Exploring Multidimensional Free Energy Landscapes Using Time-Dependent Biases on Collective Variables

Probing the orientation and membrane permeation of rhodamine voltage reporters through molecular simulations and free energy calculations

The transmembrane potential of plasma membranes and membrane-bound organelles plays a fundamental role in cellular functions such as signal transduction, ATP synthesis, and homeostasis. Rhodamine voltage reporters (RhoVRs), which operate based on the photoinduced electron transfer (PeT) mechanism, are non-invasive, small-molecule voltage sensors that can detect rapid voltage changes, with some of them specifically targeting the inner mitochondrial membrane. In this work, we conducted extensive molecular dynamics simulations and free-energy calculations to investigate the physicochemical properties governing the orientation as well as membrane permeation barriers of three RhoVRs. Our results indicate that the positioning of the most polarized functional group relative to the hydrophobic molecular wire dictates the alignment of RhoVRs with the membrane normal, thereby, significantly affecting their voltage sensitivity. Free-energy calculations in different membrane systems identify significantly higher barriers against the permeation of RhoVR 1 compared to SPIRIT RhoVR 1, explaining their distinct subcellular localization profiles. Subsequent free-energy calculations of the distinguishing components from the two different RhoVRs provide additional insight into the physicochemical properties governing their membrane permeation. The connection between chemical composition and membrane orientation, as well as permeation behaviors of RhoVRs revealed by our calculations provides general guiding principles for the rational design of PeT-based fluorescent dyes with enhanced voltage sensitivity and desired subcellular distribution.

Molecular Insights into the Adsorption of Deposit Control Additives from Hydrocarbon Fuels

Engine deposits can reduce performance and increase emissions, particularly for modern direct-injection fuel delivery systems. Surfactants known as deposit control additives (DCAs) adsorb and self-assemble on the surface of deposit precursors to keep them suspended in the fuel. Here, we show how molecular simulations can be used to virtually screen the ability of surfactants to bind to polyaromatic hydrocarbons, comprising a major class of carbonaceous deposits. We use molecular dynamics with the adaptive biasing force method to generate the potential of mean force as a function of the vertical distance between the surfactants and deposits in gasoline and diesel fuel surrogates. We find that a zwitterionic surfactant outperforms a conventional polyisobutylene succinimide for binding to these aromatic species. The amine groups in the succinimide headgroup only weakly adsorb on the polyaromatic deposit, while additional functional groups in the zwitterionic surfactant, particularly the quarternary ammonium ion, markedly enhance the binding strength. We decompose the adsorption free energies of the surfactants into their entropic and enthalpic components, to find that the latter dominates the attraction from these non-aqueous solvents. The adsorption free energy of both surfactants is slightly weaker from n-hexadecane (diesel) than iso-octane (gasoline), which is due to the larger steric barrier from stronger molecular layering of the former on the deposit. Density functional theory calculations of the adsorption of DCA fragments validate the force field used in the molecular dynamics simulations and provide further insights into the nature of the intermolecular interactions. The approach introduced here shows considerable promise for accelerating the discovery of novel DCAs to facilitate more advanced fuel formulations to reduce emissions.

Atomic-level mechanisms of abnormal activation in NRAS oncogenes from two-dimensional free energy landscapes

The NRAS-mutant subset of melanoma is one of the most aggressive and lethal types associated with poor overall survival. Unfortunately, a low understanding of the NRAS-mutant dynamic behavior has led to the lack of clinically approved therapeutic agents able to directly target NRAS oncogenes. In this work, accurate local structures of NRAS and its mutants have been fully explored through the corresponding free energy surfaces obtained by microsecond scale well-tempered metadynamics simulations. Free energy calculations are crucial to reveal the precise mechanisms of Q61 mutations at the atomic level. Considering specific atom-atom distances d and angles ϕ as appropriate reaction coordinates we have obtained free energy surfaces revealing local and global minima together with their main transition states, unveiling the mechanisms of abnormal NRAS activation from the atomic-level and quantitatively analyzing the corresponding stable states. This will help in advancing our understanding of the basic mechanisms of NRAS mutations, offering new opportunities for the design of potential inhibitors.

Expanded Functionality and Portability for the Colvars Library

Colvars is an open-source C++ library that provides a modular toolkit for collective-variable-based molecular simulations. It allows practitioners to easily create and implement descriptors that best fit a process of interest and to apply a wide range of biasing algorithms in collective variable space. This paper reviews several features and improvements to Colvars that were added since its original introduction. Special attention is given to contributions that significantly expanded the capabilities of this software or its distribution with major MD simulation packages. Collective variables can now be optimized either manually or by machine-learning methods, and the space of descriptors can be explored interactively using the graphical interface included in VMD. Beyond the spatial coordinates of individual molecules, Colvars can now apply biasing forces to mesoscale structures and alchemical degrees of freedom and perform simulations guided by experimental data within ensemble averages or probability distributions. It also features advanced computational schemes to boost the accuracy, robustness, and general applicability of simulation methods, including extended-system and multiple-walker adaptive biasing force, boundary conditions for metadynamics, replica exchange with biasing potentials, and adiabatic bias molecular dynamics. The library is made available directly within the main distributions of the academic software GROMACS, LAMMPS, NAMD, Tinker-HP, and VMD. The robustness of the software and the reliability of the results are ensured through the use of continuous integration with a test suite within the source repository.

Elucidating Protein Structures in the Gas Phase: Traversing Configuration Space with Biasing Methods

Achieving accurate characterization of protein structures in the gas phase continues to be a formidable challenge. To tackle this issue, the present study employs Molecular Dynamics (MD) simulations in tandem with enhanced sampling techniques (methods designed to efficiently explore protein conformations). The objective is to identify suitable structures of proteins by contrasting their calculated Collision Cross-Section (CCS) with those observed experimentally. Significant discrepancies were observed between the initial MD-simulated and experimentally measured CCS values through Ion Mobility-Mass Spectrometry (IMS-MS). To bridge this gap, we employed two distinct enhanced sampling methods, Harmonic Biasing Potential and Adaptive Biasing Force, which help the proteins overcome energy barriers to adopt more compact configurations. These techniques leverage the radius of gyration as a reaction coordinate (guiding parameter), guiding the system toward compressed states that potentially match experimental configurations more closely. The guiding forces are only employed to overcome existing barriers and are removed to allow the protein to naturally arrive at a potential gas phase configuration. The results demonstrated close alignment (within ∼4%) between simulated and experimental CCS values despite using different strengths and/or methods, validating their efficacy. This work lays the groundwork for future studies aimed at optimizing biasing methods and expanding the collective variables used for more accurate gas-phase structural predictions.

