On the importance of statistics in molecular simulations for thermodynamics, kinetics and simulation box size

Structure-Based Experimental Datasets for Benchmarking Protein Simulation Force Fields [Article v0.1]

This review article provides an overview of structurally oriented experimental datasets that can be used to benchmark protein force fields, focusing on data generated by nuclear magnetic resonance (NMR) spectroscopy and room temperature (RT) protein crystallography. We discuss what the observables are, what they tell us about structure and dynamics, what makes them useful for assessing force field accuracy, and how they can be connected to molecular dynamics simulations carried out using the force field one wishes to benchmark. We also touch on statistical issues that arise when comparing simulations with experiment. We hope this article will be particularly useful to computational researchers and trainees who develop, benchmark, or use protein force fields for molecular simulations.

Structural features of the glassy state and their impact on the solid-state properties of organic molecules in pharmaceutical systems

This paper reviews the structure and properties of amorphous active pharmaceutical ingredients (APIs), including small molecules and proteins, in the glassy state (below the glass transition temperature, Tg). Amorphous materials in the neat state and formulated with excipients as miscible amorphous mixtures are included, and the role of absorbed water in affecting glass structure and stability has also been considered. We defined the term "structure" to indicate the way the various molecules in a glass interact with each other and form distinctive molecular arrangements as regions or domains of varying number of molecules, molecular packing, and density. Evidence is presented to suggest that such systems generally exist as heterogeneous structures made up of high-density domains surrounded by a lower density arrangement of molecules, termed the microstructure. It has been shown that the method of preparation and the time frame for handling and storage can give rise to variable glass structures and varying physical properties. Throughout this paper, examples are given of theoretical, computer simulation, and experimental studies which focus on the nature of intermolecular interactions, the size of heterogeneous higher density domains, and the impact of such systems on the relative physical and chemical stability of pharmaceutical systems.

The Role of Vimentin Peptide Citrullination in the Structure and Dynamics of HLA-DRB1 Rheumatoid Arthritis Risk-Associated Alleles

Citrullination, a post-translational modification (PTM), plays a critical role in rheumatoid arthritis (RA) by triggering immune responses to citrullinated self-antigens. Some HLA-DRB1 genes encode molecules with the shared epitope (QKRAA/QRRAA) sequence in the peptide-binding groove which preferentially presents citrulline-modified peptides, like vimentin, that intensifies the immune response in RA. In this study, we used computational approaches to evaluate intermolecular interactions between vimentin peptide-ligands (with/without PTM) and HLA-DRB1 alleles associated with a significantly increased risk for RA development. Crystal structures for HLA-DRB1*04:01, *04:04, and *04:05 bound to citrullinated peptides (PDB ID: 4MCY, 4MD5, 6BIR) were retrieved from the Protein Data Bank and non-citrullinated 3D structures were generated by mutating citrulline to arginine. The pHLA complexes were submitted to four rounds (50 ns each) of molecular dynamic simulations (MD) with Gromacs v.2022. Our results show that citrulline strengthens the interaction between vimentin and the HLA-DRB1 molecules, therefore impacting both the peptide affinity to the HLAs and pHLA stability; it also induces more intermolecular hydrogen bond formation during MD in the pHLA. Citrulline prevents repulsion between amino acid 71β and the P4-residue of native vimentin. Thus, vimentin citrullination seems to affect pHLA binding and dynamics, which may influence RA-related immune responses.

PME Switching in Confinement Simulations of Charged Solutes

The confinement method is a reaction coordinate-free enhanced sampling method for the calculation of conformational free energy differences. We show that in explicit solvent, artifacts occur when treating charged solutes. These artifacts are resolved by switching off the particle mesh Ewald (PME) method at the start of confinement. Calculations of the free energy cost of this switching converge rapidly, with small statistical error. The effectiveness and accuracy of confinement with PME switching is demonstrated by its application to a series of solutes of different charge; its ability to treat complex systems is illustrated by evaluating the free energy difference between B and Z-DNA.

System size effects on the free energy landscapes from molecular dynamics of phase-separating bilayers

The "lipid raft" hypothesis proposes that cell membranes contain distinct domains of varying lipid compositions, where "rafts" of ordered lipids and cholesterol coexist with disordered lipid regions. Experimental and theoretical phase diagrams of model membranes have revealed multiple coexisting phases. Molecular dynamics (MD) simulations can also capture spontaneous phase separation of bilayers. However, these methods merely determine the sign of the free energy change upon phase separation-whether or not it is favorable-but not the amplitude. Recently, we developed a workflow to compute the free energy of phase separation from MD simulations using the weighted ensemble method. However, while theoretical treatments generally focus on infinite systems and experimental measurements on mesoscopic to macroscopic systems, MD simulations are comparatively small. Therefore, if we are to put the results of these calculations into the appropriate context, we need to understand the effects the finite size of the simulation has on the computed free energy landscapes. In this study, we investigate this phenomenon by computing free energy profiles for a model phase-separating system as a function of system size, ranging from 324 to 10 110 lipids. The results suggest that, within the limits of statistical uncertainty, bulk-like behavior emerges once the systems contain roughly 4000 lipids.

