 can also be decreased by HA, and this phenomenon is particularly obvious for small molecular HA. Moreover, we found that large molecular HA can link two adjacent membranes in the extracellular matrix, increasing the adhesion between the membranes in the periplasm. The results of the present study indicate that HA is a natural regulator of AQP3, revealing the synergetic function of HA and AQP3 in the extracellular matrix of the skin.

Modulation of membrane permeability by carbon dioxide.

Promoting drug delivery across the biological membrane is a common strategy to improve bioavailability. Inspired by the observation that carbonated alcoholic beverages can increase the absorption rate of ethanol, we speculate that carbon dioxide (CO2 ) molecules could also enhance membrane permeability to drugs. In the present work, we have investigated the effect of CO2 on the permeability of a model membrane formed by 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine lipids to three drug-like molecules, namely, ethanol, 2',3'-dideoxyadenosine, and trimethoprim. The free-energy and fractional-diffusivity profiles underlying membrane translocation were obtained from µs-timescale simulations and combined in the framework of the fractional solubility-diffusion model. We find that addition of CO2 in the lipid environment results in an increase of the membrane permeability to the three substrates. Further analysis of the permeation events reveals that CO2 expands and loosens the membrane, which, in turn, facilitates permeation of the drug-like molecules. © 2019 Wiley Periodicals, Inc.

Development and clinical application of a rapid IgM-IgG combined antibody test for SARS-CoV-2 infection diagnosis.

The outbreak of the novel coronavirus disease (COVID-19) quickly spread all over China and to more than 20 other countries. Although the virus (severe acute respiratory syndrome coronavirus [SARS-Cov-2]) nucleic acid real-time polymerase chain reaction (PCR) test has become the standard method for diagnosis of SARS-CoV-2 infection, these real-time PCR test kits have many limitations. In addition, high false-negative rates were reported. There is an urgent need for an accurate and rapid test method to quickly identify a large number of infected patients and asymptomatic carriers to prevent virus transmission and assure timely treatment of patients. We have developed a rapid and simple point-of-care lateral flow immunoassay that can detect immunoglobulin M (IgM) and IgG antibodies simultaneously against SARS-CoV-2 virus in human blood within 15 minutes which can detect patients at different infection stages. With this test kit, we carried out clinical studies to validate its clinical efficacy uses. The clinical detection sensitivity and specificity of this test were measured using blood samples collected from 397 PCR confirmed COVID-19 patients and 128 negative patients at eight different clinical sites. The overall testing sensitivity was 88.66% and specificity was 90.63%. In addition, we evaluated clinical diagnosis results obtained from different types of venous and fingerstick blood samples. The results indicated great detection consistency among samples from fingerstick blood, serum and plasma of venous blood. The IgM-IgG combined assay has better utility and sensitivity compared with a single IgM or IgG test. It can be used for the rapid screening of SARS-CoV-2 carriers, symptomatic or asymptomatic, in hospitals, clinics, and test laboratories.

Taming Rugged Free Energy Landscapes Using an Average Force.

The observation of complex structural transitions in biological and abiological molecular objects within time scales amenable to molecular dynamics (MD) simulations is often hampered by significant free energy barriers associated with entangled movements. Importance-sampling algorithms, a powerful class of numerical schemes for the investigation of rare events, have been widely used to extend simulations beyond the time scale common to MD. However, probing processes spanning milliseconds through microsecond molecular simulations still constitutes in practice a daunting challenge because of the difficulty of taming the ruggedness of multidimensional free energy surfaces by means of naive transition coordinates. To address this limitation, in recent years we have elaborated importance-sampling methods relying on an adaptive biasing force (ABF). In this Account, we review recent developments of algorithms aimed at mapping rugged free energy landscapes that correspond to complex processes of physical, chemical, and biological relevance. Through these developments, we have broadened the spectrum of applications of the popular ABF algorithm while improving its computational efficiency, notably for multidimensional free energy calculations. One major algorithmic advance, coined meta-eABF, merges the key features of metadynamics and an extended Lagrangian variant of ABF (eABF) by simultaneously shaving the barriers and flooding the valleys of the free energy landscape, and it possesses a convergence rate up to 5-fold greater than those of other importance-sampling algorithms. Through faster convergence and enhanced ergodic properties, meta-eABF represents a significant step forward in the simulation of millisecond-time-scale events. Here we introduce extensions of the algorithm, notably its well-tempered and replica-exchange variants, which further boost the sampling efficiency while gaining in numerical stability, thus allowing quantum-mechanical/molecular-mechanical free energy calculations to be performed at a lower cost. As a paradigm to bridge microsecond simulations to millisecond events by means of free energy calculations, we have applied the ABF family of algorithms to decompose complex movements in molecular objects of biological and abiological nature. We show here how water lubricates the shuttling of an amide-based rotaxane by altering the mechanism that underlies the concerted translation and isomerization of the macrocycle. Introducing novel collective variables in a computational workflow for the rigorous determination of standard binding free energies, we predict with utmost accuracy the thermodynamics of protein-ligand reversible association. Because of their simplicity, versatility, and robust mathematical foundations, the algorithms of the ABF family represent an appealing option for the theoretical investigation of a broad range of problems relevant to physics, chemistry, and biology.

Finding an Optimal Pathway on a Multidimensional Free-Energy Landscape.

An ad-hoc, yet widely adopted approach to investigate complex molecular objects in motion using importance-sampling schemes involves two steps, namely (i) mapping the multidimensional free-energy landscape that characterizes the movements in the molecular object at hand and (ii) finding the most probable transition path connecting basins of the free-energy hyperplane. To achieve this goal, we turn to an importance-sampling algorithm, coined well-tempered metadynamics-extended adaptive biasing force (WTM-eABF), aimed at mapping rugged free-energy landscapes, combined with a path-searching algorithm, which we call multidimensional lowest energy (MULE), to identify the underlying minimum free-energy pathway in the collective-variable space of interest. First, the well-tempered feature of the importance-sampling scheme confers to the latter an asymptotic convergence, while the overall algorithm inherits the advantage of high sampling efficiency of its predecessor, meta-eABF, making its performance less sensitive to user-defined parameters. Second, the Dijkstra algorithm implemented in MULE is able to identify with utmost efficiency a pathway that satisfies minimum free energy of activation among all the possible routes in the multidimensional free-energy landscape. Numerical simulations of three molecular assemblies indicate that association of WTM-eABF and MULE constitutes a reliable, efficient and robust approach for exploring coupled movements in complex molecular objects. On account of its ease of use and intrinsic performance, we expect WTM-eABF and MULE to become a tool of choice for both experts and nonexperts interested in the thermodynamics and the kinetics of processes relevant to chemistry and biology.