Finding an Optimal Pathway on a Multidimensional Free-Energy Landscape

Unraveling the folding-assisted unbinding mechanism of TCF with its binding partner β-catenin

This study utilizes molecular dynamics simulations aided with multiple walker parallel bias metadynamics to investigate the TCF unbinding mechanism from the β-catenin interface. The results, consistent with experimental binding affinity calculations, unveil a folding-assisted unbinding mechanism.

Computational Investigation of the Covalent Inhibition Mechanism of Bruton's Tyrosine Kinase by Ibrutinib

Covalent inhibitors represent a promising class of therapeutic compounds. Nonetheless, rationally designing covalent inhibitors to achieve a right balance between selectivity and reactivity remains extremely challenging. To better understand the covalent binding mechanism, a computational study is carried out using the irreversible covalent inhibitor of Bruton tyrosine kinase (BTK) ibrutinib as an example. A multi-μs classical molecular dynamics trajectory of the unlinked inhibitor is generated to explore the fluctuations of the compound associated with the kinase binding pocket. Then, the reaction pathway leading to the formation of the covalent bond with the cysteine residue at position 481 via a Michael addition is determined using the string method in collective variables on the basis of hybrid quantum mechanical-molecular mechanical (QM/MM) simulations. The reaction pathway shows a strong correlation between the covalent bond formation and the protonation/deprotonation events taking place sequentially in the covalent inhibition reaction, consistent with a 3-step reaction with transient thiolate and enolates intermediate states. Two possible atomistic mechanisms affecting deprotonation/protonation events from the thiolate to the enolate intermediate were observed: a highly correlated direct pathway involving proton transfer to the Cα of the acrylamide warhead from the cysteine involving one or a few water molecules and a more indirect pathway involving a long-lived enolate intermediate state following the escape of the proton to the bulk solution. The results are compared with experiments by simulating the long-time kinetics of the reaction using kinetic modeling.

Self-Assembly Pathways of Triblock Janus Particles into 3D Open Lattices

The self-assembly of triblock Janus particles is simulated from a fluid to 3D open lattices: pyrochlore, perovskite, and diamond. The coarse-grained model explicitly takes into account the chemical details of the Janus particles (attractive patches at the poles and repulsion around the equator) and it contains explicit solvent particles. Hydrodynamic interactions are accounted for by dissipative particle dynamics. The relative stability of the crystals depends on the patch width. Narrow, intermediate, and wide patches stabilize the pyrochlore-, the perovskite-, and the diamond-lattice, respectively. The nucleation of all three lattices follows a two-step mechanism: the particles first agglomerate into a compact and disordered liquid cluster, which does not crystallize until it has grown to a threshold size. Second, the particles reorient inside this cluster to form crystalline nuclei. The free-energy barriers for the nucleation of pyrochlore and perovskite are ≈10 kBT, which are close to the nucleation barriers of previously studied 2D kagome lattices. The barrier height for the nucleation of diamond, however, is much larger (>20 kBT), as the symmetry of the triblock Janus particles is not perfect for a diamond structure. The large barrier is associated with the reorientation of particles, i.e., the second step of the nucleation mechanism.

Targeting RdRp of SARS-CoV-2 with De Novo Molecule Generation

Viruses are known for their extremely high mutation rates, allowing them to evade both the human immune system and many forms of standard medicine. Despite this, the RNA dependent RNA polymerase (RdRp) of the RNA viruses has been largely conserved, and any significant mutation of this protein is unlikely. The recent COVID-19 pandemic presents a need for therapeutics. We have designed a de novo drug design algorithm that generates strong binding ligands from scratch, based on only the structure of the target protein's receptor. In this paper, we applied our method to target SARS-CoV-2 RdRp and generated several de novo molecules. We then chose some drug molecules based on the structural similarity to some of our strongest binding de novo molecules. Subsequently, we showed, using rigorous all-atom explicit-water free energy calculations in near-microsecond time scales using state-of-the-art well-tempered metadynamics simulations, that some of our de novo generated ligands bind more strongly to RdRp than the recent FDA approved drug remdesivir in its active form, remdesivir triphosphate (RTP). We elucidated the binding mechanism for some of the top binders and compared it with RTP. We believe that this work will be useful both by presenting lead structures for RdRp inhibition and by delivering key insights into the residues of the protein potentially involved in the binding/unbinding of these small molecule drugs, leading to more targeted studies in the future.

Collective Variable-Based Enhanced Sampling: From Human Learning to Machine Learning

Enhanced-sampling algorithms relying on collective variables (CVs) are extensively employed to study complex (bio)chemical processes that are not amenable to brute-force molecular simulations. The selection of appropriate CVs characterizing the slow movement modes is of paramount importance for reliable and efficient enhanced-sampling simulations. In this Perspective, we first review the application and limitations of CVs obtained from chemical and geometrical intuition. We also introduce path-sampling algorithms, which can identify path-like CVs in a high-dimensional free-energy space. Machine-learning algorithms offer a viable approach to finding suitable CVs by analyzing trajectories from preliminary simulations. We discuss both the performance of machine-learning-derived CVs in enhanced-sampling simulations of experimental models and the challenges involved in applying these CVs to realistic, complex molecular assemblies. Moreover, we provide a prospective view of the potential advancements of machine-learning algorithms for the development of CVs in the field of enhanced-sampling simulations.

Unveiling the State Transition Mechanisms of Ras Proteins through Enhanced Sampling and QM/MM Simulations

In cells, wild-type RasGTP complexes exist in two distinct states: active State 2 and inactive State 1. These complexes regulate their functions by transitioning between the two states. However, the mechanisms underlying this state transition have not been clearly elucidated. To address this, we conducted a detailed simulation study to characterize the energetics of the stable states involved in the state transitions of the HRasGTP complex, specifically from State 2 to State 1. This was achieved by employing multiscale quantum mechanics/molecular mechanics and enhanced sampling molecular dynamics methods. Based on the simulation results, we constructed the two-dimensional free energy landscapes that provide crucial information about the conformational changes of the HRasGTP complex from State 2 to State 1. Furthermore, we also explored the conformational changes from the intermediate state to the product state during guanosine triphosphate hydrolysis. This study on the conformational changes involved in the HRas state transitions serves as a valuable reference for understanding the corresponding events of both KRas and NRas as well.

