Modeling the Electric Double Layer at the Liposome Vesicle via Classical Density Functional Theory: Solution of Poisson's Equations for Curved Membranes

The electric double layer at the liposome vesicle membrane has been investigated by a modified fundamental-measure theory in the framework of the restricted primitive model. An analytical equation has been obtained for the mean electrostatic potential (MEP) by solving Poisson's equation for curved membranes. This study investigates the influence of vesicle size, membrane thickness, surface charges, and electrolyte concentration on the structure, composition, and width of electric double layers (EDLs) on the inner and outer membrane walls. Our findings indicate that a thin and denser layer of ions is formed at the concave wall of the membrane (inner wall) compared to that at the outer membrane. As expected, the width of the diffuse layer decreases with the concentration and surface charge. Also, when the surface charges on both concave and convex walls are the same, the absolute value of MEPs on the inner membrane, concave wall, is greater than that on the convex wall. We have also investigated the diffuse potential, which decreases with concentration, membrane thickness, and cavity size, whereas it increases with surface charges. As we expect, the contact density of counterions at the inner concave wall of the vesicle cavity is always greater than the corresponding value at the convex wall, whereas this trend reverses for co-ions. Also, the contact density of counterions (co-ions) at the inner wall decreases (increases) with cavity size, whereas it increases at the outer wall (decreases). Finally, depletion of co-ions occurs at the membrane walls with enhancement in surface charges.

The Secret Lives of Fluorescent Membrane Probes as Revealed by Molecular Dynamics Simulations

Fluorescent probes have been employed for more than half a century to study the structure and dynamics of model and biological membranes, using spectroscopic and/or microscopic experimental approaches. While their utilization has led to tremendous progress in our knowledge of membrane biophysics and physiology, in some respects the behavior of bilayer-inserted membrane probes has long remained inscrutable. The location, orientation and interaction of fluorophores with lipid and/or water molecules are often not well known, and they are crucial for understanding what the probe is actually reporting. Moreover, because the probe is an extraneous inclusion, it may perturb the properties of the host membrane system, altering the very properties it is supposed to measure. For these reasons, the need for independent methodologies to assess the behavior of bilayer-inserted fluorescence probes has been recognized for a long time. Because of recent improvements in computational tools, molecular dynamics (MD) simulations have become a popular means of obtaining this important information. The present review addresses MD studies of all major classes of fluorescent membrane probes, focusing in the period between 2011 and 2020, during which such work has undergone a dramatic surge in both the number of studies and the variety of probes and properties accessed.

Cellular absorption of small molecules: free energy landscapes of melatonin binding at phospholipid membranes

Free energy calculations are essential to unveil mechanisms at the atomic scale such as binding of small solutes and their translocation across cell membranes, eventually producing cellular absorption. Melatonin regulates biological rhythms and is directly related to carcinogenesis and neurodegenerative disorders. Free energy landscapes obtained from well-tempered metadynamics simulations precisely describe the characteristics of melatonin binding to specific sites in the membrane and reveal the role of cholesterol in free energy barrier crossing. A specific molecular torsional angle and the distance between melatonin and the center of the membrane along the normal to the membrane Z-axis have been considered as suitable reaction coordinates. Free energy barriers between two particular orientations of the molecular structure (folded and extended) have been found to be of about 18 kJ/mol for z-distances of about 1–2 nm. The ability of cholesterol to expel melatonin out of the internal regions of the membrane towards the interface and the external solvent is explained from a free energy perspective. The calculations reported here offer detailed free energy landscapes of melatonin embedded in model cell membranes and reveal microscopic information on its transition between free energy minima, including the location of relevant transition states, and provide clues on the role of cholesterol in the cellular absorption of small molecules.