Engineering of pH-dependent antigen binding properties for toxin-targeting IgG1 antibodies using light-chain shuffling

Immunoglobulin G (IgG) antibodies that bind their cognate antigen in a pH-dependent manner (acid-switched antibodies) can release their bound antigen for degradation in the acidic environment of endosomes, while the IgGs are rescued by the neonatal Fc receptor (FcRn). Thus, such IgGs can neutralize multiple antigens over time and therefore be used at lower doses than their non-pH-responsive counterparts. Here, we show that light-chain shuffling combined with phage display technology can be used to discover IgG1 antibodies with increased pH-dependent antigen binding properties, using the snake venom toxins, myotoxin II and α-cobratoxin, as examples. We reveal differences in how the selected IgG1s engage their antigens and human FcRn and show how these differences translate into distinct cellular handling properties related to their pH-dependent antigen binding phenotypes and Fc-engineering for improved FcRn binding. Our study showcases the complexity of engineering pH-dependent antigen binding IgG1s and demonstrates the effects on cellular antibody-antigen recycling.

A Comprehensive Study of Factors Affecting the Prediction of the pKa Shift of Asp26 in Thioredoxin Protein

The stable protonation state of ionizable amino acids in a protein can be predicted by computing the pKa shift of that residue within the protein environment. Thermodynamic Integration (TI) is an ideal molecular dynamics-based approach for predicting the pKa shift of ionizable protein residues. Here, we probe TI-based simulation protocols for their ability to accurately predict the pKa shift of Asp26 in thioredoxin. While implicit solvent models can predict the pKa shift accurately, explicit solvent models result in substantial errors. To understand the underlying reason for this surprising discrepancy, we investigate the role of various factors such as solvent models, conformational sampling, background charges, and polarization.

Computational Insights into Papaveroline as an In Silico Drug Candidate for Alzheimer's Disease via Fyn Tyrosine Kinase Inhibition

Alzheimer's disease (AD) poses a significant global health challenge, necessitating the exploration of novel therapeutic strategies. Fyn Tyrosine Kinase has emerged as a key player in AD pathogenesis, making it an attractive target for drug development. This study focuses on investigating the potential of Papaveroline as a drug candidate for AD by targeting Fyn Tyrosine Kinase. The research employed high-throughput virtual screening and QSAR analysis were conducted to identify compounds with optimal drug-like properties, emphasizing adherence to ADMET parameters for further evaluation. Molecular dynamics simulations to analyze the binding interactions between Papaveroline and Staurosporine with Fyn Tyrosine Kinase over a 200-ns period. The study revealed detailed insights into the binding mechanisms and stability of the Papaveroline-Fyn complex, showcasing the compound's potential as an inhibitor of Fyn Tyrosine Kinase. Comparative analysis with natural compounds and a reference compound highlighted Papaveroline's unique characteristics and promising therapeutic implications for AD treatment. Overall, the findings underscore Papaveroline's potential as a valuable drug candidate for targeting Fyn Tyrosine Kinase in AD therapy, offering new avenues for drug discovery in neurodegenerative diseases. This study contributes to advancing our understanding of molecular interactions in AD pathogenesis and paves the way for further research and development in this critical area.

Current State of Open Source Force Fields in Protein-Ligand Binding Affinity Predictions

In drug discovery, the in silico prediction of binding affinity is one of the major means to prioritize compounds for synthesis. Alchemical relative binding free energy (RBFE) calculations based on molecular dynamics (MD) simulations are nowadays a popular approach for the accurate affinity ranking of compounds. MD simulations rely on empirical force field parameters, which strongly influence the accuracy of the predicted affinities. Here, we evaluate the ability of six different small-molecule force fields to predict experimental protein-ligand binding affinities in RBFE calculations on a set of 598 ligands and 22 protein targets. The public force fields OpenFF Parsley and Sage, GAFF, and CGenFF show comparable accuracy, while OPLS3e is significantly more accurate. However, a consensus approach using Sage, GAFF, and CGenFF leads to accuracy comparable to OPLS3e. While Parsley and Sage are performing comparably based on aggregated statistics across the whole dataset, there are differences in terms of outliers. Analysis of the force field reveals that improved parameters lead to significant improvement in the accuracy of affinity predictions on subsets of the dataset involving those parameters. Lower accuracy can not only be attributed to the force field parameters but is also dependent on input preparation and sampling convergence of the calculations. Especially large perturbations and nonconverged simulations lead to less accurate predictions. The input structures, Gromacs force field files, as well as the analysis Python notebooks are available on GitHub.

Interaction of systemic drugs causing ocular toxicity with organic cation transporter: an artificial intelligence prediction

Chronic disease patients (cancer, arthritis, cardiovascular diseases) undergo long-term systemic drug treatment. Membrane transporters in ocular barriers could falsely recognize these drugs and allow their trafficking into the eye from systemic circulation. Hence, despite their pharmacological activity, these drugs accumulate and cause toxicity at the non-target site, such as the eye. Since around 40% of clinically used drugs are organic cation in nature, it is essential to understand the role of organic cation transporter (OCT1) in ocular barriers to facilitate the entry of systemic drugs into the eye. We applied machine learning techniques and computer simulation models (molecular dynamics and metadynamics) in the current study to predict the potential OCT1 substrates. Artificial intelligence models were developed using a training dataset of a known substrates and non-substrates of OCT1 and predicted the potential OCT1 substrates from various systemic drugs causing ocular toxicity. Computer simulation studies was performed by developing the OCT1 homology model. Molecular dynamic simulations equilibrated the docked protein-ligand complex. And metadynamics revealed the movement of substrates across the transporter with minimum free energy near the binding pocket. The machine learning model showed an accuracy of about 80% and predicted the potential substrates for OCT1 among systemic drugs causing ocular toxicity - not known earlier, such as cyclophosphamide, bupivacaine, bortezomib, sulphanilamide, tosufloxacin, topiramate, and many more. However, further invitro and invivo studies are required to confirm these predictions.Communicated by Ramaswamy H. Sarma.

