Free-energy landscapes of the coupled conformational transition and inclusion processes of <i>altro</i>-cyclodextrins

<p>Mono-<i>altro</i>-cyclodextrin (<i>altro</i>-CD) may undergo a conformational change of its altropyranose unit when encapsulating guest molecules of different sizes. This conformational transition is found to be coupled to the inclusion processes. In the present contribution, the possible conformational transition pathways in the four (self-)inclusion processes of <i>altro</i>-α and -β-CDs with moieties of variant shapes are explored from the insights of free-energy calculations. The two-dimensional free-energy landscapes characterising the coupled (self-)inclusion and isomerisation processes are determined, and the lowest free-energy pathways (LFEP) connecting the minima of the landscapes are located. The conformational statistics of the altropyranose units along the LFEPs reveal different transition pathways in the four (self-)inclusion processes. It can be concluded that when accommodating a free bulky guest molecule, the altropyranose unit will adjust its conformation to match the guest. However, such induced fit effect in the self-complexation of <i>altro</i>-CD derivatives will be weakened. The conformation of the altropyranose unit changes accompanying the self-complexation, but always adopts the ⁴C₁ one in the self-inclusion complex, irrespective of the shape of the guest moieties. The present results help determine the transition states of the (self-)inclusion processes of CDs and further improve the understanding of the mechanical properties of CD-based molecular shuttles.</p

Solvent and Structure Effects on the Shuttling in Pillar[5]arene/Triazole Rotaxanes

In the present contribution, a pillararene-based rotaxane, formed by a pillar[5]­arene (P[5]) and a dumbbell-shaped thread composed by four 1,2,3-triazole moieties alternatively linked by three methylene moieties and thus leading to two kinds of stations (the C-ended and N-ended ones), was investigated at the atomic level. The effect of the linkers on shuttling in CHCl₃ was investigated by building four rotaxane models with different lengths of methylene groups. The free-energy profiles delineating the shuttling of the P[5] along the thread revealed that the shuttling rate varied regularly with the length (<i>n</i>) of the methylene moieties and exhibited the slowest value for the rotaxane (<i>n</i> = 5). Decomposition of the free-energy profiles into free-energy contributions suggested that electrostatic interactions constitute the main driving force responsible for shuttling. Moreover, the stability of C-ended station is found to be much lower than the N-ended station in each rotaxane, which can also be ascribed to the electrostatic interactions of P[5] with the stations. To investigate the effect of the solvent, the shuttling movement of the rotaxane (<i>n</i> = 4) in DMSO was also studied and compared to that in CHCl₃. The shuttling barrier in DMSO decreased significantly, which can be attributed to its higher polarity and the formation of H-bonds between DMSO and the triazole units. Therefore, the polarity of the solvent and its hydrogen-bond acceptor ability can affect the shuttling rates of the rotaxanes. The present results provide understanding of the shuttling mechanism of the molecules formed by pillararenes and triazole moieties and are expected to serve in the design of pillararene-based molecular machines

Understanding the Reversible Binding of a Multichain Protein–Protein Complex through Free-Energy Calculations

We demonstrate that the binding affinity of a multichain protein–protein complex, insulin dimer, can be accurately predicted using a streamlined route of standard binding free-energy calculations. We find that chains A and C, which do not interact directly during binding, stabilize the insulin monomer structures and reduce the binding affinity of the two monomers, therefore enabling their reversible association. Notably, we confirm that although classical methods can estimate the binding affinity of the insulin dimer, conventional molecular dynamics, enhanced sampling algorithms, and classical geometrical routes of binding free-energy calculations may not fully capture certain aspects of the role played by the noninteracting chains in the binding dynamics. Therefore, this study not only elucidates the role of noninteracting chains in the reversible binding of the insulin dimer but also offers a methodological guide for investigating the reversible binding of multichain protein–protein complexes utilizing streamlined free-energy calculations

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

Unveiling the Underlying Mechanism for Compression and Decompression Strokes of a Molecular Engine

