Potential Of Mean Force Calculations Research Articles

Modeling approaches for atmospheric ion–dipole collisions: all-atom trajectory simulations and central field methods

Abstract. Ion–dipole collisions can facilitate the formation of atmospheric aerosol particles and play an important role in their detection in chemical ionization mass spectrometers. Conventionally, analytical models, or simple parametrizations, have been used to calculate the rate coefficients of ion–dipole collisions in the gas phase. Such models, however, neglect the atomistic structure and charge distribution of the collision partners. To determine the accuracy and applicability of these approaches under atmospheric conditions, we calculated collision cross sections and rate coefficients from all-atom molecular dynamics collision trajectories, sampling the relevant range of impact parameters and relative velocities, and from a central field model using an effective attractive interaction fitted to the long-range potential of mean force between the collision partners. We considered collisions between various atmospherically relevant molecular ions and dipoles and charged and neutral dipolar clusters. Based on the good agreement between collision cross sections and rate coefficients obtained from molecular dynamics trajectories and a generalized central field model, we conclude that the effective interactions between the collision partners are isotropic to a high degree, and the model is able to capture the relevant physicochemical properties of the systems. In addition, when the potential of mean force is recalculated at the respective temperatures, the central field model exhibits the correct temperature dependence of the collision process. The classical parametrization by Su and Chesnavich (1982), which combines a central field model with simplified trajectory simulations, is able to predict the collision rate coefficients and their temperature dependence quite well for molecular systems, but the agreement worsens for systems containing clusters. Based on our results, we propose the combination of potential of mean force calculation and a central field model as a viable and elegant alternative to the brute force sampling of individual collision trajectories over a large range of impact parameters and relative velocities.

Efflux dynamics of the antiseizure drug, levetiracetam, through the P-glycoprotein channel revealed by advanced comparative molecular simulations

Understanding the precise mechanistic details of the possible binding and transport of antiseizure medications (ASMs) through the P-glycoprotein (P-gp) efflux pump is essential to find strategies for the treatment of patients with epilepsy resistant to ASMs. In the present work, conventional molecular dynamics, binding free energy calculations, steered molecular dynamics and umbrella sampling were applied to study the interactions of levetiracetam and brivaracetam with P-gp and their possible egress path from the binding site. Comparative results for the control drugs, zosuquidar and verapamil, confirmed their established P-gp inhibitory activity. Brivaracetam, a non-substrate of P-gp, demonstrated stronger static and dynamic interactions with the exporter protein, than levetiracetam. The potential of mean force calculations indicated that the energy barriers through the ligand export were the lowest for levetiracetam, suggesting the drug as a P-gp substrate with facile passage through the transporter channel. Our findings also stressed the contribution of nonpolar interactions with P-gp channel lining as well as with membrane lipid molecules to hamper the ASM efflux by the transmembrane exporter. Appropriate structural engineering of the ASMs is thus recommended to address drug-resistant epilepsy.

Decoding molecular factors shaping human angiotensin converting enzyme 2 receptor usage by spike glycoprotein in lineage B beta-coronaviruses

Acquiring the human ACE2 receptor usage trait enables the coronaviruses to spill over to humans. However, the origin of the ACE2 usage trait in coronaviruses is poorly understood. Using a multi-disciplinary approach combining evolutionary bioinformatics and molecular dynamics simulation, we decode the principal driving force behind human ACE2 receptor recognition in coronaviruses. Genomic content, evolutionary divergence, and codon usage bias analysis reveal that SARS-CoV2 is evolutionarily divergent from other human ACE2-user CoVs, indicating that SARS-CoV2 originates from a different lineage. Sequence analysis shows that all the human ACE2-user CoVs contain two insertions in the receptor-binding motif (RBM) that directly interact with ACE2. However, the insertion sequences in SARS-CoV2 are divergent from other ACE2-user CoVs, implicating their different recombination origins. The potential of mean force calculations reveals that the high binding affinity of SARS-CoV2 RBD to human ACE2 is primarily attributed to its ability to form a higher number of hydrogen bonds than the other ACE2-user CoVs. The adaptive branch-site random effects likelihood method identifies positive selection bias across the ACE2 user CoVs lineages. Recombination and selection forces shape the spike evolution in human ACE2-using beta-CoVs to optimize the interfacial hydrogen bonds between RBD and ACE2. However, these evolutionary forces work within the constraints of nucleotide composition, ensuring optimum codon adaptation of the spike (S) gene within the host cell.