How is Membrane Permeation of Small Ionizable Molecules Affected by Protonation Kinetics?

According to the pH-partition hypothesis, the aqueous solution adjacent to a membrane is a mixture of the ionization states of the permeating molecule at fixed Henderson-Hasselbalch concentrations, such that each state passes through the membrane in parallel with its own specific permeability. An alternative view, based on the assumption that the rate of switching ionization states is instantaneous, represents the permeation of ionizable molecules via an effective Boltzmann-weighted average potential (BWAP). Such an assumption is used in constant-pH molecular dynamics simulations. The inhomogeneous solubility-diffusion framework can be used to compute the pH-dependent membrane permeability for each of these two limiting treatments. With biased WTM-eABF molecular dynamics simulations, we computed the potential of mean force and diffusivity of each ionization state of two weakly basic small molecules: nicotine, an addictive drug, and varenicline, a therapeutic for treating nicotine addiction. At pH = 7, the BWAP effective permeability is greater than that determined by pH-partitioning by a factor of 2.5 for nicotine and 5 for varenicline. To assess the importance of ionization kinetics, we present a Smoluchowski master equation that includes explicitly the protonation and deprotonation processes coupled with the diffusive motion across the membrane. At pH = 7, the increase in permeability due to the explicit ionization kinetics is negligible for both nicotine and varenicline. This finding is reaffirmed by combined Brownian dynamics and Markov state model simulations for estimating the permeability of nicotine while allowing changes in its ionization state. We conclude that for these molecules the pH-partition hypothesis correctly captures the physics of the permeation process. The small free energy barriers for the permeation of nicotine and varenicline in their deprotonated neutral forms play a crucial role in establishing the validity of the pH-partitioning mechanism. Essentially, BWAP fails because ionization kinetics are too slow on the time scale of membrane crossing to affect the permeation of small ionizable molecules such as nicotine and varenicline. For the singly protonated state of nicotine, the computational results agree well with experimental measurements (P1 = 1.29 × 10-7 cm/s), but the agreement for neutral (P0 = 6.12 cm/s) and doubly protonated nicotine (P2 = 3.70 × 10-13 cm/s) is slightly worse, likely due to factors associated with the aqueous boundary layer (neutral form) or leaks through paracellular pathways (doubly protonated form).

Analyzing Molecular Dynamics Trajectories Thermodynamically through Artificial Intelligence

Molecular dynamics simulations produce trajectories that correspond to vast amounts of structure when exploring biochemical processes. Extracting valuable information, e.g., important intermediate states and collective variables (CVs) that describe the major movement modes, from molecular trajectories to understand the underlying mechanisms of biological processes presents a significant challenge. To achieve this goal, we introduce a deep learning approach, coined DIKI (deep identification of key intermediates), to determine low-dimensional CVs distinguishing key intermediate conformations without a-priori assumptions. DIKI dynamically plans the distribution of latent space and groups together similar conformations within the same cluster. Moreover, by incorporating two user-defined parameters, namely, coarse focus knob and fine focus knob, to help identify conformations with low free energy and differentiate the subtle distinctions among these conformations, resolution-tunable clustering was achieved. Furthermore, the integration of DIKI with a path-finding algorithm contributes to the identification of crucial intermediates along the lowest free-energy pathway. We postulate that DIKI is a robust and flexible tool that can find widespread applications in the analysis of complex biochemical processes.

Using Metadynamics to Reveal Extractant Conformational Free Energy Landscapes

Understanding the impact of extractant functionalization on metal-binding energetics in liquid-liquid extraction is essential to guide the development of better separation processes. Traditionally, computational extractant design uses electronic structure calculations on metal-ligand clusters to determine the metal-binding energy of the lowest energy state. Although highly accurate, this approach does not account for all of the relevant physics encountered under experimental conditions. Such methodologies often neglect entropic contributions such as temperature effects and ligand flexibility, in addition to approximating solvent-extractant interactions with implicit solvent models. In this study, we use classical molecular dynamics simulations with an advanced sampling method, metadynamics, to map out extractant molecule conformational free energies in the condensed phase. We generate the complete conformational landscape in solution for a family of bidentate malonamide-based extractants with different functionalizations of the headgroup and the side chains. In particular, we show how such alkyl functionalization reshapes the free energy landscape, affecting the free energy penalty of organizing the extractant into the cis-like metal-binding conformation from the trans-like conformation of the free extractant in solution. Specifically, functionalizing alkyl tails to the center of the headgroup has a greater influence on increasing molecular rigidity and disfavoring the binding conformation than functionalizing side chains. These findings are consistent with trends in metal-binding energetics based on experimentally reported distribution ratios. We also consider a different bidentate extractant molecule, carbamoylmethylphosphine oxide, and show how the choice of solvent can further reshape the conformational energetic landscape. This study demonstrates the feasibility of using molecular dynamics simulations with advanced sampling techniques to investigate extractant conformational energetics in solution, which, more broadly, will enable extractant design that accounts for entropic effects and explicit solvation.

Standard Binding Free-Energy Calculations: How Far Are We from Automation?

Recent success stories suggest that in silico protein-ligand binding free-energy calculations are approaching chemical accuracy. However, their widespread application remains limited by the extensive human intervention required, posing challenges for the neophyte. As such, it is critical to develop automated workflows for estimating protein-ligand binding affinities with minimum personal involvement. Key human efforts include setting up and tuning enhanced-sampling or alchemical-transformation algorithms as a preamble to computational binding free-energy estimations. Additionally, preparing input files, bookkeeping, and postprocessing represent nontrivial tasks. In this Perspective, we discuss recent progress in automating standard binding free-energy calculations, featuring the development of adaptive or parameter-free algorithms, standardization of binding free-energy calculation workflows, and the implementation of user-friendly software. We also assess the current state of automated standard binding free-energy calculations and evaluate the limitations of existing methods. Last, we outline the requirements for future algorithms and workflows to facilitate automated free-energy calculations for diverse protein-ligand complexes.