Tiny but Fatty: Lipids and Fatty Acids in the Daubed Shanny (Leptoclinus Maculatus), a Small Fish in Svalbard Waters

The seasonal dynamic of lipids and their fatty acid constituents in the lipid sac and muscles of pelagic postlarval Leptoclinus maculatus, an ecologically important fish species in the Arctic food nets, in Kongsfjord, Svalbard waters was studied. The determination of the qualitative and quantitative content of the total lipids (TLs), total phospholipids (PLs), triacylglycerols (TAGs), cholesterol (Chol), cholesterol esters (Chol esters) and wax esters was analyzed by TLC, the phosphatidylserine (PS), phosphatidylethanolamine (PE), phosphatidylinositol (PI), phosphatidylcholine (PC), lysophosphatidylcholine (LPC) and sphingomyelin (SM) were determined by HPLC, and fatty acids of total lipids using GC. The lipid sac is a system of cavities filled with lipids, and it is not directly connected to organs of the digestive system. The wall’s inner layer is a multinuclear symplast that has a trophic function. The results provide additional knowledge on the role of lipids in the biochemical and physiological adaptation of fish to specific environments and clarify the relationship between fatty acids and the food specialization of postlarvae. Analysis of the fatty acid (FA) profile of TLs in the muscles and lipid sac of daubed shanny pelagic postlarvae showed it to be tissue- and organ-specific, and tightly associated with seasonal variations of environmental factors (temperature conditions and trophic resources).

Unperturbed hydrocarbon chains and liquid phase bilayer lipid chains: a computer simulation study

In this work, the properties of saturated and unsaturated fatty acid acyl chains 16:0, 18:0, 18:1(n-9)cis, 18:2(n-6)cis, 18:3(n-3)cis, 18:4(n-3)cis, 18:5(n-3)cis, 20:4(n-6)cis, 20:5(n-3)cis and 22:6(n-3)cis in a bilayer liquid crystalline state and similar hydrocarbon chains (with CH[Formula: see text] terminal groups instead of C=O groups) in the unperturbed state characterised by a lack of long-range interaction were investigated. The unperturbed hydrocarbon chains were modelled by Monte Carlo simulations at temperature [Formula: see text] K; sixteen fully hydrated homogeneous liquid crystalline phosphatidylcholine bilayers containing these chains were studied by molecular dynamics simulations at the same temperature. To eliminate effects of the simulation parameters, the molecular dynamics and Monte Carlo simulations were carried out using the same structural data and force field coefficients. From these computer simulations, the average distances between terminal carbon atoms of the chains (end-to-end distances) were calculated and compared. The trends in the end-to-end distances obtained for the unperturbed chains were found to be qualitatively similar to those obtained for the same lipid chains in the bilayers. So, for understanding of a number of processes in biological membranes (e.g., changes in fatty acid composition caused by environmental changes such as temperature and pressure), it is possible to use, at least as a first approximation, the relationships between the structure and properties for unperturbed or isolated hydrocarbon chains.

A Coarse-Grained Model of Stratum Corneum Lipids: Free Fatty Acids and Ceramide NS

Ceramide (CER)-based biological membranes are used both experimentally and in simulations as simplified model systems of the skin barrier. Molecular dynamics studies have generally focused on simulating preassembled structures using atomistically detailed models of CERs, which limit the system sizes and time scales that can practically be probed, rendering them ineffective for studying particular phenomena, including self-assembly into bilayer and lamellar superstructures. Here, we report on the development of a coarse-grained (CG) model for CER NS, the most abundant CER in human stratum corneum. Multistate iterative Boltzmann inversion is used to derive the intermolecular pair potentials, resulting in a force field that is applicable over a range of state points and suitable for studying ceramide self-assembly. The chosen CG mapping, which includes explicit interaction sites for hydroxyl groups, captures the directional nature of hydrogen bonding and allows for accurate predictions of several key structural properties of CER NS bilayers. Simulated wetting experiments allow the hydrophobicity of CG beads to be accurately tuned to match atomistic wetting behavior, which affects the whole system, since inaccurate hydrophobic character is found to unphysically alter the lipid packing in hydrated lamellar states. We find that CER NS can self-assemble into multilamellar structures, enabling the study of lipid systems more representative of the multilamellar lipid structures present in the skin barrier. The coarse-grained force field derived herein represents an important step in using molecular dynamics to study the human skin barrier, which gives a resolution not available through experiment alone.

