Evaluating Force Fields for the Computational Prediction of Ionized Arginine and Lysine Side-Chains Partitioning into Lipid Bilayers and Octanol

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.

Biomolecular Modeling and Simulation: A Prospering Multidisciplinary Field

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

Computational and Experimental Approaches to Investigate Lipid Nanoparticles as Drug and Gene Delivery Systems

Lipid nanoparticles (LNPs) have been widely applied in drug and gene delivery. More than twenty years ago, DoxilTM was the first LNPs-based drug approved by the US Food and Drug Administration (FDA). Since then, with decades of research and development, more and more LNP-based therapeutics have been used to treat diverse diseases, which often offer the benefits of reduced toxicity and/or enhanced efficacy compared to the active ingredients alone. Here, we provide a review of recent advances in the development of efficient and robust LNPs for drug/gene delivery. We emphasize the importance of rationally combining experimental and computational approaches, especially those providing multiscale structural and functional information of LNPs, to the design of novel and powerful LNP-based delivery systems.

Driving Force for the Complexation of Charged Polypeptides

The phase separation of oppositely charged polyelectrolytes in solution is of current interest. In this work, we study the driving force for polyelectrolyte complexation using molecular dynamics simulations. We calculate the potential of mean force between poly(lysine) and poly(glutamate) oligomers using three different force fields, an atomistic force field and two coarse-grained force fields. There is qualitative agreement between all force fields, i.e., the sign and magnitude of the free energy and the nature of the driving force are similar, which suggests that the molecular nature of water does not play a significant role. For fully charged peptides, we find that the driving force for association is entropic in all cases when small ions either neutralize the poly ions, or are in excess. The removal of all counterions switches the driving force, making complexation energetic. This suggests that the entropy of complexation is dominated by the counterions. When only 6 residues of a 11-mer are charged, however, the driving force is energetic in the abscence of excess salt. The simulations shed insight into the mechanism of complex coacervation and the importance of realistic models for the polyions.

Coarse-grained model of titrating peptides interacting with lipid bilayers

Molecular-level computer simulations of peptide aggregation, translocation, and protonation at and in biomembranes are impeded by the large time and length scales involved. We present a computationally efficient, coarse-grained, and solvent-free model for the interaction between lipid bilayers and peptides. The model combines an accurate description of mechanical membrane properties with a new granular representation of the dielectric mismatch between lipids and the aqueous phase. All-atom force fields can be easily mapped onto the coarse-grained model, and parameters for coarse-grained monopeptides accurately extrapolate to membrane permeation free energies for the corresponding dipeptides and tripeptides. Acid-base equilibria of titratable amino acid residues are further studied using a constant-pH ensemble, capturing protonation state changes upon membrane translocation. Important differences between histidine, lysine, and arginine are observed, which are in good agreement with experimental observations.

Characterizing the Molecular Mechanisms for Flipping Charged Peptide Flanking Loops across a Lipid Bilayer

The cell membrane largely prevents the passive diffusion of charged molecules due to the large free energy barrier associated with translocating charged groups across the hydrophobic lipid bilayer core. Despite this barrier, some peptides can interconvert between transmembrane and surface-adsorbed states by "flipping" charged flanking loops across the bilayer on a surprisingly rapid second-minute time scale. The transmembrane helices of some multispanning membrane proteins undergo similar reorientation processes, suggesting that loop-flipping may be a mechanism for regulating membrane protein topology; however, the molecular mechanisms underlying this behavior remain unknown. In this work, we study the loop-flipping behavior exhibited by a peptide with a hydrophobic transmembrane helix, charged flanking loops, and a central, membrane-exposed aspartate residue of varying protonation state. We utilize all-atom temperature accelerated molecular dynamics simulations to predict the likelihood of loop-flipping without predefining specific loop-flipping pathways. We demonstrate that this approach can identify multiple possible flipping pathways, with the prevalence of each pathway depending on the protonation state of the central residue. In particular, we find that a charged central residue facilitates loop-flipping by stabilizing membrane water defects, enabling the "self-catalysis" of charge translocation. These findings provide detailed molecular-level insights into charged loop-flipping pathways that may generalize to other charge translocation processes, such as lipid flip-flop or the large-scale conformational rearrangements of multispanning membrane proteins.