Resolving coupled pH titrations using alchemical free energy calculations

In a protein, nearby titratable sites can be coupled: the (de)protonation of one may affect the other. The degree of this interaction depends on several factors and can influence the measured p K a . Here, we derive a formalism based on double free energy differences ( Δ Δ G ) for quantifying the individual site p K a values of coupled residues. As Δ Δ G values can be obtained by means of alchemical free energy calculations, the presented approach allows for a convenient estimation of coupled residue p K a s in practice. We demonstrate that our approach and a previously proposed microscopic p K a formalism, can be combined with alchemical free energy calculations to resolve pH-dependent protein p K a values. Toy models and both, regular and constant-pH molecular dynamics simulations, alongside experimental data, are used to validate this approach. Our results highlight the insights gleaned when coupling and microstate probabilities are analyzed and suggest extensions to more complex enzymatic contexts. Furthermore, we find that naïvely computed p K a values that ignore coupling, can be significantly improved when coupling is accounted for, in some cases reducing the error by half. In short, alchemical free energy methods can resolve the p K a values of both uncoupled and coupled residues.

Identification of histidine residues that affect the T/R-state conformations of human hemoglobin using constant pH molecular dynamics simulations

Human hemoglobin (Hb) is a tetrameric protein consisting of two α and two β subunits that can adopt a low-affinity T- and high-affinity R-state conformations. Under physiological pH conditions, histidine (His) residues are the main sites for proton binding or release, and their protonation states can affect the T/R-state conformation of Hb. However, it remains unclear which His residues can effectively affect the Hb conformation. Herein, the impact of the 38 His residues of Hb on its T/R-state conformations was evaluated using constant-pH molecular dynamics (CpHMD) simulations at physiological pH while focusing on the His protonation states. Overall, the protonation states of some His residues were found to be correlated with the Hb conformation state. These residues were mainly located in the proximity of the heme (α87 and β92), and at the α1β2 and α2β1 interfaces (α89 and β97). This correlation may be partly explained by how easily hydrogen bonds can be formed, which depends on the protonation states of the His residues. Taken together, these CpHMD-based findings provide new insights into the identification of titratable His residues α87, α89, β92, and β97 that can affect Hb conformational switching under physiological pH conditions.

Predicting permeation of compounds across the outer membrane of P. aeruginosa using molecular descriptors

The ability Gram-negative pathogens have at adapting and protecting themselves against antibiotics has increasingly become a public health threat. Data-driven models identifying molecular properties that correlate with outer membrane (OM) permeation and growth inhibition while avoiding efflux could guide the discovery of novel classes of antibiotics. Here we evaluate 174 molecular descriptors in 1260 antimicrobial compounds and study their correlations with antibacterial activity in Gram-negative Pseudomonas aeruginosa. The descriptors are derived from traditional approaches quantifying the compounds' intrinsic physicochemical properties, together with, bacterium-specific from ensemble docking of compounds targeting specific MexB binding pockets, and all-atom molecular dynamics simulations in different subregions of the OM model. Using these descriptors and the measured inhibitory concentrations, we design a statistical protocol to identify predictors of OM permeation/inhibition. We find consistent rules across most of our data highlighting the role of the interaction between the compounds and the OM. An implementation of the rules uncovered in our study is shown, and it demonstrates the accuracy of our approach in a set of previously unseen compounds. Our analysis sheds new light on the key properties drug candidates need to effectively permeate/inhibit P. aeruginosa, and opens the gate to similar data-driven studies in other Gram-negative pathogens.

Integrating multiscale and machine learning approaches towards the SAMPL9 log P challenge

The partition coefficient (log P) is an important physicochemical property that provides information regarding a molecule's pharmacokinetics, toxicity, and bioavailability. Methods to accurately predict the partition coefficient have the potential to accelerate drug design. In an effort to test current methods and explore new computational techniques, the statistical assessment of the modeling of proteins and ligands (SAMPL) has established a blind prediction challenge. The ninth iteration challenge was to predict the toluene-water partition coefficient (log Ptol/w) of sixteen drug molecules. Herein, three approaches are reported broadly under the categories of quantum mechanics (QM), molecular mechanics (MM), and data-driven machine learning (ML). The three blind submissions yield mean unsigned errors (MUE) ranging from 1.53-2.93 log Ptol/w units. The MUEs were reduced to 1.00 log Ptol/w for the QM methods. While MM and ML methods outperformed DFT approaches for challenge molecules with fewer rotational degrees of freedom, they suffered for the larger molecules in this dataset. Overall, DFT functionals paired with a triple-ζ basis set were the simplest and most effective tool to obtain quantitatively accurate partition coefficients.