Markovian and Non-Markovian Modeling of Membrane Dynamics with Milestoning

We exploit atomically detailed simulations and the milestoning theory to extract coarse grained models of membrane kinetics and thermodynamics. Non-Markovian and Markovian theories for the phosphate group displacements are used to coarsely represent membrane motions. The construction of the two models makes it possible to examine their consistency and accuracy. The equilibrium and fluctuations of the phosphate groups along the normal to the membrane plane are estimated, and milestoning equations are constructed and solved. An optimal Markovian model is constructed that reproduces exactly the equilibrium and mean first passage time (MFPT) of the non-Markovian model. The equilibrium solution of both models is favorably compared to distributions obtained from straightforward molecular dynamics simulations. The picture for the kinetics is complex. Multiple local relaxation times of the mass density are illustrated emphasizing the non-Markovian characteristics of the process. In Markovian modeling, only a single relaxation time is assumed for a state. Mapping of particle dynamics to the dynamics of a field density offers a new way of coarse graining complex systems as membranes that may bridge between atomically detailed models and phenomenological descriptions of macroscopic membranes.

Force Field Development for Lipid Membrane Simulations

With the rapid development of computer power and wide availability of modelling software computer simulations of realistic models of lipid membranes, including their interactions with various molecular species, polypeptides and membrane proteins have become feasible for many research groups. The crucial issue of the reliability of such simulations is the quality of the force field, and many efforts, especially in the latest several years, have been devoted to parametrization and optimization of the force fields for biomembrane modelling. In this review, we give account of the recent development in this area, covering different classes of force fields, principles of the force field parametrization, comparison of the force fields, and their experimental validation. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Toward Atomistic Resolution Structure of Phosphatidylcholine Headgroup and Glycerol Backbone at Different Ambient Conditions

Phospholipids are essential building blocks of biological membranes. Despite a vast amount of very accurate experimental data, the atomistic resolution structures sampled by the glycerol backbone and choline headgroup in phoshatidylcholine bilayers are not known. Atomistic resolution molecular dynamics simulations have the potential to resolve the structures, and to give an arrestingly intuitive interpretation of the experimental data, but only if the simulations reproduce the data within experimental accuracy. In the present work, we simulated phosphatidylcholine (PC) lipid bilayers with 13 different atomistic models, and compared simulations with NMR experiments in terms of the highly structurally sensitive C-H bond vector order parameters. Focusing on the glycerol backbone and choline headgroups, we showed that the order parameter comparison can be used to judge the atomistic resolution structural accuracy of the models. Accurate models, in turn, allow molecular dynamics simulations to be used as an interpretation tool that translates these NMR data into a dynamic three-dimensional representation of biomolecules in biologically relevant conditions. In addition to lipid bilayers in fully hydrated conditions, we reviewed previous experimental data for dehydrated bilayers and cholesterol-containing bilayers, and interpreted them with simulations. Although none of the existing models reached experimental accuracy, by critically comparing them we were able to distill relevant chemical information: (1) increase of choline order parameters indicates the P-N vector tilting more parallel to the membrane, and (2) cholesterol induces only minor changes to the PC (glycerol backbone) structure. This work has been done as a fully open collaboration, using nmrlipids.blogspot.fi as a communication platform; all the scientific contributions were made publicly on this blog. During the open research process, the repository holding our simulation trajectories and files ( https://zenodo.org/collection/user-nmrlipids ) has become the most extensive publicly available collection of molecular dynamics simulation trajectories of lipid bilayers.

Elucidation of the binding mechanism of renin using a wide array of computational techniques and biological assays

We investigate the binding mechanism in renin complexes, involving three drugs (remikiren, zankiren and enalkiren) and one lead compound, which was selected after screening the ZINC database. For this purpose, we used ab initio methods (the effective fragment potential, the variational perturbation theory, the energy decomposition analysis, the atoms-in-molecules), docking, molecular dynamics, and the MM-PBSA method. A biological assay for the lead compound has been performed to validate the theoretical findings. Importantly, binding free energy calculations for the three drug complexes are within 3 kcal/mol of the experimental values, thus further justifying our computational protocol, which has been validated through previous studies on 11 drug-protein systems. The main elements of the discovered mechanism are: (i) minor changes are induced to renin upon drug binding, (ii) the three drugs form an extensive network of hydrogen bonds with renin, whilst the lead compound presented diminished interactions, (iii) ligand binding in all complexes is driven by favorable van der Waals interactions and the nonpolar contribution to solvation, while the lead compound is associated with diminished van der Waals interactions compared to the drug-bound forms of renin, and (iv) the environment (H2O/Na(+)) has a small effect on the renin-remikiren interaction.