Deep-Learning-Assisted Enhanced Sampling for Exploring Molecular Conformational Changes

We present a novel strategy to explore conformational changes and identify stable states of molecular objects, eliminating the need for a priori knowledge. The approach applies a deep learning method to extract information about the movement modes of the molecular object from a short, high-dimensional, and parameter-free preliminary enhanced-sampling simulation. The gathered information is described by a small set of deep-learning-based collective variables (dCVs), which steer the production-enhanced-sampling simulation. Considering the challenge of adequately exploring the configurational space using the low-dimensional, suboptimal dCVs, we incorporate a method designed for ergodic sampling, namely, Gaussian-accelerated molecular dynamics (MD), into the framework of CV-based enhanced sampling. MD simulations on both toy models and nontrivial examples demonstrate the remarkable computational efficiency of the strategy in capturing the conformational changes of molecular objects without a priori knowledge. Specifically, we achieved the blind folding of two fast folders, chignolin and villin, within a time scale of hundreds of nanoseconds and successfully reconstructed the free-energy landscapes that characterize their reversible folding. All in all, the presented strategy holds significant promise for investigating conformational changes in macromolecules, and it is anticipated to find extensive applications in the fields of chemistry and biology.

Discovering Reaction Pathways, Slow Variables, and Committor Probabilities with Machine Learning

A significant challenge faced by atomistic simulations is the difficulty, and often impossibility, to sample the transitions between metastable states of the free-energy landscape associated with slow molecular processes. Importance-sampling schemes represent an appealing option to accelerate the underlying dynamics by smoothing out the relevant free-energy barriers, but require the definition of suitable reaction-coordinate (RC) models expressed in terms of compact low-dimensional sets of collective variables (CVs). While most computational studies of slow molecular processes have traditionally relied on educated guesses based on human intuition to reduce the dimensionality of the problem at hand, a variety of machine-learning (ML) algorithms have recently emerged as powerful alternatives to discover meaningful CVs capable of capturing the dynamics of the slowest degrees of freedom. Considering a simple paradigmatic situation in which the long-time dynamics is dominated by the transition between two known metastable states, we compare two variational data-driven ML methods based on Siamese neural networks aimed at discovering a meaningful RC model─the slowest decorrelating CV of the molecular process, and the committor probability to first reach one of the two metastable states. One method is the state-free reversible variational approach for Markov processes networks (VAMPnets), or SRVs─the other, inspired by the transition path theory framework, is the variational committor-based neural networks, or VCNs. The relationship and the ability of these methodologies to discover the relevant descriptors of the slow molecular process of interest are illustrated with a series of simple model systems. We also show that both strategies are amenable to importance-sampling schemes through an appropriate reweighting algorithm that approximates the kinetic properties of the transition.

Improving Speed and Affordability without Compromising Accuracy: Standard Binding Free-Energy Calculations Using an Enhanced Sampling Algorithm, Multiple-Time Stepping, and Hydrogen Mass Repartitioning

Accurate evaluation of protein-ligand binding free energies in silico is of paramount importance for understanding the mechanisms of biological regulation and providing a theoretical basis for drug design and discovery. Based on a series of atomistic molecular dynamics simulations in an explicit solvent, using well-tempered metadynamics extended adaptive biasing force (WTM-eABF) as an enhanced sampling algorithm, the so-called "geometrical route" offers a rigorous theoretical framework for binding affinity calculations that match experimental values. However, although robust, this strategy remains expensive, requiring substantial computational time to achieve convergence of the simulations. Improving the efficiency of the geometrical route, while preserving its reliability through improved ergodic sampling, is, therefore, highly desirable. In this contribution, having identified the computational bottleneck of the geometrical route, to accelerate the calculations we combine (i) a longer time step for the integration of the equations of motion with hydrogen-mass repartitioning (HMR), and (ii) multiple time-stepping (MTS) for collective-variable and biasing-force evaluation. Altogether, we performed 50 independent WTM-eABF simulations in triplicate for the "physical" separation of the Abl kinase-SH3 domain:p41 complex, following different HMR and MTS schemes, while tuning, in distinct protocols, the parameters of the enhanced-sampling algorithm. To demonstrate the consistency and reliability of the results obtained with the best-performing setups, we carried out quintuple simulations. Furthermore, we demonstrated the transferability of our method to other complexes by triplicating a 200 ns separation simulation of nine chosen protocols for the MDM2-p53:NVP-CGM097 complex. [Holzer et al. J. Med. Chem. 2015, 58, 6348-6358.] Our results, based on an aggregate simulation time of 14.4 μs, allowed an optimal set of parameters to be identified, able to accelerate convergence by a factor of three without any noticeable loss of accuracy.

DeepWEST: Deep Learning of Kinetic Models with the Weighted Ensemble Simulation Toolkit for Enhanced Sampling

Recent advances in computational power and algorithms have enabled molecular dynamics (MD) simulations to reach greater time scales. However, for observing conformational transitions associated with biomolecular processes, MD simulations still have limitations. Several enhanced sampling techniques seek to address this challenge, including the weighted ensemble (WE) method, which samples transitions between metastable states using many weighted trajectories to estimate kinetic rate constants. However, initial sampling of the potential energy surface has a significant impact on the performance of WE, i.e., convergence and efficiency. We therefore introduce deep-learned kinetic modeling approaches that extract statistically relevant information from short MD trajectories to provide a well-sampled initial state distribution for WE simulations. This hybrid approach overcomes any statistical bias to the system, as it runs short unbiased MD trajectories and identifies meaningful metastable states of the system. It is shown to provide a more refined free energy landscape closer to the steady state that could efficiently sample kinetic properties such as rate constants.

Conformational Dynamics of Loop L3 in OmpF: Implications toward Antibiotic Translocation and Voltage Gating

In the present work, we delineate the molecular mechanism of a bulky antibiotic permeating through a bacterial channel and uncover the role of conformational dynamics of the constriction loop in this process. Using the temperature accelerated sliced sampling approach, we shed light onto the dynamics of the L3 loop, in particular the F118 to S125 segment, at the constriction regions of the OmpF porin. We complement the findings with single channel electrophysiology experiments and applied-field simulations, and we demonstrate the role of hydrogen-bond stabilization in the conformational dynamics of the L3 loop. A molecular mechanism of permeation is put forward wherein charged antibiotics perturb the network of stabilizing hydrogen-bond interactions and induce conformational changes in the L3 segment, thereby aiding the accommodation and permeation of bulky antibiotic molecules across the constriction region. We complement the findings with single channel electrophysiology experiments and demonstrate the importance of the hydrogen-bond stabilization in the conformational dynamics of the L3 loop. The generality of the present observations and experimental results regarding the L3 dynamics enables us to identify this L3 segment as the source of gating. We propose a mechanism of OmpF gating that is in agreement with previous experimental data that showed the noninfluence of cysteine double mutants that tethered the L3 tip to the barrel wall on the OmpF gating behavior. The presence of similar loop stabilization networks in porins of other clinically relevant pathogens suggests that the conformational dynamics of the constriction loop is possibly of general importance in the context of antibiotic permeation through porins.