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

Statistical Mechanical Theories of Membrane Permeability

A popular theoretical framework to compute the permeability coefficient of a molecule is provided by the classic Smoluchowski-Kramers treatment of the steady-state diffusive flux across a free-energy barrier. Within this framework, commonly termed "inhomogeneous solubility-diffusion" (ISD), the permeability, P, is expressed in closed form in terms of the potential of mean force and position-dependent diffusivity of the molecule of interest along the membrane normal. In principle, both quantities can be calculated from all-atom MD simulations. Although several methods exist for calculating the position-dependent diffusivity, each of these is at best an estimate. In addition, the ISD model does not account for memory effects along the chosen reaction coordinate. For these reasons, it is important to seek alternative theoretical formulations to determine the permeability coefficient that are able to account for the factors ignored by the ISD approximation. Using Green-Kubo linear response theory, we establish the familiar constitutive relation between the flux density across the membrane and the difference in the concentration of a permeant molecule, j = PΔC. On this basis, we derive a time-correlation function expression for the nonequilibrium flux across a membrane that is reminiscent of the transmission coefficient in the reactive flux formalism treatment of transition rates. An analysis based on the transition path theory framework is exploited to derive alternative expressions for the permeability coefficient. The different strategies are illustrated with stochastic simulations based on the generalized Langevin equation in addition to unbiased molecular dynamics simulations of water permeation of a lipid bilayer.

Protocol for calculating binding free energy of RNA:RNA interactions through molecular dynamics simulations using adaptive biasing force technique

The adaptive biasing force (ABF) technique allows sampling to proceed in a flat free energy surface when performing molecular dynamics (MD) simulations. Here, we present a protocol to perform MD simulations using the ABF technique and apply it to calculate the binding free energy of an RNA:RNA interaction. We describe steps for server setup, test running software, and building molecular models. We then detail procedures for running and configuring ABF-MD simulations and analyzing binding free energy and structural change. For complete details on the use and execution of this protocol, please refer to Fujita et al.1 and Kameda et al.2.

Membrane Stabilization of Helical Previtamin D Conformers as Possible Enhancement of Vitamin D Photoproduction

Photoinduced vitamin D formation occurs 10-15-fold faster in phospholipid bilayers (PLB) than in isotropic solution. It has been hypothesized that amphipatic interactions of the PLB with the rotationally flexible previtamin D (Pre) stabilize its helical conformers, enhancing thermal intramolecular [1,7]-hydrogen transfer, forming vitamin D. To test this hypothesis, we carried out molecular dynamics (MD) simulations of Pre in a PLB composed of dipalmitoylphosphatidylcholine (DPPC). We designed a classical force field capable of accurately describing the equilibrium composition of Pre conformers. Using adaptive biasing force MD simulations, we determined the free energy of Pre conformers in isotropic environments (hexane and gas-phase) and in the anisotropic environment of a DPPC PLB. We find a total increase of 25.5% of the population of both helical conformers (+20.5% g+Zg+ and +5% g-Zg-) in DPPC compared to hexane. In view of ab initio simulations, showing that hydrogen transfer occurs in both helical conformers, our study strongly suggests the validity of the initial hypothesis. Regarding the amphipatic interactions of Pre with the PLB, we find that, similar to cholesterol (Chol) and 7-dehydrocholesterol (7-DHC), Pre entertains hydrogen bonds mainly to the carbonyl groups of DPPC and, to a lesser extent, with phosphate oxygen atoms and rarely to water molecules at the interface. We further report order parameters of the Pre/DPPC system, which are slightly smaller than those for Chol/DPPC and 7-DHC/DPPC, but larger than for pure DPPC. This indicates a loss in membrane viscosity upon photochemical ring-opening of 7-DHC to form Pre.

An Atomic and Molecular Insight into How PFOA Reduces α-Helicity, Compromises Substrate Binding, and Creates Binding Pockets in a Model Globular Protein

Per- and polyfluoroalkyl substances (PFAS) pose significant health risks due to their widespread presence in various environmental and biological matrices. However, the molecular-level mechanisms underlying the interactions between PFAS and biological constituents, including proteins, carbohydrates, lipids, and DNA, remain poorly understood. Here, we investigate the interactions between a legacy PFAS, viz. perfluorooctanoic acid (PFOA), and the milk protein β-lactoglobulin (BLG) obtained using a combination of experimental and computational techniques. Circular dichroism studies reveal that PFOA perturbs the secondary structure of BLG, by driving a dose-dependent loss of α-helicity and alterations in its β-sheet content. Furthermore, exposure of the protein to PFOA attenuates the on-rate constant for the binding of the hydrophobic probe 8-anilino-1-naphthalene sulfonic acid (ANS), suggesting potential functional impairment of BLG by PFOA. Steered molecular dynamics and umbrella sampling calculations reveal that PFOA binding leads to the formation of an energetically favorable novel binding pocket within the protein, when residues 129-142 are steered to unfold from their initial α-helical structure, wherein a host of intermolecular interactions between PFOA and BLG's residues serve to insert the PFOA into the region between the unfolded helix and beta-sheets. Together, the data provide a novel understanding of the atomic and molecular mechanism(s) by which PFAS modulates structure and function in a globular protein, leading to a beginning of our understanding of altered biological outcomes.

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.

Unbiasing Enhanced Sampling on a High-Dimensional Free Energy Surface with a Deep Generative Model

Biased enhanced sampling methods that utilize collective variables (CVs) are powerful tools for sampling conformational ensembles. Due to their large intrinsic dimensions, efficiently generating conformational ensembles for complex systems requires enhanced sampling on high-dimensional free energy surfaces. While temperature-accelerated molecular dynamics (TAMD) can trivially adopt many CVs in a simulation, unbiasing the simulation to generate unbiased conformational ensembles requires accurate modeling of a high-dimensional CV probability distribution, which is challenging for traditional density estimation techniques. Here we propose an unbiasing method based on the score-based diffusion model, a deep generative learning method that excels in density estimation across complex data landscapes. We demonstrate that this unbiasing approach, tested on multiple TAMD simulations, significantly outperforms traditional unbiasing methods and can generate accurate unbiased conformational ensembles. With the proposed approach, TAMD can adopt CVs that focus on improving sampling efficiency and the proposed unbiasing method enables accurate evaluation of ensemble averages of important chemical features.

Mechanism of proton-powered c-ring rotation in a mitochondrial ATP synthase

Proton-powered c-ring rotation in mitochondrial ATP synthase is crucial to convert the transmembrane protonmotive force into torque to drive the synthesis of adenosine triphosphate (ATP). Capitalizing on recent cryo-EM structures, we aim at a structural and energetic understanding of how functional directional rotation is achieved. We performed multi-microsecond atomistic simulations to determine the free energy profiles along the c-ring rotation angle before and after the arrival of a new proton. Our results reveal that rotation proceeds by dynamic sliding of the ring over the a-subunit surface, during which interactions with conserved polar residues stabilize distinct intermediates. Ordered water chains line up for a Grotthuss-type proton transfer in one of these intermediates. After proton transfer, a high barrier prevents backward rotation and an overall drop in free energy favors forward rotation, ensuring the directionality of c-ring rotation required for the thermodynamically disfavored ATP synthesis. The essential arginine of the a-subunit stabilizes the rotated configuration through a salt bridge with the c-ring. Overall, we describe a complete mechanism for the rotation step of the ATP synthase rotor, thereby illuminating a process critical to all life at atomic resolution.