Modeling kinetics and equilibrium of membranes with fields: milestoning analysis and implication to permeation

Coarse graining of membrane simulations by translating atomistic dynamics to densities and fields with Milestoning is discussed. The space of the membrane system is divided into cells and the different cells are characterized by order parameters presenting the number densities. The dynamics of the order parameters are probed with Milestoning. The methodology is illustrated here for a phospholipid membrane system (a hydrated bilayer of DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) lipid molecules). Significant inhomogeneity in membrane internal number density leads to complex free energy landscape and local maps of transition times. Dynamics and distributions of cavities within the membrane assist the permeation of nonpolar solutes such as xenon atoms. It is illustrated that quantitative and detailed dynamics of water transport through DOPC membrane can be analyzed using Milestoning with fields. The reaction space for water transport includes at least two slow variables: the normal to the membrane plane, and the water density.

Understanding nanoparticle cellular entry: A physicochemical perspective

Understanding interactions between nanoparticles (NPs) with biological matter, particularly cells, is becoming increasingly important due to their growing application in medicine and materials, and consequent biological and environmental exposure. For NPs to be utilised to their full potential, it is important to correlate their functional characteristics with their physical properties, which may also be used to predict any adverse cellular responses. A key mechanism for NPs to impart toxicity is to gain cellular entry directly. Many parameters affect the behaviour of nanomaterials in a cellular environment particularly their interactions with cell membranes, including their size, shape and surface chemistry as well as factors such as the cell type, location and external environment (e.g. other surrounding materials, temperature, pH and pressure). Aside from in vitro and in vivo experiments, model cell membrane systems have been used in both computer simulations and physicochemical experiments to elucidate the mechanisms for NP cellular entry. Here we present a brief overview of the effects of NPs physical parameters on their cellular uptake, with focuses on 1) related research using model membrane systems and physicochemical methodologies; and 2) proposed physical mechanisms for NP cellular entrance, with implications to their nanotoxicity. We conclude with a suggestion that the energetic process of NP cellular entry can be evaluated by studying the effects of NPs on lipid mesophase transitions, as the molecular deformations and thus the elastic energy cost are analogous between such transitions and endocytosis. This presents an opportunity for contributions to understanding nanotoxicity from a physicochemical perspective.

Morphological transformations in polymer brushes in binary mixtures: DPD study

Morphological transformations in polymer brushes in a binary mixture of good and bad solvents are studied using dissipative particle dynamics simulations drawing on a characteristic example of polyisoprene natural rubber in an acetone-benzene mixture. A coarse-grained DPD model of this system is built based on the experimental data in the literature. We focus on the transformation of dense, collapsed brush in bad solvent (acetone) to expanded brush solvated in good solvent (benzene) as the concentration of benzene increases. Compared to a sharp globule-to-coil transition observed in individual tethered chains, the collapsed-to-expanded transformation in brushes is found to be gradual without a prominent transition point. The transformation becomes more leveled as the brush density increases. At low densities, the collapsed brush is highly inhomogeneous and patterned into bunches composed of neighboring chains due to favorable polymer-polymer interaction. At high densities, the brush is expanded even in bad solvent due to steric restrictions. In addition, we considered a model system similar to the PINR-acetone-benzene system, but with the interactions between the solvent components worsened to the limit of miscibility. Enhanced contrast between good and bad solvents facilitates absorption of the good solvent by the brush, shifting the collapsed-to-expanded transformation to lower concentrations of good solvent. This effect is especially pronounced for higher brush densities.

Modeling the interplay between protein and lipid aggregation in supported membranes

We present a theoretical model that deals with the complex interplay between lipid segregation and the self-aggregation of lipid-attached proteins. The model, in contrast to previous ones that consider proteins only as passive elements affecting the lipid distribution, describes the system including three terms: the dynamic interactions between protein monomers, the interactions between lipid components, and a mixed term considering protein-lipid interactions. It is used to explain experimental results performed on a well-defined system in which a self-aggregating soluble bacterial cytoskeletal protein polymerizes on a lipid bilayer containing two lipid components. All the elements considered in a previously described protein model, including torsion of the monomers within the filament, are needed to account for the observed filament shapes. The model also points out that lipid segregation can affect the length and curvature of the filaments and that the dynamic behavior of the lipids and proteins can have different time scales, giving rise to memory effects. This simple model that considers a dynamic protein assembly on a fluid and active lipid surface can be easily extended to other biologically relevant situations in which the interplay between protein and lipid aggregation is needed to fully describe the system.