Simulations Of Bilayers Research Articles

Structure of POPC Lipid Bilayers in OPLS3e Force Field.

It is crucial for molecular dynamics simulations of biomembranes that the force field parameters give a realistic model of the membrane behavior. In this study, we examined the OPLS3e force field for the carbon-hydrogen order parameters SCH of POPC (1-palmitoyl-2-oleoylphosphatidylcholine) lipid bilayers at varying hydration conditions and ion concentrations. The results show that OPLS3e behaves similarly to the CHARMM36 force field and relatively accurately follows the experimentally measured SCH for the lipid headgroup, the glycerol backbone, and the acyl tails. Thus, OPLS3e is a good choice for POPC bilayer simulations under many biologically relevant conditions. The exception are systems with an abundancy of ions, as similarly to most other force fields OPLS3e strongly overestimates the membrane-binding of cations, especially Ca2+. This leads to undesirable positive charge of the membrane surface and drastically lowers the concentration of Ca2+ in the surrounding solvent, which might cause issues in systems sensitive to correct charge distribution profiles across the membrane.

Efficient calculation of the free energy for protein partitioning using restraining potentials

An approach for the efficient simulation of phase-separated lipid bilayers, for use in the calculation of equilibrium free energies of partitioning between lipid domains, is proposed. The methodology exploits restraint potentials and rectangular aspect ratios that enforce lipid phase separation, allowing for the simulation of smaller systems that approximately reproduce bulk behavior. The utility of this approach is demonstrated through the calculation of potentials of mean force for the translation of a transmembrane protein between lipid domains. The impact of the imposed restraints on lipid tail ordering and lipid packing are explored, providing insight into how restraints can best be employed to compute accurate free-energy surfaces. This approach should be useful in the accurate calculation of equilibrium partition coefficients for transmembrane protein partitioning in heterogeneous membranes, providing insight into the thermodynamic driving forces that control this fundamental biophysical phenomenon.

Effects of Lipid Shape and Interactions on the Conformation, Dynamics, and Curvature of Ultrasound-Responsive Liposomes.

We perform coarse-grained molecular dynamics simulations of bilayers composed of various lipids and cholesterol at their different ratios. Simulations show that cholesterol-lipid interactions restrict the lateral dynamics of bilayers but also promote bilayer curvature, indicating that these opposite effects simultaneously occur and thus cannot significantly influence bilayer stability. In contrast, lyso-lipids effectively pack the vacancy in the bilayer composed of cone-shaped lipids and thus reduce bilayer dynamics and curvature, showing that bilayers are more significantly stabilized by lyso-lipids than by cholesterol, in agreement with experiments. In particular, the bilayer composed of cone-shaped lipids shows higher dynamics and curvature than does the bilayer composed of cylindrical-shaped lipids. To mimic ultrasound, a high external pressure was applied in the direction of bilayer normal, showing the formation of small pores that are surrounded by hydrophilic lipid headgroups, which can allow the release of drug molecules encapsulated into the liposome. These findings help to explain experimental observations regarding that liposomes are more significantly stabilized by lyso-lipids than by cholesterol, and that the liposome with cone-shaped lipids more effectively releases drug molecules upon applying ultrasound than does the liposome with cylindrical-shaped lipids.

Machine Learning-Assisted Phase Transition Temperatures from Generalized Replica Exchange Simulations of Dry Martini Lipid Bilayers.

Accurate estimation of phase transition temperatures has been a longstanding challenge for molecular simulations. Recently, the generalized Replica Exchange technique for estimating phase transition temperatures has allowed for improved sampling of the phase transition; however, it requires a significant number of simultaneous replicas both inside and outside of the transition region leading to costly computational expense. In this work, the recently developed machine learning-assisted lipid phase analysis technique for learning the phase of individual lipids has been combined with generalized Replica Exchange Molecular Dynamics to reduce the overall computational expense of evaluating transition temperatures. This technique is then applied to eight different Dry Martini lipids to demonstrate its ability to describe transition temperatures as a function of chain length and tail saturation.

Molecular substructure of the liquid-ordered phase formed by sphingomyelin and cholesterol: sphingomyelin clusters forming nano-subdomains are a characteristic feature.

As a model of lipid rafts, the liquid-ordered (Lo) phase formed by sphingomyelin (SM) and cholesterol (Cho) in bilayer membranes has long attracted the attention of biophysics researchers. New approaches and methodologies have led to a better understanding of the molecular basis of the Lo domain structure. This review summarizes studies on model membrane systems consisting of SM/unsaturated phospholipid/Cho implying that the Lo phase contains SM-based nanodomains (or nano-subdomains). Some of the Lo phase properties may be attributed to these nanodomains. Several studies suggest that the nanodomains contain clustered SM molecules packed densely to form gel-phase-like subdomains of single-digit nanometer size at physiological temperatures. Cho and unsaturated lipids located in the Lo phase are likely to be concentrated at the boundaries between the subdomains. These subdomains are not readily detected in the Lo phase formed by saturated phosphatidylcholine (PC) molecules, suggesting that they are strongly stabilized by homophilic interactions specific to SM, e.g., between SM amide groups. This model for the Lo phase is supported by experiments using dihydro-SM, which is thought to have stronger homophilic interactions than SM, as well as by studies using the enantiomer of SM having opposite stereochemistry to SM at the 2 and 3 positions and by some molecular dynamics (MD) simulations of lipid bilayers containing Lo-lipids. Nanosized gel subdomains seem to play an important role in controlling membrane organization and function in biological membranes.