Fractional Extended Diffusion Theory to capture anomalous relaxation from biased/accelerated molecular simulations

Biased and accelerated molecular simulations (BAMS) are widely used tools to observe relevant molecular phenomena occurring on time scales inaccessible to standard molecular dynamics, but evaluation of the physical time scales involved in the processes is not directly possible from them. For this reason, the problem of recovering dynamics from such kinds of simulations is the object of very active research due to the relevant theoretical and practical implications of dynamics on the properties of both natural and synthetic molecular systems. In a recent paper [A. Rapallo et al., J. Comput. Chem. 42, 586-599 (2021)], it has been shown how the coupling of BAMS (which destroys the dynamics but allows to calculate average properties) with Extended Diffusion Theory (EDT) (which requires input appropriate equilibrium averages calculated over the BAMS trajectories) allows to effectively use the Smoluchowski equation to calculate the orientational time correlation function of the head-tail unit vector defined over a peptide in water solution. Orientational relaxation of this vector is the result of the coupling of internal molecular motions with overall molecular rotation, and it was very well described by correlation functions expressed in terms of weighted sums of suitable time-exponentially decaying functions, in agreement with a Brownian diffusive regime. However, situations occur where exponentially decaying functions are no longer appropriate to capture the actual dynamical behavior, which exhibits persistent long time correlations, compatible with the so called subdiffusive regimes. In this paper, a generalization of EDT will be given, exploiting a fractional Smoluchowski equation (FEDT) to capture the non-exponential character observed in the relaxation of intramolecular distances and molecular radius of gyration, whose dynamics depend on internal molecular motions only. The calculation methods, proper to EDT, are adapted to implement the generalization of the theory, and the resulting algorithm confirms FEDT as a tool of practical value in recovering dynamics from BAMS, to be used in general situations, involving both regular and anomalous diffusion regimes.

The Molecular Mechanism of Ion Selectivity in Nanopores

Ion channels exhibit strong selectivity for specific ions over others under electrochemical potentials, such as KcsA for K+ over Na+. Based on the thermodynamic analysis, this study is focused on exploring the mechanism of ion selectivity in nanopores. It is well known that ions must lose part of their hydration layer to enter the channel. Therefore, the ion selectivity of a channel is due to the rearrangement of water molecules when entering the nanopore, which may be related to the hydrophobic interactions between ions and channels. In our recent works on hydrophobic interactions, with reference to the critical radius of solute (Rc), it was divided into initial and hydrophobic solvation processes. Additionally, the different dissolved behaviors of solutes in water are expected in various processes, such as dispersed and accumulated distributions in water. Correspondingly, as the ion approaches the nanopore, there seems to exist the "repulsive" or "attractive" forces between them. In the initial process ( Collapse

Key Words

• hydrogen bondings
• hydrophobic interactions
• ion selectivity
• nanopore
• water

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MESH Headings Collapse

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Affiliation(s)

Yan-Nan Chen
Yu-Zhen Liu
Qiang Sun Key Laboratory of Orogenic Belts and Crustal Evolution, The School of Earth and Space Sciences, Ministry of Education, Peking University, Beijing 100871, China; (Y.-N.C.); (Y.-Z.L.)

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Stability of Cytoplasmic Membrane of Escherichia coli Bacteria in Aqueous and Ethanolic Environment

The mechanism of action of any antibacterial agent or disinfectant depends largely on their interaction with the bacterial membrane. Herein, we use the SPICA (surface property fitting coarse graining) force-field and develop a coarse-grained (CG) model for the structure of the cytoplasmic membrane of Escherichia coli (E. coli) and its interaction with water and ethanol. We elucidate the impact of different concentrations of ethanol on the cytoplasmic membrane bilayers and vesicles of E. coli using the CG molecular dynamics (CG MD) simulations. Our modeling approach first focuses on the parametrization of the required force-field for POPG lipid and its interaction with water, ethanol, and POPE lipid. Subsequently, the structural stability of the E. coli bacterial membrane in the presence of high and low concentrations of ethanol is delineated. Both flat bilayers as well as vesicles of E. coli membrane were considered for the CG MD. Our results reveal that, at low ethanol concentrations (<30 mol %), the size of the E. coli vesicles increases with discernible deformations in their shapes. Because of ethanol-induced interdigitation, thinning of the E. coli vesicular membrane is also observed. However, at higher ethanol concentrations (>30 mol %), the integrity of the vesicles is lost because of deteriorating invasion of ethanol molecules into the vesicle bilayer and significant weakening of lipid-lipid interactions. At higher ethanol concentrations (40 and 70 mol %), both the multivesicle and single-vesicle bacterial membranes exhibit a similar rupturing pattern wherein the extraction of lipids from the membrane and formation of aggregates of the component lipids are observed. These aggregates consist of polar head groups of 3-5 POPE/POPG lipids with intertwined nonpolar tails.

Synergy of Mutation-Induced Effects in Human Vitamin K Epoxide Reductase: Perspectives and Challenges for Allo-Network Modulator Design

The human Vitamin K Epoxide Reductase Complex (hVKORC1), a key enzyme transforming vitamin K into the form necessary for blood clotting, requires for its activation the reducing equivalents delivered by its redox partner through thiol-disulfide exchange reactions. The luminal loop (L-loop) is the principal mediator of hVKORC1 activation, and it is a region frequently harbouring numerous missense mutations. Four L-loop hVKORC1 mutants, suggested in vitro as either resistant (A41S, H68Y) or completely inactive (S52W, W59R), were studied in the oxidised state by numerical approaches (in silico). The DYNASOME and POCKETOME of each mutant were characterised and compared to the native protein, recently described as a modular protein composed of the structurally stable transmembrane domain (TMD) and the intrinsically disordered L-loop, exhibiting quasi-independent dynamics. The DYNASOME of mutants revealed that L-loop missense point mutations impact not only its folding and dynamics, but also those of the TMD, highlighting a strong mutation-specific interdependence between these domains. Another consequence of the mutation-induced effects manifests in the global changes (geometric, topological, and probabilistic) of the newly detected cryptic pockets and the alternation of the recognition properties of the L-loop with its redox protein. Based on our results, we postulate that (i) intra-protein allosteric regulation and (ii) the inherent allosteric regulation and cryptic pockets of each mutant depend on its DYNASOME; and (iii) the recognition of the redox protein by hVKORC1 (INTERACTOME) depend on their DYNASOME. This multifaceted description of proteins produces "omics" data sets, crucial for understanding the physiological processes of proteins and the pathologies caused by alteration of the protein properties at various "omics" levels. Additionally, such characterisation opens novel perspectives for the development of "allo-network drugs" essential for the treatment of blood disorders.

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).

pSPICA Force Field Extended for Proteins and Peptides

Many coarse-grained (CG) molecular dynamics (MD) studies have been performed to investigate biological processes involving proteins and lipids. CG force fields (FFs) in these MD studies often use implicit or nonpolar water models to reduce computational costs. CG-MD using water models cannot properly describe electrostatic screening effects owing to the hydration of ionic segments and thus cannot appropriately describe molecular events involving water channels and pores through lipid membranes. To overcome this issue, we developed a protein model in the pSPICA FF, in which a polar CG water model showing the proper dielectric response was adopted. The developed CG model greatly improved the transfer free energy profiles of charged side chain analogues across the lipid membrane. Application studies on melittin-induced membrane pores and mechanosensitive channels in lipid membranes demonstrated that CG-MDs using the pSPICA FF correctly reproduced the structure and stability of the pores and channels. Furthermore, the adsorption behavior of the highly charged nona-arginine peptides on lipid membranes changed with salt concentration, indicating the pSPICA FF is also useful for simulating protein adsorption on membrane surfaces.