Peptide mediated colorimetric detection of SARS-CoV-2 using gold nanoparticles: a molecular dynamics simulation study.

The outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has necessitated the development of a rapid, simple yet selective naked-eye detection methodology that does not require any advanced instrumental techniques. In this study, we report our computational findings on the detection of SARS-CoV-2 using peptide- functionalized gold nanoparticles (GNPs). The peptide has been screened from angiotensin-converting enzyme 2 (ACE2) receptor situated on the surface of the host cell membrane which interacts with the spike protein of SARS-CoV-2, resulting entry of the virus into the host cell. As a result, the peptide-functionalized GNPs possess excellent affinity towards the spikes of SARS-CoV-2 and readily get aggregated once exposed to SARS-CoV-2 antigen or virus. The stability of the peptides on the surface of GNPs and their interaction with the spike protein of the virus have been investigated using coarse-grained molecular dynamic simulations. The potential of mean force calculation of spike protein confirmed strong binding between peptide and receptor-binding domain (RBD) of spike protein. Our in silico results demonstrate the potential of the peptide-functionalized GNPs in the development of simple and rapid colorimetric biosensors for clinical diagnosis.Supplementary InformationThe online version contains supplementary material available at 10.1007/s00894-022-05184-x.

Nonmonotonic Relationship between the Oxidation State of Graphene-Based Materials and Its Cell Membrane Damage Effects.

With the rapid development of carbon-based two-dimensional nanomaterials in biomedical applications, growing concern has emerged regarding their biocompatibility and especially their interactions with cell membranes. Our experimental studies found that the oxidation state, as one of the most important chemical parameters of graphene derivatives, regulates the hemolysis effect on human red blood cells in a nonmonotonic manner. Scanning electron microscopy and optical microscopy observations suggested that graphene oxides with medium oxygen content have the most serious destructive effects on the cell membranes. Molecular dynamics simulations and potential of mean force calculations revealed that, on the one hand, with the decrease in the surface oxygenated groups, more sp2 carbon area of graphene-based materials will be exposed, playing a facilitating role in the damage of cell membranes; on the other hand, fewer oxygenated groups also lead to the accumulation of graphene-based nanosheets in solutions. The formation of the multilayer structure of graphene-based nanosheets reduces the exposed sp2 carbon area, prevents the collective extraction of lipid molecules, and eventually results in a weakened extraction effect on cell membranes. Together, these factors generate a nonmonotonic relationship between the oxidation state of graphene oxides and their destructive effects on cell membranes.

Computational Investigation on the Efficiency of Small Molecule Inhibitors Identified from Indian Spices against SARS-CoV-2 Mpro