Guidelines for Free-Energy Calculations Involving Charge Changes

The Coulomb interactions in molecular simulations are inherently approximated due to the finite size of the molecular box sizes amenable to current-day compute power. Several methods exist for treating long-range electrostatic interactions, yet these approaches are subject to various finite-size-related artifacts. Lattice-sum methods are frequently used to approximate long-range interactions; however, these approaches also suffer from artifacts which become particularly pronounced for free-energy calculations that involve charge changes. The artifacts, however, also affect the sampling when plain simulations are performed, leading to a biased ensemble. Here, we investigate two previously described model systems to determine if artifacts continue to play a role when overall neutral boxes are considered, in the context of both free-energy calculations and sampling. We find that ensuring that no net-charge changes take place, while maintaining a neutral simulation box, may be sufficient provided that the simulation boxes are large enough. Addition of salt to the solution (when appropriate) can further alleviate the remaining artifacts in the sampling or the calculated free-energy differences. We provide practical guidelines to avoid finite-size artifacts.

Experimental and Theoretical Brownian Dynamics Analysis of Ion Transport During Cellular Electroporation of E. coli Bacteria

Escherichia coli bacterium is a rod-shaped organism composed of a complex double membrane structure. Knowledge of electric field driven ion transport through both membranes and the evolution of their induced permeabilization has important applications in biomedical engineering, delivery of genes and antibacterial agents. However, few studies have been conducted on Gram-negative bacteria in this regard considering the contribution of all ion types. To address this gap in knowledge, we have developed a deterministic and stochastic Brownian dynamics model to simulate in 3D space the motion of ions through pores formed in the plasma membranes of E. coli cells during electroporation. The diffusion coefficient, mobility, and translation time of Ca2+, Mg2+, Na+, K+, and Cl- ions within the pore region are estimated from the numerical model. Calculations of pore's conductance have been validated with experiments conducted at Gustave Roussy. From the simulations, it was found that the main driving force of ionic uptake during the pulse is the one due to the externally applied electric field. The results from this work provide a better understanding of ion transport during electroporation, aiding in the design of electrical pulses for maximizing ion throughput, primarily for application in cancer treatment.

Assessment of Halogen Off-Center Point-Charge Models Using Explicit Solvent Simulations

Compounds containing halogens can form halogen bonds (XBs) with biological targets such as proteins and membranes due to their anisotropic electrostatic potential. To accurately describe this anisotropy, off-center point-charge (EP) models are commonly used in force field methods, allowing the description of XBs at the molecular mechanics and molecular dynamics level. Various EP implementations have been documented in the literature, and despite being efficient in reproducing protein-ligand geometries and sampling of XBs, it is unclear how well these EP models predict experimental properties such as hydration free energies (ΔGhyd), which are often used to validate force field performance. In this work, we report the first assessment of three EP models using alchemical free energy calculations to predict ΔGhyd values. We show that describing the halogen anisotropy using some EP models can lead to a slight improvement in the prediction of the ΔGhyd when compared with the models without EP, especially for the chlorinated compounds; however, this improvement is not related to the establishment of XBs but is most likely due to the improvement of the sampling of hydrogen bonds. We also highlight the importance of the choice of the EP model, especially for the iodinated molecules, since a slight tendency to improve the prediction is observed for compounds with a larger σ-hole but significantly worse results were obtained for compounds that are weaker XB donors.

Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime

We derive general bounds on the probability that the empirical first-passage time τ[over ¯]_{n}≡∑_{i=1}^{n}τ_{i}/n of a reversible ergodic Markov process inferred from a sample of n independent realizations deviates from the true mean first-passage time by more than any given amount in either direction. We construct nonasymptotic confidence intervals that hold in the elusive small-sample regime and thus fill the gap between asymptotic methods and the Bayesian approach that is known to be sensitive to prior belief and tends to underestimate uncertainty in the small-sample setting. We prove sharp bounds on extreme first-passage times that control uncertainty even in cases where the mean alone does not sufficiently characterize the statistics. Our concentration-of-measure-based results allow for model-free error control and reliable error estimation in kinetic inference, and are thus important for the analysis of experimental and simulation data in the presence of limited sampling.

Ensemble-Based Approaches Ensure Reliability and Reproducibility

It is increasingly widely recognized that ensemble-based approaches are required to achieve reliability, accuracy, and precision in molecular dynamics calculations. The purpose of the present article is to address a frequently raised question: what is the optimal way to perform ensemble simulation to calculate quantities of interest?

Accurately Predicting Protein pKa Values Using Nonequilibrium Alchemy

The stability, solubility, and function of a protein depend on both its net charge and the protonation states of its individual residues. pKa is a measure of the tendency for a given residue to (de)protonate at a specific pH. Although pKa values can be resolved experimentally, theory and computation provide a compelling alternative. To this end, we assess the applicability of a nonequilibrium (NEQ) alchemical free energy method to the problem of pKa prediction. On a data set of 144 residues that span 13 proteins, we report an average unsigned error of 0.77 ± 0.09, 0.69 ± 0.09, and 0.52 ± 0.04 pK for aspartate, glutamate, and lysine, respectively. This is comparable to current state-of-the-art predictors and the accuracy recently reached using free energy perturbation methods (e.g., FEP+). Moreover, we demonstrate that our open-source, pmx-based approach can accurately resolve the pKa values of coupled residues and observe a substantial performance disparity associated with the lysine partial charges in Amber14SB/Amber99SB*-ILDN, for which an underused fix already exists.