RNA regulates cohesiveness and porosity of a biological condensate

Biological condensates have emerged as key elements of a biological cell function, concentrating disparate biomolecules to accomplish specific biological tasks. RNA was identified as a key ingredient of such condensates, however, its effect on the physical properties of the condensate was found to depend on the condensate's composition while its effect on the microstructure has remained elusive. Here, we characterize the physical properties and the microstructure of a protein-RNA condensate by means of large-scale coarse-grained (CG) molecular dynamics simulations. By developing a custom CG model of RNA compatible with a popular CG model of proteins, we systematically investigate the structural, thermodynamic, and kinetic properties of condensate droplets containing thousands of individual protein and RNA molecules over a range of temperatures. While we find RNA to increase the condensate's cohesiveness, its effect on the condensate's fluidity is more nuanced with longer molecules compacting the condensate and making it less fluid. We show that a biological condensate has a sponge-like morphology of interconnected channels of size that increases with temperature and decreases in the presence of RNA. Our results suggest that longer RNA form a dynamic scaffold within a condensate, regulating not only its fluidity but also permeability to intruder molecules.

A Rigorous Framework for Calculating Protein-Protein Binding Affinities in Membranes

Calculating the binding free energy of integral transmembrane (TM) proteins is crucial for understanding the mechanisms by which they recognize one another and reversibly associate. The glycophorin A (GpA) homodimer, composed of two α-helical segments, has long served as a model system for studying TM protein reversible association. The present work establishes a methodological framework for calculating the binding affinity of the GpA homodimer in the heterogeneous environment of a membrane. Our investigation carefully considered a variety of protocols, including the appropriate choice of the force field, rigorous standardization reflecting the experimental conditions, sampling algorithm, anisotropic environment, and collective variables, to accurately describe GpA dimerization via molecular dynamics-based approaches. Specifically, two strategies were explored: (i) an unrestrained potential mean force (PMF) calculation, which merely enhances sampling along the separation of the two binding partners without any restraint, and (ii) a so-called "geometrical route", whereby the α-helices are progressively separated with imposed restraints on their orientational, positional, and conformational degrees of freedom to accelerate convergence. Our simulations reveal that the simplified, unrestrained PMF approach is inadequate for the description of GpA dimerization. Instead, the geometrical route, tailored specifically to GpA in a membrane environment, yields excellent agreement with experimental data within a reasonable computational time. A dimerization free energy of -10.7 kcal/mol is obtained, in fairly good agreement with available experimental data. The geometrical route further helps elucidate how environmental forces drive association before helical interactions stabilize it. Our simulations also brought to light a distinct, long-lived spatial arrangement that potentially serves as an intermediate state during dimer formation. The methodological advances in the generalized geometrical route provide a powerful tool for accurate and efficient binding-affinity calculations of intricate TM protein complexes in inhomogeneous environments.

Improved Protein Model in SPICA Force Field

The previous version of the SPICA coarse-grained (CG) force field (FF) protein model focused primarily on membrane proteins and successfully reproduced the dimerization free energies of several transmembrane helices and the stable structures of various membrane protein assemblies. However, that model had limited accuracy when applied to other proteins, such as intrinsically disordered proteins (IDPs) and peripheral proteins, because the dimensions of the IDPs in an aqueous solution were too compact, and protein binding on the lipid membrane surface was overstabilized. To improve the accuracy of the SPICA FF model for the simulation of such systems, in this study, we introduce protein secondary structure-dependent nonbonded interaction parameters to the backbone segments and reoptimize almost all nonbonded parameters for amino acids. The improved FF proposed here successfully reproduces the radii of gyration of various IDPs, the binding sensitivity of several peripheral membrane proteins, and the dimerization free energies of several transmembrane helices. The new model also shows improved agreement with experiments on the free energy of peptide association in water. In addition, an extensive library of nonbonded interactions between proteins and lipids, including various glycerophospholipids, sphingolipids, and cholesterol, allows the study of specific interactions between lipids and peripheral and transmembrane proteins. Hence, the new SPICA FF (version 2) proposed herein is applicable with high accuracy for simulating a wide range of protein systems.

In silico design of a lipid-like compound targeting KRAS4B-G12D through non-covalent bonds

One of the most common drivers in human cancer is the peripheral membrane protein KRAS4B, able to promote oncogenic signalling. To signal, oncogenic KRAS4B not only requires a sufficient nucleotide exchange, but also needs to recruit effectors by exposing its effector-binding sites while anchoring to the phospholipid bilayer where KRAS4B-mediated signalling events occur. The enzyme phosphodiesterase-δ plays an important role in sequestering KRAS4B from the cytoplasm and targeting it to cellular membranes of different cell species. In this work, we present an in silico design of a lipid-like compound that has the remarkable feature of being able to target both an oncogenic KRAS4B-G12D mutant and the phosphodiesterase-δ enzyme. This double action is accomplished by adding a lipid tail (analogous to the farnesyl group of the KRAS4B protein) to an previously known active compound (2H-1,2,4-benzothiadiazine, 3,4-dihydro-,1,1-dioxide). The proposed lipid-like molecule was found to lock KRAS4B-G12D in its GDP-bound state by adjusting the effector-binding domain to be blocked by the interface of the lipid bilayer. Meanwhile, it can tune GTP-bound KRAS4B-G12D to shift from the active orientation state to the inactive state. The proposed compound is also observed to stably accommodate itself in the prenyl-binding pocket of phosphodiesterase-δ, which impairs KRAS4B enrichment at the lipid bilayer, potentially reducing the proliferation of KRAS4B inside the cytoplasm and its anchoring at the bilayer. In conclusion, we report a potential inhibitor of KRAS4B-G12D with a lipid tail attached to a specific warhead, a compound which has not yet been considered for drugs targeting RAS mutants. Our work provides new ways to target KRAS4B-G12D and can also foster drug discovery efforts for the targeting of oncogenes of the RAS family and beyond.

Free Energy Profile Decomposition Analysis for QM/MM Simulations of Enzymatic Reactions

In enzyme mechanistic studies and mutant design, it is highly desirable to know the individual residue contributions to the reaction free energy and barrier. In this work, we show that such free energy contributions from each residue can be readily obtained by postprocessing ab initio quantum mechanical molecular mechanical (ai-QM/MM) free energy simulation trajectories. Specifically, through a mean force integration along the minimum free energy pathway, one can obtain the electrostatic, polarization, and van der Waals contributions from each residue to the free energy barrier. Separately, a similar analysis procedure allows us to assess the contribution from different collective variables along the reaction coordinate. The chorismate mutase reaction is used to demonstrate the utilization of these two trajectory analysis tools.