Chasing collective variables using temporal data-driven strategies

The convergence of free-energy calculations based on importance sampling depends heavily on the choice of collective variables (CVs), which in principle, should include the slow degrees of freedom of the biological processes to be investigated. Autoencoders (AEs), as emerging data-driven dimension reduction tools, have been utilised for discovering CVs. AEs, however, are often treated as black boxes, and what AEs actually encode during training, and whether the latent variables from encoders are suitable as CVs for further free-energy calculations remains unknown. In this contribution, we review AEs and their time-series-based variants, including time-lagged AEs (TAEs) and modified TAEs, as well as the closely related model variational approach for Markov processes networks (VAMPnets). We then show through numerical examples that AEs learn the high-variance modes instead of the slow modes. In stark contrast, time series-based models are able to capture the slow modes. Moreover, both modified TAEs with extensions from slow feature analysis and the state-free reversible VAMPnets (SRVs) can yield orthogonal multidimensional CVs. As an illustration, we employ SRVs to discover the CVs of the isomerizations of N-acetyl-N'-methylalanylamide and trialanine by iterative learning with trajectories from biased simulations. Last, through numerical experiments with anisotropic diffusion, we investigate the potential relationship of time-series-based models and committor probabilities.

Force-Field-Dependent DNA Breathing Dynamics: A Case Study of Hoogsteen Base Pairing in A6-DNA

The Hoogsteen (HG) base pairing conformation, commonly observed in damaged and mutated DNA helices, facilitates DNA repair and DNA recognition. The free energy difference between HG and Watson-Crick (WC) base pairs has been computed in previous studies. However, the mechanism of the conformational transition is not well understood. A detailed understanding of the process of WC to HG base pair transition can provide a deeper understanding of DNA repair and recognition. In an earlier study, we explored the free energy landscape for this process using extensive computer simulation with the CHARMM36 force field. In this work, we study the impact of force field models in describing the WC to HG base pairing transition using meta-eABF enhanced sampling, quasi-harmonic entropy calculation, and nonbonded energy analysis. The secondary structures of both base pairing forms and the topology of the free energy landscapes were consistent over different force field models, although the relative free energy, entropy, and the interaction energies tend to vary. The relative stability of the WC and HG conformations is dictated by a delicate balance between the enthalpic stabilization and the reduced entropy of the structurally rigid HG structure. These findings highlight the impact that subtleties in force field models can have on accurately modeling DNA base pair dynamics and should stimulate further computational investigations into other dynamically important motions in DNA.

Nature-Derived Compounds as Potential Bioactive Leads against CDK9-Induced Cancer: Computational and Network Pharmacology Approaches

Given the importance of cyclin-dependent kinases (CDKs) in the maintenance of cell development, gene transcription, and other essential biological operations, CDK blockers have been generated to manage a variety of disorders resulting from CDK irregularities. Furthermore, CDK9 has a crucial role in transcription by regulating short-lived anti-apoptotic genes necessary for cancer cell persistence. Addressing CDK9 with blockers has consequently emerged as a promising treatment for cancer. This study scrutinizes the effectiveness of nature-derived compounds (geniposidic acid, quercetin, geniposide, curcumin, and withanolide C) against CDK9 through computational approaches. A molecular docking study was performed after preparing the protein and the ligands. The selected blockers of the CDK9 exerted reliable binding affinities (−8.114 kcal/mol to −13.908 kcal/mol) against the selected protein, resulting in promising candidates compared to the co-crystallized ligand (LCI). The binding affinity of geniposidic acid (−13.908 kcal/mol) to CDK9 is higher than quercetin (−10.775 kcal/mol), geniposide (−9.969 kcal/mol), curcumin (−9.898 kcal/mol), withanolide C (−8.114 kcal/mol), and the co-crystallized ligand LCI (−11.425 kcal/mol). Therefore, geniposidic acid is a promising inhibitor of CDK9. Moreover, the molecular dynamics studies assessed the structure–function relationships and protein–ligand interactions. The network pharmacology study for the selected ligands demonstrated the auspicious compound–target–pathway signaling pathways vital in developing tumor, tumor cell growth, differentiation, and promoting tumor cell progression. Moreover, this study concluded by analyzing the computational approaches the natural-derived compounds that have potential interacting activities against CDK9 and, therefore, can be considered promising candidates for CKD9-induced cancer. To substantiate this study’s outcomes, in vivo research is recommended.

Computer simulation of the early stages of self-assembly and thermal decomposition of ZIF-8

We employ all-atom well-tempered metadynamics simulations to study the mechanistic details of both the early stages of nucleation and crystal decomposition for the benchmark metal–organic framework (MOF) ZIF-8. To do so, we developed and validated a force field that reliably models the modes of coordination bonds via a Morse potential functional form and employs cationic and anionic dummy atoms to capture coordination symmetry. We also explored a set of physically relevant collective variables and carefully selected an appropriate subset for our problem at hand. After a rapid increase of the Zn–N connectivity, we observe the evaporation of small clusters in favor of a few large clusters, which leads to the formation of an amorphous highly connected aggregate. [Formula: see text] and [Formula: see text] complexes are observed with lifetimes in the order of a few picoseconds, while larger structures, such as four-, five-, and six-membered rings, have substantially longer lifetimes of a few nanoseconds. The free ligands act as “templating agents” for the formation of sodalite cages. ZIF-8 crystal decomposition results in the formation of a vitreous phase. Our findings contribute to a fundamental understanding of MOF’s synthesis that paves the way to controlling synthesis products. Furthermore, our developed force field and methodology can be applied to model solution processes that require coordination bond reactivity for other ZIFs besides ZIF-8.