Determination of Ionic Hydration Free Energies with Grand Canonical Monte Carlo/Molecular Dynamics Simulations in Explicit Water

Grand canonical Monte Carlo (GCMC) simulations of ionic solutions with explicit solvent models are known to be challenging. One challenge arises from the treatment of long-range electrostatics and finite-box size in Monte Carlo simulations when periodic boundary condition and Ewald summation methods are used. Another challenge is that constant excess chemical potential GCMC simulations for charged solutes suffer from inadequate insertion and deletion acceptance ratios. In this work, we address those problems by implementing an oscillating excess chemical potential GCMC algorithm with smooth particle mesh Ewald and finite-box-size corrections to treat the long-range electrostatics. The developed GCMC simulation program was combined with GROMACS to perform GCMC/MD simulations of ionic solutions individually containing Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺, F^-, Cl^-, Br^-, I^-, Ca²⁺, and Mg²⁺, respectively. Our simulation results show that the combined GCMC/MD approach can approximate the ionic hydration free energies with proper treatment of long-range electrostatics. Our developed simulation approach can open up new avenues for simulating complex chemical and biomolecular systems and for drug discovery.

Free Energy Calculations of Membrane Permeation: Challenges Due to Strong Headgroup-Solute Interactions

Understanding how different classes of molecules move across biological membranes is a prerequisite to predicting a solute's permeation rate, which is a critical factor in the fields of drug design and pharmacology. We use biased molecular dynamics computer simulations to calculate and compare the free energy profiles of translocation of several small molecules across 1,2-dioleoyl- sn-glycero-3-phosphocholine (DOPC) lipid bilayers as a first step toward determining the most efficient method for free energy calculations. We study the translocation of arginine, a sodium ion, alanine, and a single water molecule using the metadynamics, umbrella sampling, and replica exchange umbrella sampling techniques. Within the fixed lengths of our simulations, we find that all methods produce similar results for charge-neutral permeants, but not for polar or positively charged molecules. We identify the long relaxation time scale of electrostatic interactions between lipid headgroups and the solute to be the principal cause of this difference and show that this slow process can lead to an erroneous dependence of computed free energy profiles on the initial system configuration. We demonstrate the use of committor analysis to validate the proper sampling of the presumed transition state, which in our simulations is achieved only in replica exchange calculations. On the basis of these results we provide some useful guidance to perform and evaluate free energy calculations of membrane permeation.

Refining amino acid hydrophobicity for dynamics simulation of membrane proteins

Coarse-grained (CG) models have been successful in simulating the chemical properties of lipid bilayers, but accurate treatment of membrane proteins and lipid-protein molecular interactions remains a challenge. The CgProt force field, original developed with the multiscale coarse graining method, is assessed by comparing the potentials of mean force for sidechain insertion in a DOPC bilayer to results reported for atomistic molecular dynamics simulations. Reassignment of select CG sidechain sites from the apolar to polar site type was found to improve the attractive interfacial behavior of tyrosine, phenylalanine and asparagine as well as charged lysine and arginine residues. The solvation energy at membrane depths of 0, 1.3 and 1.7 nm correlates with experimental partition coefficients in aqueous mixtures of cyclohexane, octanol and POPC, respectively, for sidechain analogs and Wimley-White peptides. These experimental values serve as important anchor points in choosing between alternate CG models based on their observed permeation profiles, particularly for Arg, Lys and Gln residues where the all-atom OPLS solvation energy does not agree well with experiment. Available partitioning data was also used to reparameterize the representation of the peptide backbone, which needed to be made less attractive for the bilayer hydrophobic core region. The newly developed force field, CgProt 2.4, correctly predicts the global energy minimum in the potentials of mean force for insertion of the uncharged membrane-associated peptides LS3 and WALP23. CgProt will find application in studies of lipid-protein interactions and the conformational properties of diverse membrane protein systems.

Critical Comparison of Biomembrane Force Fields: Protein-Lipid Interactions at the Membrane Interface

Molecular dynamics (MD) simulations offer the possibility to study biological processes at high spatial and temporal resolution often not reachable by experiments. Corresponding biomolecular force field parameters have been developed for a wide variety of molecules ranging from inorganic ligands and small organic molecules over proteins and lipids to nucleic acids. Force fields have typically been parametrized and validated on thermodynamic observables and structural characteristics of individual compounds, e.g. of soluble proteins or lipid bilayers. Less strictly, due to the added complexity and missing experimental data to compare to, force fields have hardly been tested on the properties of mixed systems, e.g. on protein-lipid systems. Their selection and combination for mixed systems is further complicated by the partially differing parametrization strategies. Additionally, the presence of other compounds in the system may shift the subtle balance of force field parameters. Here, we assessed the protein-lipid interactions as described in the four atomistic force fields GROMOS54a7, CHARMM36 and the two force field combinations Amber14sb/Slipids and Amber14sb/Lipid14. Four observables were compared, focusing on the membrane-water interface: the conservation of the secondary structure of transmembrane proteins, the positioning of transmembrane peptides relative to the lipid bilayer, the insertion depth of side chains of unfolded peptides absorbed at the membrane interface, and the ability to reproduce experimental insertion energies of Wimley-White peptides at the membrane interface. Significant differences between the force fields were observed that affect e.g. membrane insertion depths and tilting of transmembrane peptides.