Computation of Absolute Binding Free Energies for Noncovalent Inhibitors with SARS-CoV-2 Main Protease

Accurate, routine calculation of absolute binding free energies (ABFEs) for protein-ligand complexes remains a key goal of computer-aided drug design since it can enable screening and optimization of drug candidates. For development and testing of related methods, it is important to have high-quality datasets. To this end, from our own experimental studies, we have selected a set of 16 inhibitors of the SARS-CoV-2 main protease (Mpro) with structural diversity and well-distributed BFEs covering a 5 kcal/mol range. There is also minimal structural uncertainty since X-ray crystal structures have been deposited for 12 of the compounds. For methods testing, we report ABFE results from 2 μs molecular dynamics (MD) simulations using free energy perturbation (FEP) theory. The correlation of experimental and computed results is encouraging, with a Pearson's r2 of 0.58 and a Kendall τ of 0.24. The results indicate that current FEP-based ABFE calculations can be used for identification of active compounds (hits). While their accuracy for lead optimization is not yet sufficient, this activity remains addressable in separate lead series by relative BFE calculations.

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.

Salt Effect on Donnan Equilibrium in Montmorillonite Demonstrated with Molecular Dynamics Simulations

Donnan equilibrium governs the distribution of ions in many systems such as ion exchange membranes and biological cells in contact with an external electrolyte. Herein, Donnan equilibrium between bulk salt solution and bihydrated montmorillonite was investigated because such a system is of great importance for many nuclear waste disposal concepts. Specifically, we used molecular dynamics simulations to determine the partition coefficient of chloride, which was achieved by calculating the free-energy difference of chloride in the interlayer and the bulk using enhanced sampling methodology. Montmorillonite in equilibrium with either NaCl or CaCl₂ was examined to elucidate the general difference between 1:1 and 2:1 salts. The concentration dependence of the partition coefficient for each salt was determined using three and four concentrations for NaCl and CaCl₂, respectively. In the case of NaCl, we found that the partition coefficient increased linearly with the concentration, while for CaCl₂, the increase was proportional to the square root of the concentration. A derivation of the partition coefficient using general Donnan theory that includes excess free energy contributions beyond the electrostatic Donnan potential is also presented. For both salts, the agreement between the partition coefficient from the simulations and Donnan theory was excellent. Although Donnan theory is a continuum theory derived without any reference to atomistic details, the present results justify its application to systems with nanoscale pores.

CHARMM-GUI Enhanced Sampler for various collective variables and enhanced sampling methods

Enhanced sampling methodologies modifying underlying Hamiltonians can be used for the systems with a rugged potential energy surface that makes it hard to observe convergence using conventional unbiased molecular dynamics (MD) simulations. We present CHARMM-GUI Enhanced Sampler, a web-based tool to prepare various enhanced sampling simulations inputs with user-selected collective variables (CVs). Enhanced Sampler provides inputs for the following nine methods: accelerated MD, Gaussian accelerated MD, conformational flooding, metadynamics, adaptive biasing force, steered MD, temperature replica exchange MD, replica exchange solute tempering 2, and replica exchange umbrella sampling for the method-implemented MD packages including AMBER, CHARMM, GENESIS, GROMACS, NAMD, and OpenMM. Users only need to select a group of atoms via intuitive web-implementation in order to define commonly used nine CVs of interest: center of mass based distance, angle, dihedral, root-mean-square-distance, radius of gyration, distance projected on axis, two types of angles projected on axis, and coordination numbers. The enhanced sampling methods are tested with several biological systems to illustrate their efficiency over conventional MD. Enhanced Sampler with carefully optimized system-dependent parameters will help users to get meaningful results from their enhanced sampling simulations.

Multi-scale modeling of folic acid-functionalized TiO2 nanoparticles for active targeting of tumor cells

Strategies based on the active targeting of tumor cells are emerging as smart and efficient nanomedical procedures. Folic acid (FA) is a vitamin and a well-established tumor targeting agent because of its strong affinity for the folate receptor (FR), which is an overexpressed protein on the cell membranes of the tumor cells. FA can be successfully anchored to several nanocarriers, including inorganic nanoparticles (NPs) based on transition metal oxides. Among them, TiO₂ is extremely interesting because of its excellent photoabsorption and photocatalytic properties, which can be exploited in photodynamic therapy. However, it is not yet clear in which respects direct anchoring of FA to the NP or the use of spacers, based on polyethylene glycol (PEG) chains, are different and whether one approach is better than the other. In this work, we combine Quantum Mechanics (QM) and classical Molecular Dynamics (MD) to design and optimize the FA functionalization on bare and PEGylated TiO₂ models and to study the dynamical behavior of the resulting nanoconjugates in a pure water environment and in physiological conditions. We observe that they are chemically stable, even under the effect of increasing temperature (up to 500 K). Using the results from long MD simulations (100 ns) and from free energy calculations, we determine how the density of FA molecules on the TiO₂ NP and the presence of PEG spacers impact on the actual exposure of the ligands, especially by affecting the extent of FA-FA intermolecular interactions, which are detrimental for the targeting ability of FA towards the folate receptor. This analysis provides a solid and rational basis for experimentalists to define the optimal FA density and the more appropriate mode of anchoring to the carrier, according to the final purpose of the nanoconjugate.

Transition Rates and Efficiency of Collective Variables from Time-Dependent Biased Simulations

Simulations with adaptive time-dependent bias enable an efficient exploration of the conformational space of a system. However, the dynamic information is altered by the bias. Infrequent metadynamics recovers the transition rate of crossing a barrier, if the collective variables are ideal and there is no bias deposition near the transition state. Unfortunately, these conditions are not always fulfilled. To overcome these limitations, and inspired by single-molecule force spectroscopy, we use Kramers' theory for calculating the barrier-crossing rate when a time-dependent bias is added to the system. We assess the efficiency of collective variables parameter by measuring how efficiently the bias accelerates the transitions. We present approximate analytical expressions of the survival probability, reproducing the barrier-crossing time statistics and enabling the extraction of the unbiased transition rate even for challenging cases. We explore the limits of our method and provide convergence criteria to assess its validity.

A Multi-Scale Approach to Model K+ Permeation Through the KcsA Channel

K+ channels allow a very efficient passage of K+ ions through the membrane while excluding Na+ ions, and these properties are essential for life. The 3D structure of the KcsA K+ channel, solved more than 20 years ago, allows to address many relevant aspects of K+ permeation and selectivity mechanisms at the molecular level. Recent crystallographic data and molecular dynamics (MD) studies suggest that no water is normally present inside the selectivity filter (SF), which can instead accommodate four adjacent K+ ions. Using a multi-scale approach, whereby information taken from a low-level simulation approach is used to feed a high-level model, we studied the mechanism of K+ permeation through KcsA channels. More specifically, we used MD to find stable ion configurations under physiological conditions. They were characterized by two adjacent K+ ions occupying the more central positions of the SF (sites S2 and S3), while the other two K+ ions could be found at the external and internal entrances to the SF. Sites S1 and S4 were instead not occupied by K+. A continuum Bikerman–Poisson–Boltzmann model that takes into account the volume of the ions and their dehydration when entering the SF fully confirmed the MD results, showing peaks of K+ occupancy at S2, S3, and the external and internal entrances, with S1 and S4 sites being virtually never occupied by K+. Inspired by the newly found ion configuration in the SF at equilibrium, we developed a simple kinetic permeation model which, fed with kinetic rate constants assessed from molecular meta-dynamics, reproduced the main permeation properties of the KcsA channel found experimentally, including sublinear current-voltage and saturating conductance-concentration relationships. This good agreement with the experimental data also implies that the ion configuration in the SF we identified at equilibrium would also be a key configuration during permeation.