Manufacturing at the molecular level engines to power nanocars represents a challenge in the development of nanomachines. A molecular engine formed of β-cyclodextrin (β-CD), aryl, and amide moiety has been studied by means of molecular dynamics simulations combined with free-energy calculations. The compression and decompression strokes involving the binding processes of the (<i>Z</i>)- and (<i>E</i>)-isomers of this engine with 1-adamantanol (AD) have been elucidated by determining the underlying potentials of mean force (PMFs). The difference in the binding-free energies, considered as the work generated by and stored within this engine, is calculated to be +1.5 kcal/mol, in remarkable agreement with the experimentally measured quantity. Partitioning the PMFs into physically meaningful free-energy components suggests that the two binding processes are primarily controlled by the favorable inclusion of AD by the β-CD. The work generated by the engine is harnessed to push the alkyl moiety from the hydrophobic cavity of the CD to water, to modify a dihedral angle by a twisting motion about the C–Cα bond, and to increase the tilt angle between the mean plane of the sugar unit, which connects the amide moiety, and the mean plane of the CD. By deciphering the intricate mechanism whereby the present molecular engine operates, our understanding of how similar nanomachines work is expected to be improved significantly, helping in turn the design of novel, more effective ones

Solvent-Controlled Shuttling in a Molecular Switch

Rotaxanes driven by solvents have been shown to facilitate translocation of drugs into cells. Shuttling is critical to fulfill this function. Despite the importance of this solvent-driven motion, the mechanism that underlies shuttling remains unclear. In the present contribution, a molecular shuttle controlled by solvent, and formed of α-cyclodextrin (α-CD), dodecamethylene, and bipyridinium moieties, has been studied by means of microsecond time scale molecular dynamics simulations combined with free-energy calculations. Shuttling driven by both solvent and temperature has been investigated by determining the potentials of mean force (PMF) that delineate the process of moving the α-CD along the thread in DMSO and water, at 300 and 400 K. In DMSO, the barriers of the PMFs at both temperatures appear to be virtually the same. At low temperature, however, site exchange of the CD is slowed down. In contrast, the barrier in water is shown to be 4.0 kcal/mol higher than in DMSO, thwarting site exchange. Partitioning the PMFs into free-energy components suggests, in contrast with DMSO, that water interacts favorably with the bipyridium moieties, but less so with the alkyl chain, hence yielding a higher free-energy barrier. This observation is supported by the analysis of the structural features of the rotaxanes from the molecular dynamics trajectories

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

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

Cooperative Recruitment of Amphotericin B Mediated by a Cyclodextrin Dimer

γ-Cyclodextrin (γ-CD) and hydroxypropyl-γ-CD (HP-γ-CD) improve the bioavailability of amphotericin B (AmB) while reducing its toxicity. In a recent study, AmB was found to possess two sites within its prolonged macrolide ring, binding to γ-CD. In the present contribution, cooperative binding of AmB to a γ-CD dimer, a hydroxypropyl-γ-CD (HP-γ-CD) dimer and a hybrid dimer formed by the latter two cyclic oligosaccharides was examined by molecular dynamics simulations and free-energy calculations in an aqueous solution. The potentials of mean force (PMFs) characterizing the dimerization of the CDs on the macrolide ring of AmB were determined for four different spatial arrangements, namely head-to-head (H–H), head-to-tail (H–T), tail-to-head (T–H), and tail-to-tail (T–T). The PMFs allowed the most stable supramolecular organization to be identified along the transition coordinate for every possible orientation of the participating cyclic oligosaccharides. To estimate the absolute binding free energy of each spatial arrangement, alchemical transformations were carried out using free-energy perturbation. T−H corresponds to the most stable orientation for the γ-CD dimer, whereas for the HP-γ-CD and hybrid dimers, the H–T motif is preferred. Our simulations also indicate that, among the three different dimers, the hybrid γ-CD/HP-γ-CD possesses the highest binding affinity toward AmB, in line with experiment. Hydrogen-bonding interactions and spatial matching of the host:guest complex play an important role in the cooperative binding of AmB to CD dimers. The difference in the propensity of the three CD dimers to bind AmB can rationalize the experimental observation that the hybrid γ-CD/HP-γ-CD dimer is a better carrier to enhance the bioavailability of AmB

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