Challenges in Protein QM/MM Simulations with Intra-Backbone Link Atoms

Hybrid quantum mechanical/molecular mechanical (QM/MM) simulations fuel discoveries in many fields of science including computational biochemistry and enzymology. Development of more convenient tools leads to an increase in the number of works in which mechanical insights into enzymes' mode of operation are obtained. Most commonly, these tools feature hydrogen-capping (link atom) approach to provide coupling between QM and MM subsystems across a covalent bond. Extensive studies were conducted to provide a solid foundation for the correctness of such an approach when a bond to a nonpolar MM atom is considered. However, not every task may be accomplished this way. Certain scenarios of using QM/MM in computational enzymology encourage or even necessitate the incorporation of backbone atoms into the QM region. Two out of three backbone atoms are polar, and in QM/MM with electrostatic embedding, a neighboring link atom will be hyperpolarized. Several schemes to mitigate this effect were previously proposed alongside a rigorous assessment of quantitative effects on model systems. However, it was not clear whether they may translate into qualitatively different results and how link atom hyperpolarization may manifest itself in a real-life enzymological scenario. Here, we show that the consequences of such an artifact may be severe and may completely overturn the conclusions drawn from the simulations. Our case advocates for the use of charge redistribution schemes whenever intra-backbone QM/MM boundaries are considered. Moreover, we addressed how different boundary types and charge redistribution schemes influence backbone dynamics. We showed that the results are heavily dependent on which boundary MM terms are retained, with charge alteration being of secondary importance. In the worst case, only three intra-backbone boundaries may be used with relative confidence in the adequacy of resulting simulations, irrespective of the hyperpolarization mitigation scheme. Thus, advances in the field are certainly needed to fuel new discoveries. As of now, we believe that issues raised in this work might encourage authors in the field to report what boundaries, boundary MM terms, and charge redistribution schemes they are using, so their results may be correctly interpreted.

Brave new surfactant world revisited by thermoalkalophilic lipases: computational insights into the role of SDS as a substrate analog

Non-ionic surfactants were shown to stabilize the active conformation of thermoalkalophilic lipases by mimicking the lipid substrate while the catalytic interactions formed by anionic surfactants have not been well characterized. In this study, we combined μs-scale molecular dynamics (MD) simulations and lipase activity assays to analyze the effect of ionic surfactant, sodium dodecyl sulfate (SDS), on the structure and activity of thermoalkalophilic lipases. Both the open and closed lipase conformations that differ in geometry were recruited to the MD analysis to provide a broader understanding of the molecular effect of SDS on the lipase structure. Simulations at 298 K showed the potential of SDS for maintaining the active lipase through binding to the sn-1 acyl-chain binding pocket in the open conformation or transforming the closed conformation to an open-like state. Consistent with MD findings, experimental analysis showed increased lipase activity upon SDS incubation at ambient temperature. Notably, the lipase cores stayed intact throughout 2 μs regardless of an increase in the simulation temperature or SDS concentration. However, the surface structures were unfolded in the presence of SDS and at elevated temperature for both conformations. Simulations of the dimeric lipase were also carried out and showed reduced flexibility of the surface structures which were unfolded in the monomer, indicating the insulating role of dimer interactions against SDS. Taken together, this study provides insights into the possible substrate mimicry by the ionic surfactant SDS for the thermoalkalophilic lipases without temperature elevation, underscoring SDS's potential for interfacial activation at ambient temperatures.

Structural Investigation of DHICA Eumelanin Using Density Functional Theory and Classical Molecular Dynamics Simulations

Eumelanin is an important pigment, for example, in skin, hair, eyes, and the inner ear. It is a highly heterogeneous polymer with 5,6-dihydroxyindole-2-carboxylic acid (DHICA) and 5,6-dihydroxyindole (DHI) building blocks, of which DHICA is reported as the more abundant in natural eumelanin. The DHICA-eumelanin protomolecule consists of three building blocks, indole-2-carboxylic acid-5,6-quinone (ICAQ), DHICA and pyrrole-2,3,5-tricarboxylic acid (PTCA). Here, we focus on the self-assembly of DHICA-eumelanin using multi-microsecond molecular dynamics (MD) simulations at various concentrations in aqueous solutions. The molecule was first parameterized using density functional theory (DFT) calculations. Three types of systems were studied: (1) uncharged DHICA-eumelanin, (2) charged DHICA-eumelanin corresponding to physiological pH, and (3) a binary mixture of both of the above protomolecules. In the case of uncharged DHICA-eumelanin, spontaneous aggregation occurred and water molecules were present inside the aggregates. In the systems corresponding to physiological pH, all the carboxyl groups are negatively charged and the DHICA-eumelanin model has a net charge of -4. The effect of K+ ions as counterions was investigated. The results show high probability of binding to the deprotonated oxygens of the carboxylate anions in the PTCA moiety. Furthermore, the K+ counterions increased the solubility of DHICA-eumelanin in its charged form. A possible explanation is that the charged protomolecules favor binding to the K+ ions rather than aggregating and binding to other protomolecules. The binary mixtures show aggregation of uncharged DHICA-eumelanins; unlike the charged systems with no aggregation, a few charged DHICA-eumelanins are present on the surface of the uncharged aggregation, binding to the K+ ions.

