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

Multifaceted Activity of Fabimycin: Insights from Molecular Dynamics Studies on Bacterial Membrane Models

Membranes─cells' essential scaffolds─are valid molecular targets for substances with an antimicrobial effect. While certain substances, such as octenidine, have been developed to target membranes for antimicrobial purposes, the recently reported molecule, fabimycin (F2B)─a novel agent targeting drug-resistant Gram-negative bacteria─has not received adequate attention regarding its activity on membranes in the literature. The following study aims to investigate the effects of F2B on different bacterial membrane models, including simple planar bilayers and more complex bilayer systems that mimic the Escherichia coli shell equipped with double inner and outer bilayers. Our results show that F2B exhibited more pronounced interactions with bacterial membrane systems compared to the control PC system. Furthermore, we observed significant changes in local membrane property homeostasis in both the inner and outer membrane models, specifically in the case of lateral diffusion, membrane thickness, and membrane resilience (compressibility, tilt). Finally, our results showed that the effect of F2B differed in a complex system and a single membrane system. Our study provides new insights into the multifaceted activity of F2B, demonstrating its potential to disrupt bacterial membrane homeostasis, indicating that its activity extends the currently known mechanism of FabI enzyme inhibition. This disruption, coupled with the ability of F2B to penetrate the outer membrane layers, sheds new light on the behavior of this antimicrobial molecule. This highlights the importance of the interaction with the membrane, crucial in combating bacterial infections, particularly those caused by drug-resistant strains.

Molecular guidelines for promising antimicrobial agents

Antimicrobial resistance presents a pressing challenge to public health, which requires the search for novel antimicrobial agents. Various experimental and theoretical methods are employed to understand drug-target interactions and propose multistep solutions. Nonetheless, efficient screening of drug databases requires rapid and precise numerical analysis to validate antimicrobial efficacy. Diptool addresses this need by predicting free energy barriers and local minima for drug translocation across lipid membranes. In the current study employing Diptool free energy predictions, the thermodynamic commonalities between selected antimicrobial molecules were characterized and investigated. To this end, various clustering methods were used to identify promising groups with antimicrobial activity. Furthermore, the molecular fingerprinting and machine learning approach (ML) revealed common structural elements and physicochemical parameters in these clusters, such as long carbon chains, charged ammonium groups, and low dipole moments. This led to the establishment of guidelines for the selection of effective antimicrobial candidates based on partition coefficients (logP) and molecular mass ranges. These guidelines were implemented within the Reinforcement Learning for Structural Evolution (ReLeaSE) framework, generating new chemicals with desired properties. Interestingly, ReLeaSE produced molecules with structural profiles similar to the antimicrobial agents tested, confirming the importance of the identified features. In conclusion, this study demonstrates the ability of molecular fingerprinting and AI-driven methods to identify promising antimicrobial agents with a broad range of properties. These findings deliver substantial implications for the development of antimicrobial drugs and the ongoing battle against antibiotic-resistant bacteria.

Passive permeability controls synthesis for the allelochemical sorgoleone in sorghum root exudate

Competition for soil nutrients and water with other plants foster competition within the biosphere for access to these limited resources. The roots for the common grain sorghum produce multiple small molecules that are released via root exudates into the soil to compete with other plants. Sorgoleone is one such compound, which suppresses weed growth near sorghum by acting as a quinone analog and interferes with photosynthesis. Since sorghum also grows photosynthetically, and may be susceptible to sorgoleone action if present in tissues above ground, it is essential to exude sorgoleone efficiently. However, since the P450 enzymes that synthesize sorgoleone are intracellular, the release mechanism for sorgoleone remain unclear. In this study, we conducted an in silico assessment for sorgoleone and its precursors to passively permeate biological membranes. To facilitate accurate simulation, CHARMM parameters were newly optimized for sorgoleone and its precursors. These parameters were used to conduct 1 μs of unbiased molecular dynamics simulations to compare the permeability of sorgoleone with its precursors molecules. We find that interleaflet transfer is maximized for sorgoleone, suggesting that the precursor molecules may remain in the same leaflet for access by biosynthetic P450 enzymes. Since no sorgoleone was extracted during unbiased simulations, we compute a permeability coefficient using the inhomogeneous solubility diffusion model. The requisite free energy and diffusivity profiles for sorgoleone through a sorghum membrane model were determined through Replica Exchange Umbrella Sampling (REUS) simulations. The REUS calculations highlight that any soluble sorgoleone would quickly insert into a lipid bilayer, and would readily transit. When sorgoleone forms aggregates in root exudate as indicated by our equilibrium simulations, aggregate formation would lower the effective concentration in aqueous solution, creating a concentration gradient that would facilitate passive transport. This suggests that sorgoleone synthesis occurs within sorghum root cells and that sorgoleone is exuded by permeating through the cell membrane without the need for a transport protein once the extracellular sorgoleone aggregate is formed.