Consistent Picture of Phosphate-Divalent Cation Binding from Models with Implicit and Explicit Electronic Polarization

The binding of divalent cations to the ubiquitous phosphate group is essential for a number of key biological processes, such as DNA compaction, RNA folding, or interactions of some proteins with membranes. Yet, probing their binding sites, modes, and associated binding free energy is a challenge for both experiments and simulations. In simulations, standard force fields strongly overestimate the interaction between phosphate groups and divalent cations. Here, we examine how different strategies to include electronic polarization effects in force fields─implicitly, through the use of scaled charges or pair-specific Lennard-Jones parameters, or explicitly, with the polarizable force fields Drude and AMOEBA─capture the interactions of a model phosphate compound, dimethyl phosphate, with calcium and magnesium divalent cations. We show that both implicit and explicit approaches, when carefully parameterized, are successful in capturing the overall binding free energy and that common trends emerge from the comparison of different simulation approaches. Overall, the binding is very moderate, slightly weaker for Ca²⁺ than Mg²⁺, and the solvent-shared ion pair is slightly more stable than the contact monodentate ion pair. The bidentate ion pair is higher in energy (or even fully unstable for Mg²⁺). Our results thus suggest practical ways to capture the divalent cations with biomolecular phosphate groups in complex biochemical systems. In particular, the computational efficiency of implicit models makes them ideally suited for large-scale simulations of biological assemblies, with improved accuracy compared to state-of-the-art fixed-charge force fields.

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.

Deciphering Ethanol-Driven Swelling, Rupturing, Aggregation, and Fusion of Lipid Vesicles Using Coarse-Grained Molecular Dynamics Simulations

Traditionally, liquid ethanol is known to enhance the permeability of lipid membranes and causes vesicle aggregation and fusion. However, how the amphiphilic ethanol molecules perturb the lipid vesicles to facilitate their aggregation or fusion has not been addressed at any level of molecular simulations. Herein, not only have we developed a coarse-grained (CG) model for liquid ethanol, its aqueous mixture, and hydrated lipid membranes for molecular dynamics (MD) simulations, but also utilized it to delineate the aggregation and fusion of lipid vesicles using CG-MD simulations with multimillion particles. We have systematically parametrized the force-field for pure ethanol and its interactions with hydrated POPC and POPE model lipid membranes. In this process, we have successfully reproduced the bulk ethanol structure and concentration-dependent density of aqueous ethanol. To quantify the interaction of ethanol with lipid membranes, we have reproduced the transfer free energy of the ethanol molecule across the hydrated bilayers, and the concentration-dependent distribution of ethanol molecules across the lipid bilayers. After having acceptable force-field parameters for ethanol-membrane interactions, we have checked the effect of ethanol toward the vesicles comprising POPC lipids. We observe a rapid increase in the size of the POPC lipid vesicles with increasing amounts of ethanol up to 30 mol %. We unambiguously observe swelling and decrease in the thickness of the POPC vesicles with increasing amounts of ethanol up to 30 mol %, beyond which the vesicles begin to lose their integrity and rupture at higher mol % of ethanol. The fusion study of two vesicles demonstrates that fused vesicles can be obtained from 20 to 30 mol % of ethanol provided that they are brought closer than a critical distance at a particular mol %. The multivesicle simulations show that along with the increase in the sizes of vesicles the propensity of vesicle aggregation increases as the mol % of ethanol increases.

Protective Mechanism of a Layer-by-Layer-Assembled Artificial Cell Wall on Probiotics

Constructing an artificial cell wall (AFCW) based on the layer-by-layer assembly of polymer films to protect probiotics in harsh conditions is highly desirable. Early findings showed that encapsulating yeast cells by an AFCW improved the cell viability by 50% in antibiotic solution. However, the detailed molecular interaction mechanism remains unclear by experiments. Herein, two ciprofloxacin (CPFX) permeation models, including models 1 and 2 that were, respectively, composed of just the yeast cell membrane and the AFCW coating cell membrane, were investigated by molecular dynamics simulations. The free energy profiles delineating the permeation process of CPFX reveal that the permeation of CPFX through the cell membrane of model 2 is more difficult than through that of model 1. The analysis results show that the AFCW leads to two sharp increases in free energy barriers, amounting to 8.9 and 6.2 kcal/mol, thereby reducing the penetrating rate of CPFX into the cell membrane. Moreover, decomposition of the potentials of mean force into free energy components suggested that the electrostatic interactions of CPFX with the AFCW predominantly contributed to the high free energy barriers. The current results provide a good understanding of the protective mechanism of the self-assembled cell walls against CPFX and help to design other AFCWs.

Predicting the conformational variability of oncogenic GTP-bound G12D mutated KRas-4B proteins at zwitterionic model cell membranes

KRas proteins are the largest family of mutated Ras isoforms, participating in a wide variety of cancers. Due to their importance, large effort is being carried out on drug development by small-molecule inhibitors. However, understanding protein conformational variability remains a challenge in drug discovery. In the case of the Ras family, their multiple conformational states can affect the binding of potential drug inhibitors. To overcome this challenge, we propose a computational framework based on combined all-atom Molecular Dynamics and Metadynamics simulations in order to accurately access conformational variants of the target protein. We tested the methodology using a G12D mutated GTP bound oncogenic KRas-4B protein located at the interface of a DOPC/DOPS/cholesterol model anionic cell membrane. Two main orientations of KRas-4B at the anionic membrane have been determined. The corresponding torsional angles are taken as reliable reaction coordinates so that free-energy landscapes are obtained by well-tempered metadynamics simulations, revealing local and global minima of the free-energy hypersurface and unveiling reactive paths of the system between the two preferential orientations. We have observed that GTP-binding to KRas-4B has huge influence on the stabilisation of the protein and it can potentially help to open Switch I/II druggable pockets, lowering energy barriers between stable states and resulting in cumulative conformers of KRas-4B. This may highlight new opportunities for targeting the unique meta-stable states through the design of new efficient drugs.

Human Learning for Molecular Simulations: The Collective Variables Dashboard in VMD

The Collective Variables Dashboard is a software tool for real-time, seamless exploration of molecular structures and trajectories in a customizable space of collective variables. The Dashboard arises from the integration of the Collective Variables Module (also known as Colvars) with the visualization software VMD, augmented with a fully discoverable graphical interface offering interactive workflows for the design and analysis of collective variables. Typical use cases include a priori design of collective variables for enhanced sampling and free energy simulations as well as analysis of any type of simulation or collection of structures in a collective variable space. A combination of those cases commonly occurs when preliminary simulations, biased or unbiased, reveal that an optimized set of collective variables is necessary to improve sampling in further simulations. Then the Dashboard provides an efficient way to intuitively explore the space of likely collective variables, validate them on existing data, and use the resulting collective variable definitions directly in further biased simulations using the Collective Variables Module. Visualization of biasing energies and forces is proposed to help analyze or plan biased simulations. We illustrate the use of the Dashboard on two applications: discovering coordinates to describe ligand unbinding from a protein binding site and designing volume-based variables to bias the hydration of a transmembrane pore.