Recently, small compounds from Indian spices (Carnosol, Arjunglucoside-I, and Rosmanol) have been identified as SARS-CoV-2 main protease (Mpro) inhibitors. The structural dynamics and characteristic features of binding of these small molecules to the SARS-CoV-2 Mpro are not well understood. Here, we have constructed the potential of mean force (PMF) for dissociating Mpro-small molecule inhibitor complexes from the umbrella sampling simulations using the weighted histogram analysis method. Mpro-small molecule inhibitor complexes exhibited relatively higher dissociation energy values than the alpha-ketoamide-Mpro complex (positive control) from the PMF calculations. We found that binding affinity between protein and ligand is higher in Mpro-Arjunglucoside-I complex [∆Gbind = -19.74 kcal mol-1 from MM-GBSA and ∆Gbind = -9.13 kcal mol-1 from MM-PBSA] than in other three SARS-CoV-2 small molecule complexes. The MM-GBSA/MM-PBSA calculations revealed that the small molecule inhibitors studied in this work have substantially higher binding affinity for Mpro. We found the residues present in SARS-CoV-2 Mpro's binding pocket contributed the most binding free energy to SARS-CoV-2 Mpro-small molecule interactions. Our findings emphasize the structural and binding features of the identified small molecule inhibitors with SARS-CoV-2 Mpro, which could be relevant in developing therapeutic candidates to combat SARS-CoV-2.

Different Binding Modes of SARS-CoV-1 and SARS-CoV-2 Fusion Peptides to Cell Membranes: The Influence of Peptide Helix Length.

Although the amino acid sequences of SARS-CoV-1 and SARS-CoV-2 fusion peptides (FPs) are highly conserved, the cryo-electron microscopy structures of the SARS-CoV-1 and SARS-CoV-2 spike proteins show that the helix length of SARS-CoV-1 FP is longer than that of SARS-CoV-2 FP. In this work, we simulated the membrane-binding models of SARS-CoV-1 and SARS-CoV-2 FPs and compared the binding modes of the FPs with the POPC/POPE/cholesterol bilayer membrane. Our simulation results show that the SARS-CoV-2 FP binds to the bilayer membrane more effectively than the SARS-CoV-1 FP. It is seen that the short N-terminal helix of SARS-CoV-2 FP is more favorable to insert into the target membrane than the long N-terminal helix of SARS-CoV-1 FP. Meanwhile, the potential of mean force calculations showed that the SARS-CoV-2 FP would prefer only one binding mode (N-terminal binding), whereas the SARS-CoV-1 FP has two favorable membrane-binding modes (C-terminal and N-terminal binding modes). Moreover, in the case of SARS-CoV-1 FP binding to the target membrane, the transition between the two binding modes is relatively fast. Finally, we discovered that the membrane-binding mode would influence the helix length of SARS-CoV-1 FP, while the helix length of SARS-CoV-2 FP could be stably maintained in the membrane-bound configurations. This work suggests that the short helix might endow the FP with high membrane-anchoring strength. In particular, the membrane-penetrating residues (Phe, Ile, and Leu) of short α-helix interact with the cell membrane more strongly than those of long α-helix.

Improving the Potential of Mean Force and Nonequilibrium Pulling Simulations by Simultaneous Alchemical Modifications.

We present an approach combining alchemical modifications and physical-pathway methods to calculate absolute binding free energies. The employed physical-pathway method is either a stratified umbrella sampling to calculate a potential of mean force or nonequilibrium pulling. We devised two basic approaches: the simultaneous approach (S-approach), where, along the physical unbinding pathway, an alchemical transformation of ligand-protein interactions is installed and deinstalled, and the prior-plus-simultaneous approach (PPS-approach), where, prior to the physical-pathway simulation, an alchemical transformation of ligand-protein interactions is installed in the binding site and deinstalled during the physical-pathway simulation. Using a mutant of T4 lysozyme with a benzene ligand as an example, we show that installation and deinstallation of soft-core interactions concurrent with physical ligand unbinding (S-approach) allow successful potential of mean force calculations and nonequilibrium pulling simulations despite the problems posed by the occluded nature of the lysozyme binding pocket. Good agreement between the potential of the mean-force-based S-approach and double decoupling simulations as well as a remarkable efficiency and accuracy of the nonequilibrium-pulling-based S-approach is found. The latter turned out to be more compute-efficient than the potential of mean force calculation by approximately 70%. Furthermore, we illustrate the merits of reducing ligand-protein interactions prior to potential of mean force calculations using the murine double minute homologue protein MDM2 with a p53-derived peptide ligand (PPS-approach). Here, the problem of breaking strong interactions in the binding pocket is transferred to a prior alchemical transformation that reduces the free-energy barrier between the bound and unbound state in the potential of mean force. Besides, disentangling physical ligand displacement from the deinstallation of ligand-protein interactions was seen to allow a more uniform sampling of distance histograms in the umbrella sampling. In the future, physical ligand unbinding combined with simultaneous alchemical modifications may prove useful in the calculation of protein-protein binding free energies, where sampling problems posed by multiple, possibly sticky interactions and potential steric clashes can thus be reduced.