Interaction of Uperin Peptides with Model Membranes: Molecular Dynamics Study

The interaction of antimicrobial and amyloid peptides with cell membranes is a critical step in their activities. Peptides of the uperin family obtained from the skin secretion of Australian amphibians demonstrate antimicrobial and amyloidogenic properties. All-atomic molecular dynamics and an umbrella sampling approach were used to study the interaction of uperins with model bacterial membrane. Two stable configurations of peptides were found. In the bound state, the peptides in helical form were located right under the head group region in parallel orientation with respect to the bilayer surface. Stable transmembrane configuration was observed for wild-type uperin and its alanine mutant in both alpha-helical and extended unstructured forms. The potential of mean force characterized the process of peptide binding from water to the lipid bilayer and its insertion into the membrane, and revealed that the transition of uperins from the bound state to the transmembrane position was accompanied by the rotation of peptides and passes through the energy barrier of 4-5 kcal/mol. Uperins have a weak effect on membrane properties.

Effect of Local Stress on Accurate Modeling of Bacterial Outer Membranes Using All-Atom Molecular Dynamics

Biological membranes are fundamental components of living organisms that play an undeniable role in their survival. Molecular dynamics (MD) serves as an essential computational tool for studying biomembranes on molecular and atomistic scales. The status quo of MD simulations of biomembranes studies a nanometer-sized membrane patch periodically extended under periodic boundary conditions (PBCs). In nature, membranes are usually composed of different lipids in their two layers (referred to as leaflets). This compositional asymmetry imposes a fixed ratio of lipid numbers between the two leaflets in a periodically constrained membrane, which needs to be set appropriately. The widely adopted methods of defining a leaflet lipid ratio suffer from the lack of control over the mechanical tension of each leaflet, which could significantly influence research findings. In this study, we investigate the role of membrane-building protocol and the resulting initial stress state on the interaction between small molecules and asymmetric membranes. We model the outer membrane of Pseudomonas aeruginosa bacteria using two different building protocols and probe their interactions with the Pseudomonas quinolone signal (PQS). Our results show that differential stress could shift the position of free energy minimum for the PQS molecule between the two leaflets of the asymmetric membrane. This work provides critical insights into the relationship between the initial per-leaflet tension and the spontaneous intercalation of PQS.

Calculation of the permeability coefficients of small molecules through lipid bilayers by free-energy reaction network analysis following the explicit treatment of the internal conformation of the solute

Biomembrane permeation represents a major barrier to pharmacokinetics. During preclinical drug discovery, the coefficients of the permeation of molecules through lipid bilayers account for a valuable property of such molecules. Therefore, the control of the permeation of molecules through lipid bilayers is an essential factor in drug design, and the estimation of the permeation phenomena is a crucial study in pharmacy. Thus, there are many published studies on the theoretical estimations of permeation coefficients. Here, we propose a molecular dynamics (MD) simulation method for estimating the permeation of small molecules through lipid bilayers based on the free-energy reaction network (FERN) analysis. In this method, the collective variables (CVs) of the free energy calculations explicitly include the conformational changes in the rotational bonds of the solute molecules. The advantages of the present method over the other method are that it is possible to estimate reaction pathways and their reaction rates, i.e., permeation coefficients or passage times, in multidimensional space spanned by CVs though conventional methods such as the umbrella sampling method and target MDs often dealt with a few degrees of freedom. To demonstrate the efficacy of our method, we calculate the coefficients of the permeation of three small aromatic peptides, namely N-acetylphenylalanineamide (Ac-Phe-NH2 or NAFA), N-acetyltyrosineamide (Ac-Tyr-NH2 or NAYA), and N-acetyltryptophanamide (Ac-Trp-NH2 or NATA), through a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer. In these cases we adopted one CV for the permeation direction and four CVs for the internal rotational coordinates. The results reveal that the permeation coefficients of NAFA, NAYA, and NATA are 1.7 × 10^-2, 0.51 × 10^-4, and 5.7 × 10^-4 cm s^-1, respectively. Compared with the experimental data, our simulation results followed the same trend, i.e., NAFA > NATA > NAYA. By analyzing the structures of metastable points of the solute molecules, our simulation result reveals that the aforementioned trend is caused by the differences in stability among their rotamers. Furthermore, we evaluate the statistical fluctuation of the rotamers, and the time scale of flipping the side chain reveals that the structures rigidify as the ligand moves deeper into the membrane.

Enhanced Expansion and Reduced Kiss-and-Run Events in Fusion Pores Steered by Synaptotagmin-1 C2B Domains

The fusion pore controls the release of exocytotic vesicle contents through a precise orchestration of lipids from the fusing membranes and proteins. There is a major lipid reorganization during the different stages in life of the fusion pore (membrane fusion, nucleation, and expansion) that can be scrutinized thermodynamically. In this work, using umbrella sampling simulations we describe the expansion of the fusion pore. We have calculated free energy profiles to drive a nascent, just nucleated, fusion pore to its expanded configuration. We have quantified the effects on the free energy of one and two Synaptotagmin-1 C2B domains in the cytosolic space. We show that C2B domains cumulatively reduce the cost for expansion, favoring the system to evolve toward full fusion. Finally, by conducting thousands of unbiased molecular dynamics simulations, we show that C2B domains significantly decrease the probability of kiss-and-run events.