Small molecules enhance the potency of natural antimicrobial peptides

The skin-associated microbiome plays an important role in general well-being and in a variety of treatable skin conditions. In this regard, endogenous antimicrobial peptides have both a direct and indirect role in determining the composition of the microbiota. We demonstrate here that certain small molecular species can amplify the antimicrobial potency of naturally occurring antimicrobial peptides. In this study, we have used niacinamide, a form of vitamin B3 naturally found in foods and widely used in cosmetic skincare products, and two of its structural analogs, to investigate their cooperativity with the human antimicrobial peptide LL37 on the bacterium Staphylococcus aureus. We observed a clear synergistic effect of niacinamide and, to some extent, N-methylnicotinamide, whereas isonicotinamide showed no significant cooperativity with LL37. Adaptively biased molecular dynamics simulations using simplified model membrane substrates and single peptides revealed that these molecules partition into the headgroup region of an anionic bilayer used to mimic the bacterial membrane. The simulated effects on the physical properties of the simulated model membrane are well correlated with experimental activity observed in real biological assays despite the simplicity of the model. In contrast, these molecules have little effect on zwitterionic bilayers that mimic a mammalian membrane. We conclude that niacinamide and N-methylnicotinamide can therefore potentiate the activity of host peptides by modulating the physical properties of the bacterial membrane, and to a lesser extent through direct interactions with the peptide. The level of cooperativity is strongly dependent on the detailed chemistry of the additive, suggesting an opportunity to fine-tune the behavior of host peptides.

An Efficient Gaussian-Accelerated Molecular Dynamics (GaMD) Multilevel Enhanced Sampling Strategy: Application to Polarizable Force Fields Simulations of Large Biological Systems

We introduce a novel multilevel enhanced sampling strategy grounded on Gaussian-accelerated Molecular Dynamics (GaMD). First, we propose a GaMD multi-GPUs-accelerated implementation within the Tinker-HP molecular dynamics package. We introduce the new "dual-water" mode and its use with the flexible AMOEBA polarizable force field. By adding harmonic boosts to the water stretching and bonding terms, it accelerates the solvent-solute interactions while enabling speedups, thanks to the use of fast multiple-time step integrators. To further reduce the time-to-solution, we couple GaMD to Umbrella Sampling (US). The GaMD─US/dual-water approach is tested on the 1D Potential of Mean Force (PMF) of the solvated CD2-CD58 system (168 000 atoms), allowing the AMOEBA PMF to converge within 1 kcal/mol of the experimental value. Finally, Adaptive Sampling (AS) is added, enabling AS-GaMD capabilities but also the introduction of the new Adaptive Sampling-US-GaMD (ASUS-GaMD) scheme. The highly parallel ASUS-GaMD setup decreases time to convergence by, respectively, 10 and 20 times, compared to GaMD-US and US. Overall, beside the acceleration of PMF computations, Tinker-HP now allows for the simultaneous use of Adaptive Sampling and GaMD-"dual water" enhanced sampling approaches increasing the applicability of polarizable force fields to large-scale simulations of biological systems.

Computational investigation of the impact of core sequence on immobile DNA four-way junction structure and dynamics

Immobile four-way junctions (4WJs) are core structural motifs employed in the design of programmed DNA assemblies. Understanding the impact of sequence on their equilibrium structure and flexibility is important to informing the design of complex DNA architectures. While core junction sequence is known to impact the preferences for the two possible isomeric states that junctions reside in, previous investigations have not quantified these preferences based on molecular-level interactions. Here, we use all-atom molecular dynamics simulations to investigate base-pair level structure and dynamics of four-way junctions, using the canonical Seeman J1 junction as a reference. Comparison of J1 with equivalent single-crossover topologies and isolated nicked duplexes reveal conformational impact of the double-crossover motif. We additionally contrast J1 with a second junction core sequence termed J24, with equal thermodynamic preference for each isomeric configuration. Analyses of the base-pair degrees of freedom for each system, free energy calculations, and reduced-coordinate sampling of the 4WJ isomers reveal the significant impact base sequence has on local structure, isomer bias, and global junction dynamics.

Pyranose Ring Puckering Thermodynamics for Glycan Monosaccharides Associated with Vertebrate Proteins

The conformational properties of carbohydrates can contribute to protein structure directly through covalent conjugation in the cases of glycoproteins and proteoglycans and indirectly in the case of transmembrane proteins embedded in glycolipid-containing bilayers. However, there continue to be significant challenges associated with experimental structural biology of such carbohydrate-containing systems. All-atom explicit-solvent molecular dynamics simulations provide a direct atomic resolution view of biomolecular dynamics and thermodynamics, but the accuracy of the results depends on the quality of the force field parametrization used in the simulations. A key determinant of the conformational properties of carbohydrates is ring puckering. Here, we applied extended system adaptive biasing force (eABF) all-atom explicit-solvent molecular dynamics simulations to characterize the ring puckering thermodynamics of the ten common pyranose monosaccharides found in vertebrate biology (as represented by the CHARMM carbohydrate force field). The results, along with those for idose, demonstrate that the CHARMM force field reliably models ring puckering across this diverse set of molecules, including accurately capturing the subtle balance between 4C1 and 1C4 chair conformations in the cases of iduronate and of idose. This suggests the broad applicability of the force field for accurate modeling of carbohydrate-containing vertebrate biomolecules such as glycoproteins, proteoglycans, and glycolipids.

Molecular Simulations of Surfactant Adsorption on Iron Oxide from Hydrocarbon Solvents

The performance of organic friction modifiers (OFMs) depends on their ability to adsorb onto surfaces and form protective monolayers. Understanding the relationship between OFM concentration in the base oil and the resulting surface coverage is important for improving lubricant formulations. Here, we use molecular dynamics (MD) simulations to study the adsorption of three OFMs─stearic acid (SA), glycerol monoostearate (GMS), and glycerol monooleate (GMO)─onto a hematite surface from two hydrocarbon solvents─n-hexadecane and poly(α-olefin) (PAO). We calculate the potential of mean force of the adsorption process using the adaptive biasing force algorithm, and the adsorption strength increases in the order SA < GMS < GMO. We estimate the minimum area occupied by OFM molecules on the surface using annealing MD simulations and obtained a similar hard-disk area for GMS and GMO but a lower value for SA. Using the MD results, we determine the adsorption isotherms using the molecular thermodynamic theory (MTT), which agree well with one previous experimental data set for SA on hematite. For two other experimental data sets for SA, lateral interactions between surfactant molecules need to be accounted for within the MTT framework. SA forms monolayers with lower surface coverage than GMO and GMS at low concentrations but also has the highest plateau coverage. We validate the adsorption energies from the MD simulations using high-frequency reciprocating rig friction experiments with different concentrations of the OFMs in PAO. For OFMs with saturated tailgroups (SA and GMS), we obtain good agreement between the simulations and the experiments. The results deviate for OFMs containing Z-unsaturated tailgroups (GMO) due to the additional steric hindrance, which is not accounted for in the current simulation framework. This study demonstrates that MD simulations, alongside MTT, are an accurate and efficient tool to predict adsorption isotherms at solid-liquid interfaces.