Binding mechanism of oseltamivir and influenza neuraminidase suggests perspectives for the design of new anti-influenza drugs

Oseltamivir is a widely used influenza virus neuraminidase (NA) inhibitor that prevents the release of new virus particles from host cells. However, oseltamivir-resistant strains have emerged, but effective drugs against them have not yet been developed. Elucidating the binding mechanisms between NA and oseltamivir may provide valuable information for the design of new drugs against NA mutants resistant to oseltamivir. Here, we conducted large-scale (353.4 μs) free-binding molecular dynamics simulations, together with a Markov State Model and an importance-sampling algorithm, to reveal the binding process of oseltamivir and NA. Ten metastable states and five major binding pathways were identified that validated and complemented previously discovered binding pathways, including the hypothesis that oseltamivir can be transferred from the secondary sialic acid binding site to the catalytic site. The discovery of multiple new metastable states, especially the stable bound state containing a water-mediated hydrogen bond between Arg118 and oseltamivir, may provide new insights into the improvement of NA inhibitors. We anticipated the findings presented here will facilitate the development of drugs capable of combating NA mutations.

Influenza virus neuraminidase (NA), a viral membrane glycoprotein, plays an important role in the interactions with host cell surface receptors. The emergence and spread of influenza mutants resistant to neuraminidase inhibitors (NAIs), such as oseltamivir, has been of great concern. Despite many improvements to NAIs, no new first-line NAIs are currently in clinical use. Although there have been previous molecular dynamics simulation studies on the binding and dissociation process of oseltamivir-NA, we discovered new binding pathways and states of oseltamivir through larger-scale simulations and more systematic analysis, which may provide new ideas for the improvement of oseltamivir and even a series of NAIs. In our study, we strongly demonstrate that a detailed understanding of the drug−receptor association process is of fundamental importance for drug design and provide methodological references for the improvement of other drugs.

Statistically optimal analysis of the extended-system adaptive biasing force (eABF) method

The extended-system adaptive biasing force (eABF) method and its newer variants offer rapid exploration of the configuration space of chemical systems. Instead of directly applying the ABF bias to collective variables, they are harmonically coupled to fictitious particles, which separates the problem of enhanced sampling from that of free energy estimation. The prevalent analysis method to obtain the potential of mean force (PMF) from eABF is thermodynamic integration. However, besides the PMF, most information is lost as the unbiased probability of visited configurations is never recovered. In this contribution, we show how statistical weights of individual frames can be computed using the Multistate Bennett's Acceptance Ratio (MBAR), putting the post-processing of eABF on one level with other frequently used sampling methods. In addition, we apply this formalism to the prediction of nuclear magnetic resonance shieldings, which are very sensitive to molecular geometries and often require extensive sampling. The results show that the combination of enhanced sampling by means of extended-system dynamics with the MBAR estimator is a highly useful tool for the calculation of ensemble properties. Furthermore, the extension of the presented scheme to the recently published Gaussian-accelerated molecular dynamics eABF hybrid is straightforward and approximation free.

Enhanced Sampling Simulation Reveals How Solvent Influences Chirogenesis of the Intra-Molecular Diels-Alder Reaction

The timescale involved in chemical reactions is quite often beyond that of normal molecular dynamics simulations. Here, we combine metadynamics with selective integrated tempering sampling to simulate an intra-molecular Diels-Alder reaction in explicit solvents. Based on a one-dimensional collective variable obtained from harmonic linear discriminant analysis, four chiral isomers of products were observed in the simulation. Analyses of reactive trajectories showed that this reaction follows a concerted mechanism in all four solvents. In addition, the hydrogen bond between the reactant and water solvent plays an important role in the water-accelerated reaction mechanism. The dynamics of chirality formation varies significantly with solvents. The chirality of products forms significantly before the transition state, especially in ionic liquid.

A favorable path to domain separation in the orange carotenoid protein

The orange carotenoid protein (OCP) is responsible for nonphotochemical quenching (NPQ) in cyanobacteria, a defense mechanism against potentially damaging effects of excess light conditions. This soluble two-domain protein undergoes profound conformational changes upon photoactivation, involving translocation of the ketocarotenoid inside the cavity followed by domain separation. Domain separation is a critical step in the photocycle of OCP because it exposes the N-terminal domain (NTD) to perform quenching of the phycobilisomes. Many details regarding the mechanism and energetics of OCP domain separation remain unknown. In this work, we apply metadynamics to elucidate the protein rearrangements that lead to the active, domain-separated, form of OCP. We find that translocation of the ketocarotenoid canthaxanthin has a profound effect on the energetic landscape and that domain separation only becomes favorable following translocation. We further explore, characterize, and validate the free energy surface (FES) using equilibrium simulations initiated from different states on the FES. Through pathway optimization methods, we characterize the most probable path to domain separation and reveal the barriers along that pathway. We find that the free energy barriers are relatively small (<5 kcal/mol), but the overall estimated kinetic rate is consistent with experimental measurements (>1 ms). Overall, our results provide detailed information on the requirement for canthaxanthin translocation to precede domain separation and an energetically feasible pathway to dissociation.

How to obtain reaction free energies from free-energy profiles

For chemical reactions that occur via the rearrangement of atoms from a configuration about one minimum (reactant, R) of the potential energy surface (PES) to a configuration about another minimum (product, P), an exact relation between the Helmholtz reaction free energy (Δ FRP) and the free-energy profile (FEP) can be derived. Since the FEP assumes a form similar to that of the PES along the minimum energy path between R and P, there is an unfortunate tendency to regard the FEP as the “free-energy” analog of the minimum energy path and consequently to equate Δ FRP to the difference between the values of the FEP at the minima corresponding to R and P. Analytic treatments of one- and two-dimensional models are presented that show how this mistaken idea leads to errors. In effect, treating the FEP by analogy with the minimum energy path neglects the role of entropy. The FEP is a function of a collective variable (CV), which must be chosen to describe the course of the rearrangement consistently with the exact relation between Δ FRP and the FEP. For large systems of common interest, the PES is often so complex that a straightforward way of choosing a CV is lacking. Consequently, one is forced to make an educated guess. A criterion for judging the quality of the guess is proposed and applied to a two-dimensional model.