Interactions between Rhodamine Dyes and Model Membrane Systems—Insights from Molecular Dynamics Simulations

Background: rhodamines are dyes widely used as fluorescent tags in cell imaging, probing of mitochondrial membrane potential, and as P-glycoprotein model substrates. In all these applications, detailed understanding of the interaction between rhodamines and biomembranes is fundamental. Methods: we combined atomistic molecular dynamics (MD) simulations and fluorescence spectroscopy to characterize the interaction between rhodamines 123 and B (Rh123 and RhB, respectively) and POPC bilayers. Results: while the xanthene moiety orients roughly parallel to the membrane plane in unrestrained MD simulations, variations on the relative position of the benzoic ring (below the xanthene for Rh123, above it for RhB) were observed, and related to the structure of the two dyes and their interactions with water and lipids. Subtle distinctions were found among different ionization forms of the probes. Experimentally, RhB displayed a lipid/water partition coefficient more than two orders of magnitude higher than Rh123, in agreement with free energy profiles obtained from umbrella sampling MD. Conclusions: this work provided detailed insights on the similarities and differences in the behavior of bilayer-inserted Rh123 and RhB, related to the structure of the probes. The much higher affinity of RhB for the membranes increases the local concentration and explains its higher apparent affinity for P-glycoprotein reconstituted in model membranes.

Synaptotagmin-1 C2B domains cooperatively stabilize the fusion stalk via a master-servant mechanism

Synaptotagmin-1 is a low-affinity Ca2+ sensor that triggers synchronous vesicle fusion. It contains two similar C2 domains (C2A and C2B) that cooperate in membrane binding, being the C2B domain the...

Crossing of the Cystic Barriers of Toxoplasma gondii by the Fluorescent Coumarin Tetra-Cyclopeptide

FR235222 is a natural tetra-cyclopeptide with a strong inhibition effect on histone deacetylases, effective on mammalian cells as well as on intracellular apicomplexan parasites, such as Toxoplasma gondii, in the tachyzoite and bradyzoite stages. This molecule is characterized by two parts: the zinc-binding group, responsible for the binding to the histone deacetylase, and the cyclic tetrapeptide moiety, which plays a crucial role in cell permeability. Recently, we have shown that the cyclic tetrapeptide coupled with a fluorescent diethyl-amino-coumarin was able to maintain properties of cellular penetration on human cells. Here, we show that this property can be extended to the crossing of the Toxoplasma gondii cystic cell wall and the cell membrane of the parasite in its bradyzoite form, while maintaining a high efficacy as a histone deacetylase inhibitor. The investigation by molecular modeling allows a better understanding of the penetration mechanism.

Substrate Access Mechanism in a Novel Membrane-Bound Phospholipase A of Pseudomonas aeruginosa Concordant with Specificity and Regioselectivity

PlaF is a cytoplasmic membrane-bound phospholipase A₁ from Pseudomonas aeruginosa that alters the membrane glycerophospholipid (GPL) composition and fosters the virulence of this human pathogen. PlaF activity is regulated by a dimer-to-monomer transition followed by tilting of the monomer in the membrane. However, how substrates reach the active site and how the characteristics of the active site tunnels determine the activity, specificity, and regioselectivity of PlaF for natural GPL substrates have remained elusive. Here, we combined unbiased and biased all-atom molecular dynamics (MD) simulations and configurational free-energy computations to identify access pathways of GPL substrates to the catalytic center of PlaF. Our results map out a distinct tunnel through which substrates access the catalytic center. PlaF variants with bulky tryptophan residues in this tunnel revealed decreased catalysis rates due to tunnel blockage. The MD simulations suggest that GPLs preferably enter the active site with the sn-1 acyl chain first, which agrees with the experimentally demonstrated PLA₁ activity of PlaF. We propose that the acyl chain-length specificity of PlaF is determined by the structural features of the access tunnel, which results in favorable free energy of binding of medium-chain GPLs. The suggested egress route conveys fatty acid (FA) products to the dimerization interface and, thus, contributes to understanding the product feedback regulation of PlaF by FA-triggered dimerization. These findings open up opportunities for developing potential PlaF inhibitors, which may act as antibiotics against P. aeruginosa.

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

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

Characterization of cisplatin/membrane interactions by QM/MM energy decomposition analysis

We extend for the first time a quantum mechanical energy decomposition analysis scheme based on deformation electron densities to a hybrid electrostatic embedding quantum mechanics/molecular mechanics framework. The implemented approach is applied to characterize the interactions between cisplatin and a dioleyl-phosphatidylcholine membrane, which play a key role in the permeation mechanism of the drug inside the cells. The interaction energy decomposition into electrostatic, induction, dispersion and Pauli repulsion contributions is performed for ensembles of geometries to account for conformational sampling. It is evidenced that the electrostatic and repulsive components are predominant in both polar and non-polar regions of the bilayer.

Improving the accuracy and convergence of drug permeation simulations via machine-learned collective variables

Understanding the permeation of biomolecules through cellular membranes is critical for many biotechnological applications, including targeted drug delivery, pathogen detection, and the development of new antibiotics. To this end, computer simulations are routinely used to probe the underlying mechanisms of membrane permeation. Despite great progress and continued development, permeation simulations of realistic systems (e.g., more complex drug molecules or biologics through heterogeneous membranes) remain extremely challenging if not intractable. In this work, we combine molecular dynamics simulations with transition-tempered metadynamics and techniques from the variational approach to conformational dynamics to study the permeation mechanism of a drug molecule, trimethoprim, through a multicomponent membrane. We show that collective variables (CVs) obtained from an unsupervised machine learning algorithm called time-structure based Independent Component Analysis (tICA) improve performance and substantially accelerate convergence of permeation potential of mean force (PMF) calculations. The addition of cholesterol to the lipid bilayer is shown to increase both the width and height of the free energy barrier due to a condensing effect (lower area per lipid) and increase bilayer thickness. Additionally, the tICA CVs reveal a subtle effect of cholesterol increasing the resistance to permeation in the lipid head group region, which is not observed when canonical CVs are used. We conclude that the use of tICA CVs can enable more efficient PMF calculations with additional insight into the permeation mechanism.