Probing a Continuous Polar Defect: A Reaction Coordinate for Pore Formation in Lipid Membranes

Various biophysical processes involve the formation of aqueous pores over lipid membranes, including processes of membrane fusion, antimicrobial peptide activity, lipid flip-flop, and membrane permeation. Reliable and efficient free-energy calculations of pore formation using molecular dynamics simulations remained challenging due to the lack of good reaction coordinates (RCs) for pore formation. We present a new RC for pore formation that probes the formation and rupture of a continuous polar defect over the membrane. Potential of mean force (PMF) calculations along the new RC rapidly converge and exhibit no hysteresis between pore-opening and pore-closing pathways, in contrast to calculations based on previous RCs. We show that restraints along the new RC may restrain the system tightly to the transition state of pore formation, rationalizing the absence of hysteresis. We observe that the PMF of pore formation in a tension-free membrane of dimyristoylphosphatidylcholine (DMPC) reveals a free-energy barrier for pore nucleation, confirming a long-hypothesized metastable prepore state. We test the influence of the lipid force field, the cutoff distance used for Lennard-Jones interactions, and the lateral membrane size on the free energies of pore formation. In contrast to PMF calculations based on previous RCs, we find that such parameters have a relatively small influence on the free energies of pore nucleation. However, the metastability of the open pore in DMPC may depend on such parameters. The RC has been implemented into an extension of the GROMACS simulation software. The new RC allows for reliable and computationally efficient free-energy calculations of pore formation in lipid membranes.

Grafting Charged Species to Membrane-Embedded Scaffolds Dramatically Increases the Rate of Bilayer Flipping

The cell membrane is a barrier to the passive diffusion of charged molecules due to the chemical properties of the lipid bilayer. Surprisingly, recent experiments have identified processes in which synthetic and biological charged species directly transfer across lipid bilayers on biologically relevant time scales. In particular, amphiphilic nanoparticles have been shown to insert into lipid bilayers, requiring the transport of charged species across the bilayer. The molecular factors facilitating this rapid insertion process remain unknown. In this work, we use atomistic molecular dynamics simulations to calculate the free energy barrier associated with "flipping" charged species across a lipid bilayer for species that are grafted to a membrane-embedded scaffold, such as a membrane-embedded nanoparticle. We find that the free energy barrier for flipping a grafted ligand can be over 7 kcal/mol lower than the barrier for translocating an isolated, equivalent ion, yielding a 5 order of magnitude decrease in the corresponding flipping time scale. Similar results are found for flipping charged species grafted to either nanoparticle or protein scaffolds. These results reveal new mechanistic insight into the flipping of charged macromolecular components that might play an important, yet overlooked, role in signaling and charge transport in biological settings. Furthermore, our results suggest guidelines for the design of synthetic materials capable of rapidly flipping charged moieties across the cell membrane.

Glycosylation and Lipids Working in Concert Direct CD2 Ectodomain Orientation and Presentation

Proteins embedded in the plasma membrane mediate interactions with the cell environment and play decisive roles in many signaling events. For cell-cell recognition molecules, it is highly likely that their structures and behavior have been optimized in ways that overcome the limitations of membrane tethering. In particular, the ligand binding regions of these proteins likely need to be maximally exposed. Here we show by means of atomistic simulations of membrane-bound CD2, a small cell adhesion receptor expressed by human T-cells and natural killer cells, that the presentation of its ectodomain is highly dependent on membrane lipids and receptor glycosylation acting in apparent unison. Detailed analysis shows that the underlying mechanism is based on electrostatic interactions complemented by steric interactions between glycans in the protein and the membrane surface. The findings are significant for understanding the factors that render membrane receptors accessible for binding and signaling.