Mechanism and biomass association of glucuronoyl esterase: an α/β hydrolase with potential in biomass conversion

Glucuronoyl esterases (GEs) are α/β serine hydrolases and a relatively new addition in the toolbox to reduce the recalcitrance of lignocellulose, the biggest obstacle in cost-effective utilization of this important renewable resource. While biochemical and structural characterization of GEs have progressed greatly recently, there have yet been no mechanistic studies shedding light onto the rate-limiting steps relevant for biomass conversion. The bacterial GE OtCE15A possesses a classical yet distinctive catalytic machinery, with easily identifiable catalytic Ser/His completed by two acidic residues (Glu and Asp) rather than one as in the classical triad, and an Arg side chain participating in the oxyanion hole. By QM/MM calculations, we identified deacylation as the decisive step in catalysis, and quantified the role of Asp, Glu and Arg, showing the latter to be particularly important. The results agree well with experimental and structural data. We further calculated the free-energy barrier of post-catalysis dissociation from a complex natural substrate, suggesting that in industrial settings non-catalytic processes may constitute the rate-limiting step, and pointing to future directions for enzyme engineering in biomass utilization.

Zong and coworkers combine computational and experimental methods to decipher in detail the mechanism of action of glucuronoyl esterases, enzymes with significant biotechnological potential for decoupling lignin from polysaccharides in biomass.

Accurate determination of protein:ligand standard binding free energies from molecular dynamics simulations

Designing a reliable computational methodology to calculate protein:ligand standard binding free energies is extremely challenging. The large change in configurational enthalpy and entropy that accompanies the association of ligand and protein is notoriously difficult to capture in naive brute-force simulations. Addressing this issue, the present protocol rests upon a rigorous statistical mechanical framework for the determination of protein:ligand binding affinities together with the comprehensive Binding Free-Energy Estimator 2 (BFEE2) application software. With the knowledge of the bound state, available from experiments or docking, application of the BFEE2 protocol with a reliable force field supplies in a matter of days standard binding free energies within chemical accuracy, for a broad range of protein:ligand complexes. Limiting undesirable human intervention, BFEE2 assists the end user in preparing all the necessary input files and performing the post-treatment of the simulations towards the final estimate of the binding affinity.

A Companion Guide to the String Method with Swarms of Trajectories: Characterization, Performance, and Pitfalls

The string method with swarms of trajectories (SMwST) is an algorithm that identifies a physically meaningful transition pathway─a one-dimensional curve, embedded within a high-dimensional space of selected collective variables. The SMwST algorithm leans on a series of short, unbiased molecular dynamics simulations spawned at different locations of the discretized path, from whence an average dynamic drift is determined to evolve the string toward an optimal pathway. However conceptually simple in both its theoretical formulation and practical implementation, the SMwST algorithm is computationally intensive and requires a careful choice of parameters for optimal cost-effectiveness in applications to challenging problems in chemistry and biology. In this contribution, the SMwST algorithm is presented in a self-contained manner, discussing with a critical eye its theoretical underpinnings, applicability, inherent limitations, and use in the context of path-following free-energy calculations and their possible extension to kinetics modeling. Through multiple simulations of a prototypical polypeptide, combining the search of the transition pathway and the computation of the potential of mean force along it, several practical aspects of the methodology are examined with the objective of optimizing the computational effort, yet without sacrificing accuracy. In light of the results reported here, we propose some general guidelines aimed at improving the efficiency and reliability of the computed pathways and free-energy profiles underlying the conformational transitions at hand.

Conformational Change from U- to I-Shape of Ion Transporters Facilitates K+ Transport across Lipid Bilayers

We have investigated, at the atomic level, the ion-fishing mechanism underlying the ion transport across membranes mediated by an artificial ion transporter composed of a hydroxyl-rich cholesterol group, a flexible alkyl chain, and a crown ether. Our results show that the transporter can spontaneously insert into the membrane and switch between the folded (U-shaped) and extended (I-shaped) conformations. The free-energy profile associated with the conformational transition indicates that compared with the U-shaped conformation of the transporter, the I-shaped one is thermodynamically more favorable. Furthermore, the free-energy profiles describing the ion translocation reveal that the transporter capturing the ion in U-shape on one side of the membrane and releasing it in I-shape on the other side constitutes a key way for the highly efficient transport of K⁺ ions. We present herewith a rigorous and rational framework to decipher the detailed ion-fishing mechanism of transmembrane ion transport with exceptionally high activity.

Characterizing fenestration size in sodium channel subtypes and their accessibility to inhibitors

Voltage-gated sodium channels (Nav) underlie the electrical activity of nerve and muscle cells. Humans have nine different subtypes of these channels, which are the target of small-molecule inhibitors commonly used to treat a range of conditions. Structural studies have identified four lateral fenestrations within the Nav pore module that have been shown to influence Nav pore blocker access during resting-state inhibition. However, the structural differences among the nine subtypes are still unclear. In particular, the dimensions of the four individual fenestrations across the Nav subtypes and their differential accessibility to pore blockers is yet to be characterized. To address this, we applied classical molecular dynamics simulations to study the recently published structures of Nav1.1, Nav1.2, Nav1.4, Nav1.5, and Nav1.7. Although there is significant variability in the bottleneck sizes of the Nav fenestrations, the subtypes follow a common pattern, with wider DI-II and DIII-IV fenestrations, a more restricted DII-III fenestration, and the most restricted DI-IV fenestration. We further identify the key bottleneck residues in each fenestration and show that the motions of aromatic residue sidechains govern the bottleneck radii. Well-tempered metadynamics simulations of Nav1.4 and Nav1.5 in the presence of the pore blocker lidocaine also support the DI-II fenestration being the most likely access route for drugs. Our computational results provide a foundation for future in vitro experiments examining the route of drug access to sodium channels. Understanding the fenestrations and their accessibility to drugs is critical for future analyses of diseases mutations across different sodium channel subtypes, with the potential to inform pharmacological development of resting-state inhibitors and subtype-selective drug design.

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.