Predicting the Membrane Permeability of Fentanyl and Its Analogues by Molecular Dynamics Simulations

The lipid membrane is considered a crucial component of opioid general anesthesia. The main drug used for the induction and maintenance of opioid anesthesia is fentanyl and its various analogues. However, these drugs have different clinical effects, and detailed atomic-level insight into the drug–membrane interactions could lead to a better understanding how these drugs exert their anesthetic properties. In this study, we have used extensive umbrella sampling molecular dynamics simulations to study the permeation process of fentanyl and three of its analogues into a variety of simple phospholipid membrane models. Our simulations show that we can accurately predict the permeability coefficients of these drug molecules, which is an important process in understanding how pharmaceuticals reach their molecular targets. We were also able to show that one phospholipid provides more accurate predictions than other lipids commonly used in these types of permeation studies, which will aid future studies of these types of processes.

The Permeation Mechanism of Cisplatin Through a Dioleoylphosphocholine Bilayer*

The investigation of the intermolecular interactions between platinum-based anticancer drugs and lipid bilayers is of special relevance to unveil the mechanisms involved in different steps of the anticancer mode of action of these drugs. We have simulated the permeation of cisplatin through a model membrane composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine lipids by means of umbrella sampling classical molecular dynamics simulations. The initial physisorption of cisplatin into the polar region of the lipid membrane is controlled by long-range electrostatic interactions with the choline groups in a first step and, in a second step, by long-range electrostatic and hydrogen bond interactions with the phosphate groups. The second half of the permeation pathway, in which cisplatin diffuses through the nonpolar region of the bilayer, is characterized by the drop of the interactions with the polar heads and the rise of attractive interactions with the non-polar tails, which are dominated by van der Waals contributions. The permeation free-energy profile is explained by a complex balance between the drug/lipid interactions and the energy and entropy contributions associated with the dehydration of the drug along the permeation pathway and with the decrease and increase of the membrane ordering along the first and second half of the mechanism, respectively.

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.

Interface-Mediated Mechanism of Action-The Root of the Cytoprotective Effect of Immediate-Release Omeprazole

Omeprazole is usually administered under an enteric coating. However, there is a Food and Drug Administration-approved strategy that enables its release in the stomach. When locally absorbed, omeprazole shows a higher efficacy and a cytoprotective effect, whose mechanism was still unknown. Therefore, we aimed to assess the effect of the absorption route on the gastric mucosa. 2D and 3D models of dipalmitoylphosphatidylcholine (DPPC) at different pH values (5.0 and 7.4) were used to mimic different absorption conditions. Several experimental techniques, namely, fluorescence studies, X-ray scattering methodologies, and Langmuir monolayers coupled with microscopy, X-ray diffraction, and infrared spectroscopy techniques, were combined with molecular dynamics simulations. The results showed that electrostatic and hydrophobic interactions between omeprazole and DPPC rearranged the conformational state of DPPC. Omeprazole intercalates among DPPC molecules, promoting domain formation with untilted phospholipids. Hence, the local release of omeprazole enables its action as a phospholipid-like drug, which can reinforce and protect the gastric mucosa.

Partitioning of Aβ Peptide Fragments into Blood-Brain Barrier Mimetic Bilayer

We used all-atom replica-exchange umbrella sampling molecular dynamics simulations to investigate the partitioning of the charged tetrapeptide KLVF and its neutral apolar counterpart VVIA into the blood-brain barrier (BBB)-mimetic bilayer. Our findings allowed us to reconstruct the partitioning mechanism for these two Aβ peptide fragments. Despite dissimilar sequences, their permeation shares significant common features. Computations of free energies and permeabilities show that partitioning of both peptides is highly unfavorable, ruling out passive transport. The peptides experience multiple rotational transitions within the bilayer and typically cause considerable lipid disorder and bilayer thinning. Near the bilayer midplane, they lose almost entirely their solvation shell and the interactions with the lipid headgroups. The peptides cause complex reorganization within the proximal bilayer region. Upon insertion, they induce striking cholesterol influx reversed by its depletion and the influx of DMPC when the peptides reach the midplane. The differences in partitioning mechanisms are due to the much higher polarity of KLVF peptide, the permeation of which is more unfavorable and which exclusively assumes vertical orientations within the bilayer. In contrast, VVIA positions itself flat between the leaflets, causing minor disorder and even thickening of the BBB-mimetic bilayer. Due to the high density of the cholesterol-rich BBB bilayer, the unfavorable work associated with the peptide insertion provides a significant, but not dominant, contribution to the partition free energy, which is still governed by dehydration and loss of peptide-headgroup interactions. Comparison with experiments indicates that KLVF and VVIA permeation is similar to that of proline tetrapeptide, mannitol, or cimetidine, all of which exhibit no passive transport.