Atomic-Level View of the Functional Transition in Vertebrate Hemoglobins: The Case of Antarctic Fish Hbs

Tetrameric hemoglobins (Hbs) are prototypal systems for studies aimed at unveiling basic structure-function relationships as well as investigating the molecular/structural basis of adaptation of living organisms to extreme conditions. However, a chronological analysis of decade-long studies conducted on Hbs is illuminating on the difficulties associated with the attempts of gaining functional insights from static structures. Here, we applied molecular dynamics (MD) simulations to explore the functional transition from the T to the R state of the hemoglobin of the Antarctic fish Trematomus bernacchii (HbTb). Our study clearly demonstrates the ability of the MD technique to accurately describe the transition of HbTb from the T to R-like states, as shown by a number of global and local structural indicators. A comparative analysis of the structural states that HbTb assumes in the simulations with those detected in previous MD analyses conducted on HbA (human Hb) highlights interesting analogies (similarity of the transition pathway) and differences (distinct population of intermediate states). In particular, the ability of HbTb to significantly populate intermediate states along the functional pathway explains the observed propensity of this protein to assume these structures in the crystalline state. It also explains some functional data reported on the protein that indicate the occurrence of other functional states in addition to the canonical R and T ones. These findings are in line with the emerging idea that the classical two-state view underlying tetrameric Hb functionality is probably an oversimplification and that other structural states play important roles in these proteins. The ability of MD simulations to accurately describe the functional pathway in tetrameric Hbs suggests that this approach may be effectively applied to unravel the molecular and structural basis of Hbs exhibiting peculiar functional properties as a consequence of the environmental adaptation of the host organism.

Implementation of Telescoping Boxes in Adaptive Steered Molecular Dynamics

Long-time dynamical processes, such as those involving protein unfolding and ligand interactions, can be accelerated and realized through steered molecular dynamics (SMD). The challenge has been the extraction of information from such simulations that generalize for complex nonequilibrium processes. The use of Jarzynski's equality opened the possibility of determining the free energy along the steered coordinate, but sampling over the nonequilibrium trajectories is slow to converge. Adaptive steered molecular dynamics (ASMD) and other related techniques have been introduced to overcome this challenge through the use of stages. Here, we take advantage of these stages to address the numerical cost that arises from the required use of very large solvent boxes. We introduce telescoping box schemes within adaptive steered molecular dynamics (ASMD) in which we adjust the solvent box between stages and thereby vary (and optimize) the required number of solvent molecules. We have benchmarked the method on a relatively long α-helical peptide, Ala₃₀, with respect to the potential of mean force and hydrogen bonds. We show that the use of telescoping boxes introduces little numerical error while significantly reducing the computational cost.

Seeking antiviral drugs to inhibit SARS-CoV-2 RNA dependent RNA polymerase: A molecular docking analysis

COVID-19 outbreak associated with the severe acute respiratory syndrome coronavirus (SARS-CoV-2) raised health concerns across the globe and has been considered highly transmissible between people. In attempts for finding therapeutic treatment for the new disease, this work has focused on examining the polymerase inhibitors against the SARS-CoV-2 nsp12 and co-factors nsp8 and nsp7. Several polymerase inhibitors were examined against PDB ID: 6M71 using computational analysis evaluating the ligand's binding affinity to replicating groove to the active site. The findings of this analysis showed Cytarabine of -5.65 Kcal/mol with the highest binding probability (70%) to replicating groove of 6M71. The complex stability was then examined over 19 ns molecular dynamics simulation suggesting that Cytarabine might be possible potent inhibitor for the SARS-CoV-2 RNA Dependent RNA Polymerase.

Pre-exascale HPC approaches for molecular dynamics simulations. Covid-19 research: A use case

Exascale computing has been a dream for ages and is close to becoming a reality that will impact how molecular simulations are being performed, as well as the quantity and quality of the information derived for them. We review how the biomolecular simulations field is anticipating these new architectures, making emphasis on recent work from groups in the BioExcel Center of Excellence for High Performance Computing. We exemplified the power of these simulation strategies with the work done by the HPC simulation community to fight Covid-19 pandemics. This article is categorized under:Data Science > Computer Algorithms and ProgrammingData Science > Databases and Expert SystemsMolecular and Statistical Mechanics > Molecular Dynamics and Monte-Carlo Methods.

Large Scale Study of Ligand-Protein Relative Binding Free Energy Calculations: Actionable Predictions from Statistically Robust Protocols

The accurate and reliable prediction of protein-ligand binding affinities can play a central role in the drug discovery process as well as in personalized medicine. Of considerable importance during lead optimization are the alchemical free energy methods that furnish an estimation of relative binding free energies (RBFE) of similar molecules. Recent advances in these methods have increased their speed, accuracy, and precision. This is evident from the increasing number of retrospective as well as prospective studies employing them. However, such methods still have limited applicability in real-world scenarios due to a number of important yet unresolved issues. Here, we report the findings from a large data set comprising over 500 ligand transformations spanning over 300 ligands binding to a diverse set of 14 different protein targets which furnish statistically robust results on the accuracy, precision, and reproducibility of RBFE calculations. We use ensemble-based methods which are the only way to provide reliable uncertainty quantification given that the underlying molecular dynamics is chaotic. These are implemented using TIES (Thermodynamic Integration with Enhanced Sampling). Results achieve chemical accuracy in all cases. Ensemble simulations also furnish information on the statistical distributions of the free energy calculations which exhibit non-normal behavior. We find that the "enhanced sampling" method known as replica exchange with solute tempering degrades RBFE predictions. We also report definitively on numerous associated alchemical factors including the choice of ligand charge method, flexibility in ligand structure, and the size of the alchemical region including the number of atoms involved in transforming one ligand into another. Our findings provide a key set of recommendations that should be adopted for the reliable application of RBFE methods.