Energy landscapes and dynamics of ion translocation through membrane transporters: a meeting ground for physics, chemistry, and biology

The dynamics of ion translocation through membrane transporters is visualized from a comprehensive point of view by a Gibbs energy landscape approach. The ΔG calculations have been performed with the Kirkwood-Tanford-Warshel (KTW) electrostatic theory that properly takes into account the self-energies of the ions. The Gibbs energy landscapes for translocation of a single charge and an ion pair are calculated, compared, and contrasted as a function of the order parameter, and the characteristics of the frustrated system with bistability for the ion pair are described and quantified in considerable detail. These calculations have been compared with experimental data on the ΔG of ion pairs in proteins. It is shown that, under suitable conditions, the adverse Gibbs energy barrier can be almost completely compensated by the sum of the electrostatic energy of the charge-charge interactions and the solvation energy of the ion pair. The maxima in ΔG_KTW with interionic distance in the bound H⁺ - A^- charge pair on the enzyme is interpreted in thermodynamic and molecular mechanistic terms, and biological implications for molecular mechanisms of ATP synthesis are discussed. The timescale at which the order parameter moves between two stable states has been estimated by solving the dynamical equations of motion, and a wealth of novel insights into energy transduction during ATP synthesis by the membrane-bound F_OF₁-ATP synthase transporter is offered. In summary, a unifying analytical framework that integrates physics, chemistry, and biology has been developed for ion translocation by membrane transporters for the first time by means of a Gibbs energy landscape approach.

Force-Correction Analysis Method for Derivation of Multidimensional Free-Energy Landscapes from Adaptively Biased Replica Simulations

A methodology is proposed for the calculation of multidimensional free-energy landscapes of molecular systems, based on analysis of multiple molecular dynamics trajectories wherein adaptive biases have been applied to enhance the sampling of different collective variables. In this approach, which we refer to as the Force-Correction Analysis Method (FCAM), local averages of the total and biasing forces are evaluated post hoc, and the latter are subtracted from the former to obtain unbiased estimates of the mean force across collective-variable space. Multidimensional free-energy surfaces and minimum free-energy pathways are then derived by integrating the mean-force landscape with a kinetic Monte Carlo algorithm. To evaluate the proposed method, a series of numerical tests and comparisons with existing approaches were carried out for small molecules, peptides, and proteins, based on all-atom trajectories generated with standard, concurrent, and replica-exchange metadynamics in collective-variable spaces ranging from one to six dimensional. The tests confirm the correctness of the FCAM formulation and demonstrate that calculated mean forces and free energies converge rapidly and accurately, outperforming other methods used to unbias this kind of simulation data.

Fast and Accurate Multidimensional Free Energy Integration

Enhanced sampling and free energy calculation algorithms of the thermodynamic integration family (such as the adaptive biasing force (ABF) method) are not based on the direct computation of a free energy surface but rather of its gradient. Integrating the free energy surface is nontrivial in dimensions higher than one. Here, the author introduces a flexible, portable implementation of a Poisson equation formalism to integrate free energy surfaces from estimated gradients in dimensions 2 and 3 using any combination of periodic and nonperiodic (Neumann) boundary conditions. The algorithm is implemented in portable C++ and provided as a standalone tool that can be used to integrate multidimensional gradient fields estimated on a grid using any algorithm, such as umbrella integration as a post-treatment of umbrella sampling simulations. It is also included in the implementation of ABF (and its extended-system variant eABF) in the Collective Variables Module, enabling the seamless computation of multidimensional free energy surfaces within ABF and eABF simulations. A Python-based analysis toolchain is provided to easily plot and analyze multidimensional ABF simulation results, including metrics to assess their convergence. The Poisson integration algorithm can also be used to perform Helmholtz decomposition of noisy gradient estimates on the fly, resulting in an efficient implementation of the projected ABF (pABF) method proposed by Leliévre and co-workers. In numerical tests, pABF is found to lead to faster convergence with respect to ABF in simple cases of low intrinsic dimension but seems detrimental to convergence in a more realistic case involving degenerate coordinates and hidden barriers due to slower exploration. This suggests that variance reduction schemes do not always yield convergence improvements when applied to enhanced sampling methods.

Mechanistic Insight on BioIL-Induced Structural Alterations in DMPC Lipid Bilayer

The emerging application risks of traditional ionic liquids (ILs) toward the ecosystem have changed the perception regarding their greenness. This resulted in the exploration of their more biocompatible alternatives known as biocompatible ILs (BioILs). Here, we have investigated the impact of two such biocompatible cholinium amino acid-based ILs on the structural behavior of model homogeneous DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) lipid bilayer using all-atom molecular dynamics simulation technique. Two classic cholinium-amino acid-based ILs, cholinium glycinate ([Ch][Gly]) and cholinium phenylalaninate ([Ch][Phe]), which differ only by the side chain lengths and hydrophobicity of the anions, have been utilized in the present work. Simultaneous analysis of the bilayer structural properties reveals that the existence of [Ch][Gly] BioIL above a particular concentration induces phase transition from fluid phase to gel phase in the DMPC lipid bilayer. Such a freezing of lipid bilayer upon the exposure to concentrated aqueous solution of [Ch][Gly] BioIL indicates the harmfulness of this BioIL toward the cell membranes majorly containing DMPC lipids, as the cell freezing can negatively affect its stability and functionality. Despite having a more hydrophobic amino acid side chain of [Phe]^- anion in [Ch][Phe], in the case of bilayer-[Ch][Phe] systems we observe the minimal impact of [Ch][Phe] BioIL on the DMPC bilayer properties up to 10 mol % concentration. In the presence of these BioIL, we observe the thickening of the bilayer and accumulation of the cations and anions of the BioILs at the interface of DMPC lipid heads and tails. The transfer free-energy profile of a [Phe]^- anion from aqueous phase to membrane center also indicates the anion partitioning at lipid head-tail interface and its inability to penetrate in the lipid membrane tail region. In contrast, the free-energy profile for a [Gly]^- anion offers a very high energy barrier to the insertion of [Gly]^- into the membrane interior, leading to accumulation of [Gly]^- anions at the lipid head-water region.

Diptool-A Novel Numerical Tool for Membrane Interactions Analysis, Applying to Antimicrobial Detergents and Drug Delivery Aids

The widespread problem of resistance development in bacteria has become a critical issue for modern medicine. To limit that phenomenon, many compounds have been extensively studied. Among them were derivatives of available drugs, but also alternative novel detergents such as Gemini surfactants. Over the last decade, they have been massively synthesized and studied to obtain the most effective antimicrobial agents, as well as the most selective aids for nanoparticles drug delivery. Various protocols and distinct bacterial strains used in Minimal Inhibitory Concentration experimental studies prevented performance benchmarking of different surfactant classes over these last years. Motivated by this limitation, we designed a theoretical methodology implemented in custom fast screening software to assess the surfactant activity on model lipid membranes. Experimentally based QSAR (quantitative structure-activity relationship) prediction delivered a set of parameters underlying the Diptool software engine for high-throughput agent-membrane interactions analysis. We validated our software by comparing score energy profiles with Gibbs free energy from the Adaptive Biasing Force approach on octenidine and chlorhexidine, popular antimicrobials. Results from Diptool can reflect the molecule behavior in the lipid membrane and correctly predict free energy of translocation much faster than classic molecular dynamics. This opens a new venue for searching novel classes of detergents with sharp biologic activity.