Comparison of umbrella sampling and steered molecular dynamics methods for computing free energy profiles of aromatic substrates through phospholipid bilayers

Understanding the permeation of molecules through lipid membranes is fundamental for predicting the cellular uptake of solutes and drug delivery mechanisms. In molecular simulations, the usual approach is to compute the free energy (FE) profile of a molecule across a model lipid bilayer, which can then be used to estimate the permeability of the molecule. Umbrella Sampling (US), which involves carrying out a series of biased simulations along a defined reaction coordinate (usually the bilayer normal direction), is a popular method for the computation of such FE profiles. However, US can be challenging to implement because the results are dependent on the strength of the biasing potential and the spacing of windows along the reaction coordinate, which, in practice, are usually optimized by an inefficient trial and error approach. The Steered Molecular Dynamics implementation of the Jarzynski Equality (JE-SMD) has been identified as an alternative to equilibrium sampling methods for measuring the FE change across a reaction coordinate. In the JE-SMD approach, equilibrium FE values are evaluated from the average of rapid non-equilibrium trajectories, thus avoiding the practical issues that come with US. Here, we use three different corrections of the JE-SMD method to calculate the FE change for the translocation of two aromatic substrates, phenylalanine and toluene, across a lipid bilayer and compare the accuracy and computational efficiency of these approaches to the results obtained using US. We show evidence that when computing the free energy profile, the JE-SMD approach suffers from insufficient sampling convergence of the bilayer environment and is dependent on the characteristic of the aromatic substrate itself. We deduce that, despite its drawbacks, US remains the more viable approach of the two for computing the FE profile.

Molecular Dynamics Simulations Based on Polarizable Models Show that Ion Permeation Interconverts between Different Mechanisms as a Function of Membrane Thickness

Different mechanisms have been proposed to explain the permeation of charged compounds through lipid membranes. Overall, it is expected that an ion-induced defect permeation mechanism, where substantial membrane deformations accompany ion movement, should be dominant in thin membranes but that a solubility-diffusion mechanism, where ions partition into the membrane core with large associated dehydration energy costs, becomes dominant in thicker membranes. However, while this physical picture is intuitively reasonable, capturing the interconversion between these two permeation mechanisms in molecular dynamics (MD) simulations based on atomic models is challenging. In particular, simulations relying on nonpolarizable force fields are artificially unfavorable to the solubility-diffusion mechanism, as induced polarization of the nonpolar hydrocarbon is ignored, causing overestimated free energy costs for charged molecules to enter into this region of the membrane. In this study, all-atom MD simulations based on nonpolarizable and polarizable force fields are used to quantitatively characterize the permeation process for the arginine side chain analog methyl-guanidinium through bilayer membranes of mono-unsaturated phosphatidylcholine lipids with and without cholesterol, resulting in thicknesses spanning from ∼24 to ∼42 Å. With simulations based on a nonpolarizable force field, ion translocation can take place solely through an ion-induced defect mechanism, with free energy barriers increasing linearly from 14 to 40 kcal/mol, depending on the thickness. However, with simulations based on a polarizable force field, ion translocation is predominantly dominated by an ion-induced defect mechanism in thin membranes, which progressively converts to a solubility-diffusion mechanism as the membranes get thicker. The transition between the two mechanisms occurs at a thickness of ∼29 Å, with lipid tails of 22 or more carbon atoms. This situation appears to represent the upper limit for ion-induced defect permeation within the current polarizable models. Beyond this thickness, it becomes energetically preferable for the ion to dehydrate and partition into the membrane core-a phenomenon that cannot be captured using the nonpolarizable models. Induced electronic polarizability therefore leads not just to a shift in permeation energetics but to an interconversion between two strikingly different physical mechanisms. The result highlights the importance of induced polarizability in modeling lipid membranes.

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

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

Recent Open Issues in Coarse Grained Force Fields

This viewpoint intends to show recent open issues of using coarse grained models in molecular dynamics simulation. It reviews the current knowledge of the comparison between experimental and simulation data of structural and physical chemical properties that depend on the hydrophilic and hydrophobic behavior of the molecule.

Molecular Dynamics Simulation of Small Molecules Interacting with Biological Membranes

Cell membranes protect and compartmentalise cells and their organelles. The semi-permeable nature of these membranes controls the exchange of solutes across their structure. Characterising the interaction of small molecules with biological membranes is critical to understanding of physiological processes, drug action and permeation, and many biotechnological applications. This review provides an overview of how molecular simulations are used to study the interaction of small molecules with biological membranes, with a particular focus on the interactions of water, organic compounds, drugs and short peptides with models of plasma cell membrane and stratum corneum lipid bilayers. This review will not delve on other types of membranes which might have different composition and arrangement, such as thylakoid or mitochondrial membranes. The application of unbiased molecular dynamics simulations and enhanced sampling methods such as umbrella sampling, metadynamics and replica exchange are described using key examples. This review demonstrates how state-of-the-art molecular simulations have been used successfully to describe the mechanism of binding and permeation of small molecules with biological membranes, as well as associated changes to the structure and dynamics of these membranes. The review concludes with an outlook on future directions in this field.