GROMACS in the Cloud: A Global Supercomputer to Speed Up Alchemical Drug Design

We assess costs and efficiency of state-of-the-art high-performance cloud computing and compare the results to traditional on-premises compute clusters. Our use case is atomistic simulations carried out with the GROMACS molecular dynamics (MD) toolkit with a particular focus on alchemical protein-ligand binding free energy calculations. We set up a compute cluster in the Amazon Web Services (AWS) cloud that incorporates various different instances with Intel, AMD, and ARM CPUs, some with GPU acceleration. Using representative biomolecular simulation systems, we benchmark how GROMACS performs on individual instances and across multiple instances. Thereby we assess which instances deliver the highest performance and which are the most cost-efficient ones for our use case. We find that, in terms of total costs, including hardware, personnel, room, energy, and cooling, producing MD trajectories in the cloud can be about as cost-efficient as an on-premises cluster given that optimal cloud instances are chosen. Further, we find that high-throughput ligand-screening can be accelerated dramatically by using global cloud resources. For a ligand screening study consisting of 19 872 independent simulations or ∼200 μs of combined simulation trajectory, we made use of diverse hardware available in the cloud at the time of the study. The computations scaled-up to reach peak performance using more than 4 000 instances, 140 000 cores, and 3 000 GPUs simultaneously. Our simulation ensemble finished in about 2 days in the cloud, while weeks would be required to complete the task on a typical on-premises cluster consisting of several hundred nodes.

Free Energy and Stacking of Eumelanin Nanoaggregates

Eumelanin, a member of the melanin family, is a black-brown insoluble pigment. It possesses a broad range of properties such as antioxidation, free radical scavenging, photoprotection, and charge carrier transportation. Surprisingly, the exact molecular structure of eumelanin remains undefined. It is, however, generally considered to consist of two main building blocks, 5,6-dihydroxyindole (DHI) and 5,6- dihydroxyindole carboxylic acid (DHICA). We focus on DHI and report, for the first time, a computational investigation of the structural properties of DHI-eumelanin aggregates in aqueous solutions. First, multimicrosecond molecular dynamics (MD) simulations at different concentrations were performed to investigate the aggregation and ordering of tetrameric DHI-eumelanin protomolecules. This was followed by umbrella sampling (US) and density functional theory (DFT) calculations to study the physical mechanisms of stacking. Aggregation occurs through formation of nanoscale stacks and was observed in all systems. Further analyses showed that aggregation and coarsening of the domains is due to a decrease in hydrogen bonds between the eumelanins and water; while domains exist, there is no long-range order. The results show noncovalent stacks with the interlayer distance between eumelanin protomolecules being less than 3.5 Å. This is in good agreement with transmission electron microscopy data. Both free energy calculations and DFT revealed strong stacking interactions. The electrostatic potential map provides an explanation and a rationale for the slightly sheared relative orientations and, consequently, for the curved shapes of the nanoscale domains.

Alchemical absolute protein-ligand binding free energies for drug design

The recent advances in relative protein-ligand binding free energy calculations have shown the value of alchemical methods in drug discovery. Accurately assessing absolute binding free energies, although highly desired, remains a challenging endeavour, mostly limited to small model cases. Here, we demonstrate accurate first principles based absolute binding free energy estimates for 128 pharmaceutically relevant targets. We use a novel rigorous method to generate protein-ligand ensembles for the ligand in its decoupled state. Not only do the calculations deliver accurate protein-ligand binding affinity estimates, but they also provide detailed physical insight into the structural determinants of binding. We identify subtle rotamer rearrangements between apo and holo states of a protein that are crucial for binding. When compared to relative binding free energy calculations, obtaining absolute binding free energies is considerably more challenging in large part due to the need to explicitly account for the protein in its apo state. In this work we present several approaches to obtain apo state ensembles for accurate absolute ΔG calculations, thus outlining protocols for prospective application of the methods for drug discovery.

Quaternary Structure Transitions of Human Hemoglobin: An Atomic-Level View of the Functional Intermediate States

Human hemoglobin (HbA) is one of the prototypal systems used to investigate structure-function relationships in proteins. Indeed, HbA has been used to develop the basic concepts of protein allostery, although the atomic-level mechanism underlying the HbA functionality is still highly debated. This is due to the fact that most of the three-dimensional structural information collected over the decades refers to the endpoints of HbA functional transition with little data available for the intermediate states. Here, we report molecular dynamics (MD) simulations by focusing on the relevance of the intermediate states of the protein functional transition unraveled by the crystallographic studies carried out on vertebrate Hbs. Fully atomistic simulations of the HbA T-state indicate that the protein undergoes a spontaneous transition toward the R-state. The inspection of the trajectory structures indicates that the protein significantly populates the intermediate HL-(C) state previously unraveled by crystallography. In the structural transition, it also assumes the intermediate states crystallographically detected in Antarctic fish Hbs. This finding suggests that HbA and Antarctic fish Hbs, in addition to the endpoints of the transitions, also share a similar deoxygenation pathway despite a distace of hundreds of millions of years in the evolution scale. Finally, using the essential dynamic sampling methodology, we gained some insights into the reverse R to T transition that is not spontaneously observed in classic MD simulations.