Markovian Weighted Ensemble Milestoning (M-WEM): Long-Time Kinetics from Short Trajectories

We introduce a rare-event sampling scheme, named Markovian Weighted Ensemble Milestoning (M-WEM), which inlays a weighted ensemble framework within a Markovian milestoning theory to efficiently calculate thermodynamic and kinetic properties of long-time-scale biomolecular processes from short atomistic molecular dynamics simulations. M-WEM is tested on the Müller-Brown potential model, the conformational switching in alanine dipeptide, and the millisecond time-scale protein-ligand unbinding in a trypsin-benzamidine complex. Not only can M-WEM predict the kinetics of these processes with quantitative accuracy but it also allows for a scheme to reconstruct a multidimensional free-energy landscape along additional degrees of freedom, which are not part of the milestoning progress coordinate. For the ligand-receptor system, the experimental residence time, association and dissociation kinetics, and binding free energy could be reproduced using M-WEM within a simulation time of a few hundreds of nanoseconds, which is a fraction of the computational cost of other currently available methods, and close to 4 orders of magnitude less than the experimental residence time. Due to the high accuracy and low computational cost, the M-WEM approach can find potential applications in kinetics and free-energy-based computational drug design.

Semiflexible oligomers crystallize via a cooperative phase transition

Semicrystalline polymers are ubiquitous, yet despite their fundamental and industrial importance, the theory of homogeneous nucleation from a melt remains a subject of debate. A key component of the controversy is that polymer crystallization is a non-equilibrium process, making it difficult to distinguish between effects that are purely kinetic and those that arise from the underlying thermodynamics. Due to computational cost constraints, simulations of polymer crystallization typically employ non-equilibrium molecular dynamics techniques with large degrees of undercooling that further exacerbate the coupling between thermodynamics and kinetics. In a departure from this approach, in this study, we isolate the near-equilibrium nucleation behavior of a simple model of a melt of short, semiflexible oligomers. We employ several Monte Carlo methods and compute a phase diagram in the temperature-density plane along with two-dimensional free energy landscapes (FELs) that characterize the nucleation behavior. The phase diagram shows the existence of ordered nematic and crystalline phases in addition to the disordered melt phase. The minimum free energy path in the FEL for the melt-crystal transition shows a cooperative transition, where nematic order and monomer positional order move in tandem as the system crystallizes. This near-equilibrium phase transition mechanism broadly agrees with recent evidence that polymer stiffness plays an important role in crystallization but differs in the specifics of the mechanism from several recent theories. We conclude that the computation of multidimensional FELs for models that are larger and more fine-grained will be important for evaluating and refining theories of homogeneous nucleation for polymer crystallization.

Rationalizing the generation of broad spectrum antibiotics with the addition of a positive charge

Antibiotic resistance of Gram-negative bacteria is largely attributed to the low permeability of their outer membrane (OM). Recently, we disclosed the eNTRy rules, a key lesson of which is that the introduction of a primary amine enhances OM permeation in certain contexts. To understand the molecular basis for this finding, we perform an extensive set of molecular dynamics (MD) simulations and free energy calculations comparing the permeation of aminated and amine-free antibiotic derivatives through the most abundant OM porin of E. coli, OmpF. To improve sampling of conformationally flexible drugs in MD simulations, we developed a novel, Monte Carlo and graph theory based algorithm to probe more efficiently the rotational and translational degrees of freedom visited during the permeation of the antibiotic molecule through OmpF. The resulting pathways were then used for free-energy calculations, revealing a lower barrier against the permeation of the aminated compound, substantiating its greater OM permeability. Further analysis revealed that the amine facilitates permeation by enabling the antibiotic to align its dipole to the luminal electric field of the porin and form favorable electrostatic interactions with specific, highly-conserved charged residues. The importance of these interactions in permeation was further validated with experimental mutagenesis and whole cell accumulation assays. Overall, this study provides insights on the importance of the primary amine for antibiotic permeation into Gram-negative pathogens that could help the design of future antibiotics. We also offer a new computational approach for calculating free-energy of processes where relevant molecular conformations cannot be efficiently captured.

Mechanistic Understanding from Molecular Dynamics in Pharmaceutical Research 2: Lipid Membrane in Drug Design

We review the use of molecular dynamics (MD) simulation as a drug design tool in the context of the role that the lipid membrane can play in drug action, i.e., the interaction between candidate drug molecules and lipid membranes. In the standard "lock and key" paradigm, only the interaction between the drug and a specific active site of a specific protein is considered; the environment in which the drug acts is, from a biophysical perspective, far more complex than this. The possible mechanisms though which a drug can be designed to tinker with physiological processes are significantly broader than merely fitting to a single active site of a single protein. In this paper, we focus on the role of the lipid membrane, arguably the most important element outside the proteins themselves, as a case study. We discuss work that has been carried out, using MD simulation, concerning the transfection of drugs through membranes that act as biological barriers in the path of the drugs, the behavior of drug molecules within membranes, how their collective behavior can affect the structure and properties of the membrane and, finally, the role lipid membranes, to which the vast majority of drug target proteins are associated, can play in mediating the interaction between drug and target protein. This review paper is the second in a two-part series covering MD simulation as a tool in pharmaceutical research; both are designed as pedagogical review papers aimed at both pharmaceutical scientists interested in exploring how the tool of MD simulation can be applied to their research and computational scientists interested in exploring the possibility of a pharmaceutical context for their research.

GSK1702934A and M085 directly activate TRPC6 via a mechanism of stimulating the extracellular cavity formed by the pore helix and transmembrane helix S6

Transient receptor potential canonical (TRPC) channels, as important membrane proteins regulating intracellular calcium (Ca2+i) signaling, are involved in a variety of physiological and pathological processes. Activation and regulation of TRPC are more dependent on membrane or intracellular signals. However, how extracellular signals regulate TRPC6 function remains to be further investigated. Here, we suggest that two distinct small molecules, M085 and GSK1702934A, directly activate TRPC6, both through a mechanism of stimulation of extracellular sites formed by the pore helix (PH) and transmembrane (TM) helix S6. In silico docking scanning of TRPC6 identified three extracellular sites that can bind small molecules, of which only mutations on residues of PH and S6 helix significantly reduced the apparent affinity of M085 and GSK1702934A and attenuated the maximal response of TRPC6 to these two chemicals by altering channel gating of TRPC6. Combing metadynamics, molecular dynamics simulations, and mutagenesis, we revealed that W679, E671, E672, and K675 in the PH and N701 and Y704 in the S6 helix constitute an orthosteric site for the recognition of these two agonists. The importance of this site was further confirmed by covalent modification of amino acid residing at the interface of the PH and S6 helix. Given that three structurally distinct agonists M085, GSK1702934A, and AM-0883, act at this site, as well as the occupancy of lipid molecules at this position found in other TRP subfamilies, it is suggested that the cavity formed by the PH and S6 has an important role in the regulation of TRP channel function by extracellular signals.