Interplay of hydrophobic and hydrophilic interactions in sequence-dependent cell penetration of spontaneous membrane-translocating peptides revealed by bias-exchange metadynamics simulations

Spontaneous Membrane Translocating Peptides (SMTPs) can translocate silently across the bilayer and, thus, have the best potential to improve the delivery of therapeutic molecules to cells without toxicity. However, how their translocation mechanisms are affected by a specific peptide sequence remains poorly understood. Here, bias-exchange metadynamics simulations were employed to investigate the translocation mechanisms of five SMTPs with the same composition of amino acids (LLRLR, LRLLR, LLLRR, RLLLR, and LRLRL). Simulation results yield sequence-dependent free energy barrier using the FESs along the z-directional distance. An in-depth analysis of sequence-dependent interactions in different regions of the bilayers indicates that the free-energy barrier height of a specific sequence is resulted from the accessibility balance of isolated or clustered hydrophobic residues (L) and hydrophilic residues (R) that leads to different levels of resistance for moving of a peptide into the hydrophobic center of the membrane. At the maximal of the free-energy barrier, all peptides have a conformation parallel to the membrane surface with the barrier height determined by their affinity to the hydrophobic region. The appropriate bilayer perturbation and GDM⁺ pairing are beneficial for peptide translocation. These results provide an improved microscopic understanding of how peptide sequence influences the translocation efficiency and mechanism.

Dynamic Protonation Dramatically Affects the Membrane Permeability of Drug-like Molecules

Permeability (P_m) across biological membranes is of fundamental importance and a key factor in drug absorption, distribution, and development. Although the majority of drugs will be charged at some point during oral delivery, our understanding of membrane permeation by charged species is limited. The canonical model assumes that only neutral molecules partition into and passively permeate across membranes, but there is mounting evidence that these processes are also facile for certain charged species. However, it is unknown whether such ionizable permeants dynamically neutralize at the membrane surface or permeate in their charged form. To probe protonation-coupled permeation in atomic detail, we herein apply continuous constant-pH molecular dynamics along with free energy sampling to study the permeation of a weak base propranolol (PPL), and evaluate the impact of including dynamic protonation on P_m. The simulations reveal that PPL dynamically neutralizes at the lipid-tail interface, which dramatically influences the permeation free energy landscape and explains why the conventional model overestimates the assigned intrinsic permeability. We demonstrate how fixed-charge-state simulations can account for this effect, and propose a revised model that better describes pH-coupled partitioning and permeation. Our results demonstrate how dynamic changes in protonation state may play a critical role in the permeation of ionizable molecules, including pharmaceuticals and drug-like molecules, thus requiring a revision of the standard picture.

Spontaneous and Stress-Induced Pore Formation in Membranes: Theory, Experiments and Simulations

The large plasticity, dynamics and adaptability of biological membranes allow different modes of intrinsic and inducible permeability. These phenomena are of physiological importance for a number of natural functions related to cell death and can also be manipulated artificially for practical purposes like gene transfer, drug delivery, prevention of infections or anticancer therapy. For these advances to develop in a controllable and specific way, we need a sufficient understanding of the membrane permeability phenomena. Since the formulation of early concepts of pore formation, there has been an enormous effort to describe membrane permeability by using theory, simulations and experiments. A major breakthrough has come recently through theoretical developments that allow building continuous trajectories of pore formation both in the absence and presence of stress conditions. The new model provides a coherent quantitative view of membrane permeabilization, useful to test the impact of known lipid properties, make predictions and postulate specific pore intermediates that can be studied by simulations. For example, this theory predicts unprecedented dependencies of the line tension on the pore radius and on applied lateral tension which explain previous puzzling results. In parallel, important concepts have also come from molecular dynamics simulations, of which the role of water for membrane permeabilization is of special interest. These advances open new challenges and perspectives for future progress in the study of membrane permeability, as experiments and simulations will need to test the theoretical predictions, while theory achieves new refinements that provide a physical ground for observations.

Molecular Dynamics Simulations of Membrane Permeability

This Review illustrates the evaluation of permeability of lipid membranes from molecular dynamics (MD) simulation primarily using water and oxygen as examples. Membrane entrance, translocation, and exit of these simple permeants (one hydrophilic and one hydrophobic) can be simulated by conventional MD, and permeabilities can be evaluated directly by Fick's First Law, transition rates, and a global Bayesian analysis of the inhomogeneous solubility-diffusion model. The assorted results, many of which are applicable to simulations of nonbiological membranes, highlight the limitations of the homogeneous solubility diffusion model; support the utility of inhomogeneous solubility diffusion and compartmental models; underscore the need for comparison with experiment for both simple solvent systems (such as water/hexadecane) and well-characterized membranes; and demonstrate the need for microsecond simulations for even simple permeants like water and oxygen. Undulations, subdiffusion, fractional viscosity dependence, periodic boundary conditions, and recent developments in the field are also discussed. Last, while enhanced sampling methods and increasingly sophisticated treatments of diffusion add substantially to the repertoire of simulation-based approaches, they do not address directly the critical need for force fields with polarizability and multipoles, and constant pH methods.