Standard Binding Free Energy and Membrane Desorption Mechanism for a Phospholipase C.

Peripheral membrane proteins (PMPs) bind temporarily to cellular membranes and play important roles in signaling, lipid metabolism, and membrane trafficking. Obtaining accurate membrane-PMP affinities using experimental techniques is more challenging than for protein-ligand affinities in an aqueous solution. At the theoretical level, calculation of the standard protein-membrane binding free energy using molecular dynamics simulations remains a daunting challenge owing to the size of the biological objects at play, the slow lipid diffusion, and the large variation in configurational entropy that accompanies the binding process. To overcome these challenges, we used a computational framework relying on a series of potential-of-mean-force (PMF) calculations including a set of geometrical restraints on collective variables. This methodology allowed us to determine the standard binding free energy of a PMP to a phospholipid bilayer using an all-atom force field. Bacillus thuringiensis phosphatidylinositol-specific phospholipase C (BtPI-PLC) was chosen due to its importance as a virulence factor and owing to the host of experimental affinity data available. We computed a standard binding free energy of -8.2 ± 1.4 kcal/mol in reasonable agreement with the reported experimental values (-6.6 ± 0.2 kcal/mol). In light of the 2.3-μs separation PMF calculation, we investigated the mechanism whereby BtPI-PLC disengages from interactions with the lipid bilayer during separation. We describe how a short amphipathic helix engages in transitory interactions to ease the passage of its hydrophobes through the interfacial region upon desorption from the bilayer.

Hydrophobic fluorinated graphene templated molecular sieving for high efficiency seawater desalination

The scarcity of freshwater is of great challenge that the world is facing nowadays. The advances of nanomaterial based on the reverse osmosis (RO) technology provide new possibilities for desalination. In this study, using molecular dynamics simulation, we propose and design an excellent RO membrane composed of fluorinated graphene (F-GRA) nanochannels, by which the exceptionally high water permeation (reaching up to 61.1 L/cm2/day/MPa) and the almost complete ion rejection are achieved. Notably, F-GRA nanochannel membranes exhibit a desalination performance much more promising than many other nanomaterials in previously theoretical studies. This superior desalination performance of F-GRA channels is attributed to the negatively charged surface and hydrophobicity of F-GRA, where the electrostatic interactions (attraction or repulsion) between ions and F-GRA surface cause the ideal ion rejection and the ultralow water friction on F-GRA mediated by its hydrophobicity results in the excellent water penetration. Moreover, potential of mean force calculations further reveal that the water molecule reflects the lowest free energy barrier relative to ions when traversing through the F-GRA channel, indicating the energetical favorability of the successful water transport instead of ions. Our theoretical study offers a fascinating approach of molecular sieving design usable for future desalination.