Coarse-grained simulations of hemolytic peptide δ-lysin interacting with a POPC bilayer

δ-lysin, secreted by a Gram-positive bacterium Staphylococcus aureus, is a 26-residue membrane active peptide that shares many common features with antimicrobial peptides (AMPs). However, it possesses a few unique features that differentiate itself from typical AMPs. In particular, δ-lysin has zero net charge, even though it has many charged residues, and it preferentially lyses eukaryotic cells over bacterial cells. Here, we present the results of coarse-grained molecular dynamics simulations of δ-lysin interacting with a zwitterionic membrane over a wide range of peptide concentrations. When the peptides concentration is low, spontaneous dimerization of peptides is observed on the membrane surface, but deep insertion of peptides or pore formation was not observed. However, the calculated free energy of peptide insertion suggests that a small fraction of peptides is likely to be present inside the membrane at the peptide concentrations typically seen in dye efflux experiments. When the simulations with multiple peptides are carried out with a single pre-inserted transmembrane peptide, spontaneous pore formation occurs with a peptide-to-lipid ratio (P/L) as low as P/L=1:42. Inter-peptide salt bridges among the transmembrane peptides seem to play a role in creating compact pores with very low level of hydration. More importantly, the transmembrane peptides making up the pore are constantly pushed to the opposite side of the membrane when the mass imbalance between the two sides of membrane is significant. Thus, the pore is very dynamic, allowing multiple peptides to translocate across the membrane simultaneously.

Estimation of Liposome Penetration Barriers of Drug Molecules with All-Atom and Coarse-Grained Models

Liposomes are common carriers of drug molecules, providing enhanced delivery and accumulation of hydrophilic agents or larger biomolecules. Molecular simulations can be used to estimate key features of the drug molecules upon interaction with the liposomes, such as penetration barriers and localization. Herein, we investigate several aspects of the computational estimation of penetration barriers, viz. the potential of mean force (PMFs) along a vector spanning the membrane. First, we provide an evaluation of the all-atom (AA) and coarse-grained (CG) parametrization of 5-aminolevulinic acid (5-ALA) and two of its alkyl esters by computing n-octanol/water partition coefficients. We find that the CG parametrization of the esters performs significantly better than the CG model of 5-ALA, highlighting the difficulty to coarse-grain small, polar molecules. However, the expected trend in partition coefficients is reproduced also with the CG models. Second, we compare PMFs in a small membrane slab described with either the AA or CG models. Here, we are able to reproduce the all-atom PMF of 5-ALA with CG. However, for the alkyl esters it is unfortunately not possible to correctly reproduce both the depth and the penetration barrier of the PMF seen in the AA simulations with any of the tested CG models. We argue that it is more important to choose a CG parametrization that reproduces the depth of the PMF. Third, we compare, using the CG model, PMFs in the membrane slab with PMFs in a large, realistic liposome. We find similar depths but slightly different penetration barriers most likely due to differences in the lipid density along the membrane axis. Finally, we compute PMFs in liposomes with three different lipid compositions. Unfortunately, differences in the PMFs could not be quantified, and it remains to be investigated to what extent liposome simulations can fully reproduce experimental findings.

Microscopic Characterization of Membrane Transporter Function by In Silico Modeling and Simulation

Membrane transporters mediate one of the most fundamental processes in biology. They are the main gatekeepers controlling active traffic of materials in a highly selective and regulated manner between different cellular compartments demarcated by biological membranes. At the heart of the mechanism of membrane transporters lie protein conformational changes of diverse forms and magnitudes, which closely mediate critical aspects of the transport process, most importantly the coordinated motions of remotely located gating elements and their tight coupling to chemical processes such as binding, unbinding and translocation of transported substrate and cotransported ions, ATP binding and hydrolysis, and other molecular events fueling uphill transport of the cargo. An increasing number of functional studies have established the active participation of lipids and other components of biological membranes in the function of transporters and other membrane proteins, often acting as major signaling and regulating elements. Understanding the mechanistic details of these molecular processes require methods that offer high spatial and temporal resolutions. Computational modeling and simulations technologies empowered by advanced sampling and free energy calculations have reached a sufficiently mature state to become an indispensable component of mechanistic studies of membrane transporters in their natural environment of the membrane. In this article, we provide an overview of a number of major computational protocols and techniques commonly used in membrane transporter modeling and simulation studies. The article also includes practical hints on effective use of these methods, critical perspectives on their strengths and weak points, and examples of their successful applications to membrane transporters, selected from the research performed in our own laboratory.