Multiscale Simulations of Biological Membranes: The Challenge To Understand Biological Phenomena in a Living Substance

Biological membranes are tricky to investigate. They are complex in terms of molecular composition and structure, functional over a wide range of time scales, and characterized by nonequilibrium conditions. Because of all of these features, simulations are a great technique to study biomembrane behavior. A significant part of the functional processes in biological membranes takes place at the molecular level; thus computer simulations are the method of choice to explore how their properties emerge from specific molecular features and how the interplay among the numerous molecules gives rise to function over spatial and time scales larger than the molecular ones. In this review, we focus on this broad theme. We discuss the current state-of-the-art of biomembrane simulations that, until now, have largely focused on a rather narrow picture of the complexity of the membranes. Given this, we also discuss the challenges that we should unravel in the foreseeable future. Numerous features such as the actin-cytoskeleton network, the glycocalyx network, and nonequilibrium transport under ATP-driven conditions have so far received very little attention; however, the potential of simulations to solve them would be exceptionally high. A major milestone for this research would be that one day we could say that computer simulations genuinely research biological membranes, not just lipid bilayers.

Different effects of cholesterol on membrane permeation of arginine and tryptophan revealed by bias-exchange metadynamics simulations

Experiments have shown that cholesterol influences the membrane permeability of small molecules, amino acids, and cell-penetrating peptides. However, their exact translocation mechanisms under the influence of cholesterol remain poorly understood. Given the practical importance of cell-penetrating peptides and the existence of varied cholesterol contents in different cell types, it is necessary to examine the permeation of amino acids in cholesterol-containing membranes at atomic level of details. Here, bias-exchange metadynamics simulations were employed to investigate the molecular mechanism of the membrane permeation of two amino acids Arg and Trp important for cell-penetrating peptides in the presence of different concentrations of cholesterol. We found that the free energy barrier of Arg+ (the protonated form) permeation increased linearly as the cholesterol concentration increased, whereas the barrier of Trp permeation had a rapid increase from 0 mol. % to 20 mol. % cholesterol-containing membranes and nearly unchanged from 20 mol. % to 40 mol. % cholesterol-containing membranes. Arg0 becomes slightly more stable than Arg+ at the center of the dipalmitoylphosphatidylcholine (DPPC) membrane with 40 mol. % cholesterol concentrations. As a result, Arg+ has a similar permeability as Trp at 0 mol. % and 20 mol. % cholesterol, but a significantly lower permeability than Trp at 40 mol. % cholesterol. This difference is caused by the gradual reduction of water defects for Arg+ as the cholesterol concentration increases but lack of water defects for Trp in cholesterol-containing membranes. Strong but different orientation dependence between Arg+ and Trp permeations is observed. These results provide an improved microscopic understanding of amino-acid permeation through cholesterol-containing DPPC membrane systems.

Orientational distribution of DPH in lipid membranes: a comparison of molecular dynamics calculations and experimental time-resolved anisotropy experiments

The behavior of the fluorescent probe diphenylhexatriene (DPH) in different lipid phases is investigated. The rotational autocorrelation functions are calculated in order to model the time-resolved fluorescence anisotropy decay. The role of the order parameters is discussed.

Effects of lipid composition on membrane distribution and permeability of natural quinones

Lipid acyl chain unsaturation modulates the barrier for ubiquinone flip-flop over the membrane.

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.

Effects of lipid composition on membrane permeation

Passive permeation through lipid membranes is an essential process in biology. In vivo membranes typically consist of mixtures of lamellar and nonlamellar lipids. Lamellar lipids are characterized by their tendency to form lamellar sheet-like structures, which are predominant in nature. Nonlamellar lipids, when isolated, instead form more geometrically complex nonlamellar phases. While mixed lamellar/nonlamellar lipid membranes tend to adopt the ubiquitous lamellar bilayer structure, the presence of nonlamellar lipids is known to have profound effects on key membrane properties, such as internal distributions of stress and elastic properties, which in turn may alter related biological processes. This work focuses on one such process, i.e., permeation, by utilising atomistic molecular dynamics simulations in order to obtain transfer free energy profiles, diffusion profiles and permeation coefficients for a series of thirteen small molecules and drugs. Each permeant is tested on two bilayer membranes of different lipid composition, i.e., purely lamellar and mixed lamellar/nonlamellar. Our results indicate that the presence of nonlamellar lipids reduces permeation for smaller molecules (molecular weight < 100) but facilitates it for the largest ones (molecular weight > 100). This work represents an advancement towards the development of more realistic in silico permeability assays, which may have a substantial future impact in the area of rational drug design.

Vitamin E Has Reduced Affinity for a Polyunsaturated Phospholipid: An Umbrella Sampling Molecular Dynamics Simulations Study

Vitamin E is an essential micronutrient. The primary function of this lipid-soluble antioxidant is to protect membrane phospholipids from oxidation. Whether vitamin E preferentially interacts with polyunsaturated phospholipids to optimize protection of the lipid species most vulnerable to oxidative attack has been an unanswered question for a long time. In this work, we compared the binding of α-tocopherol (αtoc), the form of vitamin E retained by the human body, in bilayers composed of polyunsaturated 1-stearoyl-2-docosahexaenoylphosphatidylcholine (SDPC, 18:0-22:6PC) and, as a control, monounsaturated 1-stearoyl-2-oleoylphosphatidylcholine (SOPC, 18:0-18:1PC) by umbrella sampling molecular dynamics simulations. From the potential of mean force as a function depth within the bilayer, we find that the binding energy of αtoc is less in SDPC (Δ G_bind = 16.7 ± 0.3 kcal/mol) than that in SOPC (Δ G_bind = 18.3 ± 0.4 kcal/mol). The lower value in SDPC is ascribed to the high disorder of polyunsaturated fatty acids that produces a less tightly packed arrangement. Deformation of the bilayer is observed during desorption, indicating that phosphatidylcholine (PC)-PC and αtoc-PC interactions contribute to the binding energy. Our results do not support the proposal that vitamin E interacts more favorably with polyunsaturated phospholipids.