Self-assembled nanomaterials of naphthalene monoimide in aqueous medium for multimodal detection of picric acid

Picric acid (PA) is a menacing environmental pollutant on account of its high solubility in water. Extensive usage of picric acid as a handy chemical and go-to explosive in pharmaceutical and chemical industries has been posing alarming threats to the environment and public health. The detection of PA in aqueous medium and vapor state is extremely important for military and civilian safety. Here, we report the synthesis of water soluble 1, 8-naphthalimide (ANDI) and multimodal sensing applications of aggregated nano materials for nitro explosives such as picric acid (PA) in aqueous, solid surface and vapor phase. The ANDI nano aggregates demonstrated substantial selectivity and ultrasensitive detection of PA with exceptional quenching constant 7.23×106 M−1 and limit of detection 149 ppb. The quenching takes place due to ground state charge transfer complex formation between PA and ANDI. Equilibrium simulation and the potential of mean force calculations reveal that the ANDI self-assembly is stabilized by extensive π-π interactions and the primary driving force behind the recognition of PA by the assembly is van der Waals interactions. ANDI aggregates would be potential materials for the construction of low cost and light weight nitroaromatic explosive sensors for future application.

Computational studies of the encapsulation of ibuprofen and paracetamol into cucurbit[7]uril

Herein, theoretical methods were used to study the cucurbit[7]uril (CB[7]) as a possible carrier agent for the poor water soluble drugs ibuprofen (IBF) and paracetamol (PCT). These drugs form a stable inclusion complex with the CB[7] during 50 ns of molecular dynamics simulation preserving its solvation shell. Likewise CB[7], both complexes are soluble in water with calculated solvation enthalpy of –131 and –133 kcal/mol for isolated CB[7]. The binding free energy, obtained from the potential of mean force calculations, reveals that the IBF@CB[7] complex is more stable (–16.7 kcal/mol) than the PCT@CB[7] complex (–11.7 kcal/mol). Correspondingly, the binding energies obtained in DFT-D3/B3LY/6-31G(d,p) calculation are –30.07 and –24.51 kcal/mol for IBF@CB[7] and PCT@CB[7], respectively. The high energy gap of complexes implies their chemical stability. Our results indicate that the CB[7] can be a new carrier agent for IBF and PCT, improving their solubility and chemoprotection in aqueous media.

Role of Hydration in Magnesium versus Calcium Ion Pairing with Carboxylate: Solution and the Aqueous Interface

The binding of group II metal cations such as Ca2+ and Mg2+ has been largely categorized as electrostatic or ionic using carboxylate symmetric and asymmetric stretching frequency assignments that have been historically used with little regard for the solvation environment of aqueous solutions. However, given the importance of these cations and their binding mechanisms related to biological function and in revealing surface enrichment factors for ocean to marine aerosol transfer, it is imperative that a deeper understanding be sought to include hydration effects. Here, infrared reflection-absorption and Raman spectra for surface and solution phase carboxylate binding information, respectively, are compared against bare (unbound) carboxylate and bidentate Zn2+:carboxylate spectral signatures. Spectral non-coincidence effect analysis, temperature studies, and spectral and potential of mean force calculations result in a concise interpretation of binding motifs that include the role of mediating water molecules, that is, contact and solvent-shared ion pairs. Calcium directly binds to the carboxylate group in contact ion pairs where magnesium rarely does. Moreover, we reveal the dominance of the solvent-shared ion pair of magnesium with carboxylate at the air-water interface and in solution.

Relative Affinities of Protein-Cholesterol Interactions from Equilibrium Molecular Dynamics Simulations.

Specific interactions of lipids with membrane proteins contribute to protein stability and function. Multiple lipid interactions surrounding a membrane protein are often identified in molecular dynamics (MD) simulations and are, increasingly, resolved in cryo-electron microscopy (cryo-EM) densities. Determining the relative importance of specific interaction sites is aided by determination of lipid binding affinities using experimental or simulation methods. Here, we develop a method for determining protein–lipid binding affinities from equilibrium coarse-grained MD simulations using binding saturation curves, designed to mimic experimental protocols. We apply this method to directly obtain affinities for cholesterol binding to multiple sites on a range of membrane proteins and compare our results with free energies obtained from density-based equilibrium methods and with potential of mean force calculations, getting good agreement with respect to the ranking of affinities for different sites. Thus, our binding saturation method provides a robust, high-throughput alternative for determining the relative consequence of individual sites seen in, e.g., cryo-EM derived membrane protein structures surrounded by an array of ancillary lipid densities.