Sampling errors in free energy simulations of small molecules in lipid bilayers

Free energy simulations are a powerful tool for evaluating the interactions of molecular solutes with lipid bilayers as mimetics of cellular membranes. However, these simulations are frequently hindered by systematic sampling errors. This review highlights recent progress in computing free energy profiles for inserting molecular solutes into lipid bilayers. Particular emphasis is placed on a systematic analysis of the free energy profiles, identifying the sources of sampling errors that reduce computational efficiency, and highlighting methodological advances that may alleviate sampling deficiencies. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Maximally asymmetric transbilayer distribution of anionic lipids alters the structure and interaction with lipids of an amyloidogenic protein dimer bound to the membrane surface

We used molecular dynamics simulations to explore the effects of asymmetric transbilayer distribution of anionic phosphatidylserine (PS) lipids on the structure of a protein on the membrane surface and subsequent protein-lipid interactions. Our simulation systems consisted of an amyloidogenic, beta-sheet rich dimeric protein (D42) absorbed to the phosphatidylcholine (PC) leaflet, or protein-contact PC leaflet, of two membrane systems: a single-component PC bilayer and double PC/PS bilayers. The latter comprised of a stable but asymmetric transbilayer distribution of PS in the presence of counterions, with a 1-component PC leaflet coupled to a 1-component PS leaflet in each bilayer. The maximally asymmetric PC/PS bilayer had a non-zero transmembrane potential (TMP) difference and higher lipid order packing, whereas the symmetric PC bilayer had a zero TMP difference and lower lipid order packing under physiologically relevant conditions. Analysis of the adsorbed protein structures revealed weaker protein binding, more folding in the N-terminal domain, more aggregation of the N- and C-terminal domains and larger tilt angle of D42 on the PC leaflet surface of the PC/PS bilayer versus the PC bilayer. Also, analysis of protein-induced membrane structural disruption revealed more localized bilayer thinning in the PC/PS versus PC bilayer. Although the electric field profile in the non-protein-contact PS leaflet of the PC/PS bilayer differed significantly from that in the non-protein-contact PC leaflet of the PC bilayer, no significant difference in the electric field profile in the protein-contact PC leaflet of either bilayer was evident. We speculate that lipid packing has a larger effect on the surface adsorbed protein structure than the electric field for a maximally asymmetric PC/PS bilayer. Our results support the mechanism that the higher lipid packing in a lipid leaflet promotes stronger protein-protein but weaker protein-lipid interactions for a dimeric protein on membrane surfaces.

Molecular simulation of nonfacilitated membrane permeation

This is a review. Non-electrolytic compounds typically cross cell membranes by passive diffusion. The rate of permeation is dependent on the chemical properties of the solute and the composition of the lipid bilayer membrane. Predicting the permeability coefficient of a solute is important in pharmaceutical chemistry and toxicology. Molecular simulation has proven to be a valuable tool for modeling permeation of solutes through a lipid bilayer. In particular, the solubility-diffusion model has allowed for the quantitative calculation of permeability coefficients. The underlying theory and computational methods used to calculate membrane permeability are reviewed. We also discuss applications of these methods to examine the permeability of solutes and the effect of membrane composition on permeability. The application of coarse grain and polarizable models is discussed. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Multistep Molecular Dynamics Simulations Identify the Highly Cooperative Activity of Melittin in Recognizing and Stabilizing Membrane Pores

The prototypical antimicrobial peptide, melittin, is well-known for its ability to induce pores in zwitterionic model lipid membranes. However, the mechanism by which melittin accomplishes this is not fully understood. We have conducted all-atom and coarse-grained molecular dynamics simulations which suggest that melittin employs a highly cooperative mechanism for the induction of both small and large membrane pores. The process by which this peptide induces membrane pores appears to be driven by its affinity to membrane defects via its N-terminus region. In our simulations, a membrane defect was deliberately created through either lipid flip-flop or the reorientation of one adsorbed melittin peptide. In a cooperative response, other melittin molecules also inserted their N-termini into the created defect, thus lowering the overall free energy. The insertion of these peptide molecules ultimately allowed the defect to develop into a small transmembrane pore, with an estimated diameter of ∼1.5 nm and a lifetime of the order of tens of milliseconds. In the presence of a finite membrane tension, we show that this small pore can act as a nucleation site for the stochastic rupture of the lipid bilayer, so as to create a much larger pore. We found that a threshold membrane tension of 25 mN/m was needed to create a ruptured pore. Furthermore, by actively accumulating at its edge, adsorbed peptides are able to cooperatively stabilize this larger pore. The defect-mediated pore formation mechanism revealed in this work may also apply to other amphipathic membrane-active peptides.