Optimal Hydrophobicity and Reorientation of Amphiphilic Peptides Translocating through Membrane

Cell-penetrating and some antimicrobial peptides can translocate across lipid bilayers without disrupting the membrane structure. However, the molecular properties required for efficient translocation are not fully understood. We employed the Metropolis Monte Carlo method together with coarse-grained models to systematically investigate free-energy landscapes associated with the translocation of secondary amphiphilic peptides. We studied α-helical peptides with different length, amphiphilicity, and distribution of hydrophobic content and found a common translocation path consisting of adsorption, tilting, and insertion. In the adsorbed state, the peptides are parallel to the membrane plane, whereas, in the inserted state, the peptides are perpendicular to the membrane. Our simulations demonstrate that, for all tested peptides, there is an optimal ratio of hydrophilic/hydrophobic content at which the peptides cross the membrane the easiest. Moreover, we show that the hydrophobicity of peptide termini has an important effect on the translocation barrier. These results provide general guidance to optimize peptides for use as carriers of molecular cargos or as therapeutics themselves.

Membrane Permeability: Characteristic Times and Lengths for Oxygen and a Simulation-Based Test of the Inhomogeneous Solubility-Diffusion Model

The balance of normal and radial (lateral) diffusion of oxygen in phospholipid membranes is critical for biological function. Based on the Smoluchowski equation for the inhomogeneous solubility-diffusion model, Bayesian analysis (BA) can be applied to molecular dynamics trajectories of oxygen to extract the free energy and the normal and radial diffusion profiles. This paper derives a theoretical formalism to convert these profiles into characteristic times and lengths associated with entering, escaping, or completely crossing the membrane. The formalism computes mean first passage times and holds for any process described by rate equations between discrete states. BA of simulations of eight model membranes with varying lipid composition and temperature indicate that oxygen travels 3 to 5 times further in the radial than in the normal direction when crossing the membrane in a time of 15 to 32 ns, thereby confirming the anisotropy of passive oxygen transport in membranes. Moreover, the preceding times and distances estimated from the BA are compared to the aggregate of 280 membrane exits explicitly observed in the trajectories. BA predictions for the distances of oxygen radial diffusion within the membrane are statistically indistinguishable from the corresponding simulation values, yet BA oxygen exit times from the membrane interior are approximately 20% shorter than the simulation values, averaged over seven systems. The comparison supports the BA approach and, therefore, the applicability of the Smoluchowski equation to membrane diffusion. Given the shorter trajectories required for the BA, these results validate the BA as a computationally attractive alternative to direct observation of exits when estimating characteristic times and radial distances. The effect of collective membrane undulations on the BA is also discussed.

Possible Mechanism of Glucose Uptake Enhanced by Cold Atmospheric Plasma: Atomic Scale Simulations

Cold atmospheric plasma (CAP) has shown its potential in biomedical applications, such as wound healing, cancer treatment and bacterial disinfection. Recent experiments have provided evidence that CAP can also enhance the intracellular uptake of glucose molecules which is important in diabetes therapy. In this respect, it is essential to understand the underlying mechanisms of intracellular glucose uptake induced by CAP, which is still unclear. Hence, in this study we try to elucidate the possible mechanism of glucose uptake by cells by performing computer simulations. Specifically, we study the transport of glucose molecules through native and oxidized membranes. Our simulation results show that the free energy barrier for the permeation of glucose molecules across the membrane decreases upon increasing the degree of oxidized lipids in the membrane. This indicates that the glucose permeation rate into cells increases when the CAP oxidation level in the cell membrane is increased.

Molecular Insights into the Membrane Affinities of Model Hydrophobes

Membrane-active antibiotics are of great interest in fighting bacterial resistance. α-Mangostin is a membrane-active molecule, but there are no details of its mechanism of action at the atomistic level. We have employed free-energy simulations and microsecond-long conventional molecular dynamics simulations to study the mode of interaction of α-mangostin with a model bacterial membrane and compare it with the mechanisms of three hydrophobic molecules (ciprofloxacin, xanthone, and tetracycline). We find that α-mangostin is thermodynamically more favored to insert into the membrane compared to the other three molecules. Apart from tetracycline, which is largely hydrophilic, the other three molecules aggregate in water; however, only α-mangostin can penetrate into the lipid tail region of the membrane. When it reaches a high concentration in the lipid tail region, α-mangostin can form tubular clusters that span the two head group regions of the membrane, resulting in a large number of water translocations along the transmembrane aggregates. Structure-activity relationship analysis revealed two structural properties that characterize α-mangostin, namely, the two isoprenyl groups and the polar groups present in the aromatic rings, which result in "disruptive amphiphilicity" and hence its excellent membrane activity.