Effects of Ionic Liquid Nanoconfinement on the CO2/CH4 Separation in Poly(vinylidene fluoride)/1-Ethyl-3-methylimidazolium Thiocyanate Membranes.

A combined experimental and molecular dynamics (MD) simulation approach was used to investigate the effects of the nanoconfinement of a highly CO2/CH4-selective ionic liquid (IL), 1-ethyl-3-methylimidazolium thiocyanate ([EMIM][SCN]), in porous poly(vinylidene fluoride) (PVDF) matrices on the gas separation performance of the resulting membranes. The observed experimental CO2/CH4 permselectivity increased by about 46% when the nominal pore diameter in PVDF, which is a measure of nanoconfinement, decreased from 450 to 100 nm, thus demonstrating nanoconfinement improvements of gas separation. MD simulations corroborated these experimental observations and indicated a suppression in the sorption of CH4 by [EMIM][SCN] when the IL nanoconfinement length decreased within the nonpolar PVDF surfaces. This is consistent with the experimental observation that the CH4 permeance through the IL confined in nonpolar PVDF is significantly less than the CH4 permeance through the IL confined in a water-wetting polar formulation of PVDF. The potential of mean force calculations further indicated that CO2 has more affinity to the nonpolar PVDF surface than CH4. Also, a charge/density distribution analysis of the IL in the PVDF-confined region revealed a layering of the IL into [EMIM]- and [SCN]-rich regions, where CH4 was preferentially distributed in the former and CO2 in the latter. These molecular insights into the nanoconfinement-driven mechanisms in polymer/IL membranes provide a framework for a better molecular design of such membranes for critical gas separation and CO2 capture applications.

Comparative studies of IR spectra of deprotonated serine with classical and thermostated ring polymer molecular dynamics simulations.

Here we report the vibrational spectra of deprotonated serine calculated from the classical molecular dynamics (MD) simulations and thermostated ring-polymer molecular dynamics (TRPMD) simulation with third-order density-functional tight-binding. In our earlier study [Inakollu and Yu, “A systematic benchmarking of computational vibrational spectroscopy with DFTB3: Normal mode analysis and fast Fourier transform dipole autocorrelation function,” J. Comput. Chem. 39, 2067 (2018)] of deprotonated serine, we observed a significant difference in the vibrational spectra with the classical MD simulations compared to the infrared multiple photon dissociation spectra. It was postulated that this is due to neglecting the nuclear quantum effects (NQEs). In this work, NQEs are considered in spectral calculation using the TRPMD simulations. With the help of potential of mean force calculations, the conformational space of deprotonated serine is analyzed and used to understand the difference in the spectra of classical MD and TRPMD simulations at 298.15 and 100 K. The high-frequency vibrational bands in the spectra are characterized using Fourier transform localized vibrational mode (FT-νNAC) and interatomic distance histograms. At room temperature, the quantum effects are less significant, and the free energy profiles in the classical MD and the TRPMD simulations are very similar. However, the hydrogen bond between the hydroxyl–carboxyl bond is slightly stronger in TRPMD simulations. At 100 K, the quantum effects are more prominent, especially in the 2600–3600 cm−1, and the free energy profile slightly differs between the classical MD and TRPMD simulations. Using the FT-νNAC and the interatomic distance histograms, the high-frequency vibrational bands are discussed in detail.