Ensembles Are Required to Handle Aleatoric and Parametric Uncertainty in Molecular Dynamics Simulation

Classical molecular dynamics is a computer simulation technique that is in widespread use across many areas of science, from physics and chemistry to materials, biology, and medicine. The method continues to attract criticism due its oft-reported lack of reproducibility which is in part due to a failure to submit it to reliable uncertainty quantification (UQ). Here we show that the uncertainty arises from a combination of (i) the input parameters and (ii) the intrinsic stochasticity of the method controlled by the random seeds. To illustrate the situation, we make a systematic UQ analysis of a widely used molecular dynamics code (NAMD), applied to estimate binding free energy of a ligand-bound to a protein. In particular, we replace the usually fixed input parameters with random variables, systematically distributed about their mean values, and study the resulting distribution of the simulation output. We also perform a sensitivity analysis, which reveals that, out of a total of 175 parameters, just six dominate the variance in the code output. Furthermore, we show that binding energy calculations dampen the input uncertainty, in the sense that the variation around the mean output free energy is less than the variation around the mean of the assumed input distributions, if the output is ensemble-averaged over the random seeds. Without such ensemble averaging, the predicted free energy is five times more uncertain. The distribution of the predicted properties is thus strongly dependent upon the random seed. Owing to this substantial uncertainty, robust statistical measures of uncertainty in molecular dynamics simulation require the use of ensembles in all contexts.

Uncertainty quantification in classical molecular dynamics

Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach has begun to advance from being a computer-based means of rationalizing experimental observations to producing apparently credible predictions for a number of real-world applications within industrial sectors such as advanced materials and drug discovery. However, key aspects concerning the reproducibility of the method have not kept pace with the speed of its uptake in the scientific community. Here, we present a discussion of uncertainty quantification for molecular dynamics simulation designed to endow the method with better error estimates that will enable it to be used to report actionable results. The approach adopted is a standard one in the field of uncertainty quantification, namely using ensemble methods, in which a sufficiently large number of replicas are run concurrently, from which reliable statistics can be extracted. Indeed, because molecular dynamics is intrinsically chaotic, the need to use ensemble methods is fundamental and holds regardless of the duration of the simulations performed. We discuss the approach and illustrate it in a range of applications from materials science to ligand-protein binding free energy estimation. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'.

Biomolecular Modeling and Simulation: A Prospering Multidisciplinary Field

We reassess progress in the field of biomolecular modeling and simulation, following up on our perspective published in 2011. By reviewing metrics for the field's productivity and providing examples of success, we underscore the productive phase of the field, whose short-term expectations were overestimated and long-term effects underestimated. Such successes include prediction of structures and mechanisms; generation of new insights into biomolecular activity; and thriving collaborations between modeling and experimentation, including experiments driven by modeling. We also discuss the impact of field exercises and web games on the field's progress. Overall, we note tremendous success by the biomolecular modeling community in utilization of computer power; improvement in force fields; and development and application of new algorithms, notably machine learning and artificial intelligence. The combined advances are enhancing the accuracy andscope of modeling and simulation, establishing an exemplary discipline where experiment and theory or simulations are full partners.

Mechanistic Understanding From Molecular Dynamics Simulation in Pharmaceutical Research 1: Drug Delivery

In this review, we outline the growing role that molecular dynamics simulation is able to play as a design tool in drug delivery. We cover both the pharmaceutical and computational backgrounds, in a pedagogical fashion, as this review is designed to be equally accessible to pharmaceutical researchers interested in what this new computational tool is capable of and experts in molecular modeling who wish to pursue pharmaceutical applications as a context for their research. The field has become too broad for us to concisely describe all work that has been carried out; many comprehensive reviews on subtopics of this area are cited. We discuss the insight molecular dynamics modeling has provided in dissolution and solubility, however, the majority of the discussion is focused on nanomedicine: the development of nanoscale drug delivery vehicles. Here we focus on three areas where molecular dynamics modeling has had a particularly strong impact: (1) behavior in the bloodstream and protective polymer corona, (2) Drug loading and controlled release, and (3) Nanoparticle interaction with both model and biological membranes. We conclude with some thoughts on the role that molecular dynamics simulation can grow to play in the development of new drug delivery systems.

Transient Unfolding and Long-Range Interactions in Viral BCL2 M11 Enable Binding to the BECN1 BH3 Domain

Viral BCL2 proteins (vBCL2s) help to sustain chronic infection of host proteins to inhibit apoptosis and autophagy. However, details of conformational changes in vBCL2s that enable binding to BH3Ds remain unknown. Using all-atom, multiple microsecond-long molecular dynamic simulations (totaling 17 μs) of the murine γ-herpesvirus 68 vBCL2 (M11), and statistical inference techniques, we show that regions of M11 transiently unfold and refold upon binding of the BH3D. Further, we show that this partial unfolding/refolding within M11 is mediated by a network of hydrophobic interactions, which includes residues that are 10 Å away from the BH3D binding cleft. We experimentally validate the role of these hydrophobic interactions by quantifying the impact of mutating these residues on binding to the Beclin1/BECN1 BH3D, demonstrating that these mutations adversely affect both protein stability and binding. To our knowledge, this is the first study detailing the binding-associated conformational changes and presence of long-range interactions within vBCL2s.