Out-of-Equilibrium Biophysical Chemistry: The Case for Multidimensional, Integrated Single-Molecule Approaches

Out-of-equilibrium processes are ubiquitous across living organisms and all structural hierarchies of life. At the molecular scale, out-of-equilibrium processes (for example, enzyme catalysis, gene regulation, and motor protein functions) cause biological macromolecules to sample an ensemble of conformations over a wide range of time scales. Quantifying and conceptualizing the structure–dynamics to function relationship is challenging because continuously evolving multidimensional energy landscapes are necessary to describe nonequilibrium biological processes in biological macromolecules. In this perspective, we explore the challenges associated with state-of-the-art experimental techniques to understanding biological macromolecular function. We argue that it is time to revisit how we probe and model functional out-of-equilibrium biomolecular dynamics. We suggest that developing integrated single-molecule multiparametric force–fluorescence instruments and using advanced molecular dynamics simulations to study out-of-equilibrium biomolecules will provide a path towards understanding the principles of and mechanisms behind the structure–dynamics to function paradigm in biological macromolecules.

Overcoming Free-Energy Barriers with a Seamless Combination of a Biasing Force and a Collective Variable-Independent Boost Potential

Amid collective-variable (CV)-based importance-sampling algorithms, a hybrid of the extended adaptive biasing force and the well-tempered metadynamics algorithms (WTM-eABF) has proven particularly cost-effective for exploring the rugged free-energy landscapes that underlie biological processes. However, as an inherently CV-based algorithm, this hybrid scheme does not explicitly accelerate sampling in the space orthogonal to the chosen CVs, thereby limiting its efficiency and accuracy, most notably in those cases where the slow degrees of freedom of the process at hand are not accounted for in the model transition coordinate. Here, inspired by Gaussian-accelerated molecular dynamics (GaMD), we introduce the same CV-independent harmonic boost potential into WTM-eABF, yielding a hybrid algorithm coined GaWTM-eABF. This algorithm leans on WTM-eABF to explore the transition coordinate with a GaMD-mollified potential and recovers the unbiased free-energy landscape through thermodynamic integration followed by proper reweighting. As illustrated in our numerical tests, GaWTM-eABF effectively overcomes the free-energy barriers in orthogonal space and correctly recovers the unbiased potential of mean force (PMF). Furthermore, applying both GaWTM-eABF and WTM-eABF to two biologically relevant processes, namely, the reversible folding of (i) deca-alanine and (ii) chignolin, our results indicate that GaWTM-eABF reduces the uncertainty in the PMF calculation and converges appreciably faster than WTM-eABF. Obviating the need of multiple-copy strategies, GaWTM-eABF is a robust, computationally efficient algorithm to surmount the free-energy barriers in orthogonal space and maps with utmost fidelity the free-energy landscape along selections of CVs. Moreover, our strategy that combines WTM-eABF with GaMD can be easily extended to other biasing-force algorithms.

Improved Sampling and Free Energy Estimates for Antibiotic Permeation through Bacterial Porins

Antibiotics enter into bacterial cells via protein channels that serve as low-energy pathways through the outer membrane, which is otherwise impenetrable. Insights into the molecular mechanisms underlying the transport processes are vital for the development of effective antibacterials. A much-desired prerequisite is an accurate and reproducible determination of free energy surfaces for antibiotic translocation, enabling quantitative and meaningful comparisons of permeation mechanisms for different classes of antibiotics. Inefficient sampling along the orthogonal degrees of freedom, for example, in umbrella sampling and metadynamics approaches, is however a key limitation affecting the accuracy and the convergence of free energy estimates. To overcome this limitation, two sampling methods have been employed in the present study that, respectively, combine umbrella sampling and metadynamics-style biasing schemes with temperature acceleration for improved sampling along orthogonal degrees of freedom. As a model for the transport of bulky solutes, the ciprofloxacin-OmpF system has been selected. The well-tempered metadynamics approach with multiple walkers is compared with its "temperature-accelerated" variant in terms of improvements in sampling and convergence of free energy estimates. We find that the inclusion of collective variables governing solute degrees of freedom and solute-water interactions within the sampling scheme largely alleviates sampling issues. Concerning improved sampling and convergence of free energy estimates from independent simulations, the temperature-accelerated sliced sampling approach that combines umbrella sampling with temperature-accelerated molecular dynamics performs even better as shown for the ciprofloxacin-OmpF system.

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.

Nanomachine-Assisted Ion Transport Across Membranes: From Mechanism to Rational Design and Applications

Assisting ion transport across membranes by means of sophisticated molecular machines has promising applications in the treatment of diseases induced by dysregulated ion transport. To develop such nanoscale devices imbued with specific functions, rational de novo design, upstream from costly syntheses, is eminently desirable but would require the atomic detail of the translocation mechanism, which is still largely missing. We have explored the full ion capture-transport-release process over an aggregate simulation time of 60 μs, employing leading-edge enhanced-sampling algorithms to disentangle with unprecedented detail the mechanism that underlies ion transport mediated by a membrane-spanning [2]rotaxane composed of an ion carrier linked to a wheel threaded onto an axle. Beyond validating the reliability of our methodology through careful examination of the clockwork of a documented nanomachine, we put forth an original pH-controlled nano-object that can assist transient unidirectional ion transport across membranes.

Repurposing Existing Molecular Machines through Accurate Regulation of Cooperative Motions

To understand how different external stimuli affect the cooperative motions in a molecular machine consisting of multiple components, we have investigated at the atomic level the effects of pH, solvent, and ionic strength on the mechanism underlying the ring-through-ring movement in a saturated [3]rotaxane. Our results indicate that different external stimuli regulate the stable states, the shuttling rate, and the mechanism that governs the ring-through-ring motion by controlling the cooperative movement of the components and triggering a gamut of responses, thereby opening to a vast number of potential applications, such as quaternary logical calculations. The present work cogently demonstrates that with existing nanomachines possessing a simple topology, but using different external stimuli-an approach coined multidimensional regulation-challenging tasks requiring precise control of the molecular motions at play can be achieved, and our methodology is particularly germane for de novo design of intelligent molecular machines.