Ethanol Blending to Improve Reverse Micelle Dispersity in Supercritical CO2: A Molecular Dynamics Study

Despite a great promise in the enhanced oil recovery in tight formations, CO2 flooding with surfactants is hindered due to the low surfactant solubility in supercritical CO2 (scCO2). Alcohol blending can increase the sodium bis(2-ethylhexyl) sulfosuccinate (AOT) solubility in scCO2. While this finding offers a promising solution to CO2 flooding in tight oil reservoirs, to the best of our knowledge, their working mechanism still remains elusive. Herein, we report a molecular dynamics simulation study to explore the working mechanism of alcohols in reverse micelle (RM) dispersity ("solubility") increment. The spontaneous aggregation process in two systems (System A consisting of AOT and scCO2; System B consisting of AOT, scCO2, and 10 wt % ethanol) are conducted under a typical tight oil reservoir condition (333 K and 200 bar). After 600 ns runs, the AOT molecules aggregate together and form rod-like RMs in System A, while form several small sphere-like RMs in System B. We observe that the aggregation process in System A occurs when two clusters approach each other end-to-end. More CO2 molecules are around the Na+ ion at the end of the clusters, which can be readily replaced by AOT molecules. On the other hand, the ethanol molecules can better solvate and surround Na+ ions, preventing the further aggregation of AOT clusters in System B. The potential of mean force calculations also reveal that while two small clusters formed by four AOT molecules attract each other in System A, they repel each other in System B. Our work should provide important insights into the design of scCO2-soluble surfactant formulas.

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.

Analysis of Charged Peptide Loop-Flipping across a Lipid Bilayer Using the String Method with Swarms of Trajectories.

The hydrophobic core of the lipid bilayer is conventionally considered a barrier to the translocation of charged species such that the translocation of even single ions occurs on long time scales. In contrast, experiments have revealed that some materials, including peptides, proteins, and nanoparticles, can translocate multiple charged moieties across the bilayer on experimentally relevant time scales. Understanding the molecular mechanisms underlying this behavior is challenging because resolving corresponding free-energy landscapes with molecular simulation techniques is computationally expensive. To address this challenge, we use atomistic molecular dynamics simulations with the swarms-of-trajectories (SOT) string method to analyze charge translocation pathways across single-component lipid bilayers as a function of multiple collective variables. We first demonstrate that the SOT string method can reproduce the free-energy barrier for the translocation of a charged lysine amino acid analogue in good agreement with the literature. We then obtain minimum free-energy pathways for the translocation, or flipping, of charged peptide loops across the lipid bilayer by utilizing trajectories from prior temperature-accelerated molecular dynamics (TAMD) simulations as initial configurations. The corresponding potential of mean force calculations reveal that the protonation of a central membrane-exposed aspartate residue substantially reduces the free-energy barrier for flipping charged loops by modulating the water content of the bilayer. These results provide new insight into the thermodynamics underlying loop-flipping processes and highlight how the combination of TAMD and the SOT string method can be used to understand complex charge translocation mechanisms.

ATP hydrolysis and nucleotide exit enhance maltose translocation in the MalFGK2E importer

ATP binding cassette (ABC) transporters employ ATP hydrolysis to harness substrate translocation across membranes. The Escherichia coli MalFGK2E maltose importer is an example of a type I ABC importer and a model system for this class of ABC transporters. The MalFGK2E importer is responsible for the intake of malto-oligossacharides in E.coli. Despite being extensively studied, little is known about the effect of ATP hydrolysis and nucleotide exit on substrate transport. In this work, we studied this phenomenon using extensive molecular dynamics simulations (MD) along with potential of mean force calculations of maltose transport across the pore, in the pre-hydrolysis, post-hydrolysis and nucleotide-free states. We concluded that ATP hydrolysis and nucleotide exit trigger conformational changes that result in the decrease of energetic barriers to maltose translocation towards the cytoplasm, with a concomitant increase of the energy barrier in the periplasmic side of the pore, contributing for the irreversibility of the process. We also identified key residues that aid in positioning and orientation of maltose, as well as a novel binding pocket for maltose in MalG. Additionally, ATP hydrolysis leads to conformations similar to the nucleotide-free state. This study shows the contribution of ATP hydrolysis and nucleotide exit in the transport cycle, shedding light on ABC type I importer mechanisms.