Not so rigid capsids based on cyclodextrin complexes: Keys to design

HypothesisMembranes based on cyclodextrin complexes can be used as functional nanocarrier envelopers by chemical modifications of the cyclodextrin hydroxyl groups or by encapsulating different ligands in their cavities. ExperimentsMolecular dynamics simulations of monolayers and bilayers based on supramolecular complexes consisting of two α or β-cyclodextrin and one sodium dodecylsulfate or dodecane at 283 K and at 298 K were performed. FindingsIt is shown that the structure and main interactions stabilizing the membranes, as well as their permeability to water and ions can be tuned by changing the cyclodextrin, the ligand, the number of layers or/and the temperature. These results provide new evidences about both their dynamic nature and the interactions responsible for the stabilization of the membranes and will facilitate the design of new functional capsides and applications based on cyclodextrin complexes.

Algorithm to catalogue topologies of dynamic lipid hydrogen-bond networks.

Lipid membrane interfaces host reactions essential for the functioning of cells. The hydrogen-bonding environment at the membrane interface is particularly important for binding of proteins, drug molecules, and ions. We present here the implementation and applications of a depth-first search algorithm that analyzes dynamic lipid interaction networks. Lipid hydrogen-bond networks sampled transiently during simulations of lipid bilayers are clustered according to main types of topologies that characterize three-dimensional arrangements of lipids connected to each other via short water bridges. We characterize the dynamics of hydrogen-bonded lipid clusters in simulations of model POPE and POPE:POPG membranes that are often used for bacterial membrane proteins, in a model of the Escherichia coli membrane with six different lipid types, and in POPS membranes. We find that all lipids sample dynamic hydrogen-bonded networks with linear, star, or circular arrangements of the lipid headgroups, and larger networks with combinations of these three types of topologies. Overall, linear lipid-water bridges tend to be short. Water-mediated lipid clusters in all membranes with PE lipids tend to be somewhat small, with about four lipids in all membranes studied here. POPS membranes allow circular arrangements of three POPS lipids to be sampled frequently, and complex arrangements of linear, star, and circular paths may also be sampled. These findings suggest a molecular picture of the membrane interface whereby lipid molecules transiently connect in clusters with somewhat small spatial extension.

WIND-PVPA: Water/Ion NMR Detected PVPA to assess lipid barrier integrity in vitro through quantification of passive water- and ion transport

Water/Ion NMR Detected – Phospholipid Vesicle Permeability Assay (WIND-PVPA), is presented as a novel, straightforward and automatable method to assess lipid barrier integrity in vitro. The apparent permeability constants of water- and ions across the PVPA barriers are determined in a one-pot experiment under the influence of membrane-active guest molecules. NMR spectroscopy is used to quantify the water directly (D2O) and the ions indirectly (complexed with EDTA) as a function of time. WIND-PVPA is demonstrated using four anti-microbial peptides, to show that membrane active molecules can be differentiated by their disruptive influence on the PVPA system. The results obtained are compared with explicit molecular dynamics simulations of lipid bilayers, AMPs, water and salt, where the motions of all individual water molecules relative to the lipid bilayer are monitored over the course of the simulations, allowing the calculation of theoretical apparent permeability constants of the corresponding single bilayer systems.Proof-of-principle is presented that WIND-PVPA can be used to evaluate the lipid barrier destabilizing effect of active guest molecules by measuring changes in passive water- and ion permeabilities upon exposure. The method is highly flexible in terms of barrier composition, choice of probes and membrane active compounds.

A Method for Detection of Water Permeation Events in Molecular Dynamics Simulations of Lipid Bilayers

A Method for Detection of Water Permeation Events in Molecular Dynamics Simulations of Lipid Bilayers

High-Dimensional Parameter Search Method to Determine Force Field Mixing Terms in Molecular Simulations.

Molecular dynamics (MD) force fields for lipids and ions are typically developed independently of one another. In simulations consisting of both lipids and ions, lipid-ion interaction energies are estimated using a predefined set of mixing rules for Lennard-Jones (LJ) interactions. This, however, does not guarantee their reliability. In fact, compared to the quantum mechanical reference data, Lorentz-Berthelot mixing rules substantially underestimate the binding energies of Na+ ions with small-molecule analogues of lipid headgroups, yielding errors on the order of 80 and 130 kJ/mol, respectively, for methyl acetate and diethyl phosphate. Previously, errors associated with mixing force fields have been reduced using approaches such as "NB-fix" in which LJ interactions are computed using explicit cross terms rather than those from mixing rules. Building on this idea, we derive explicit lipid-ion cross terms that also may implicitly include many-body cooperativity effects. Additionally, to account for the interdependency between cross terms, we optimize all cross terms simultaneously by performing high-dimensional searches using our ParOpt software. The cross terms we obtain reduce the errors due to mixing rules to below 10 kJ/mol. MD simulation of the lipid bilayer conducted using these optimized cross terms resolves the structural discrepancies between our previous simulations and small-angle X-ray and neutron scattering experiments. These results demonstrate that simulations of lipid bilayers with ions that are accurate up to structural data from scattering experiments can be performed without explicit polarization terms. However, it is worth noting that such NB-fix cross terms are not based on any physical principle; a polarizable lipid model would be more realistic and is still desired. Our approach is generic and can be applied to improve the accuracies of simulations employing mixed force fields.

Lipid21: Complex Lipid Membrane Simulations with AMBER.

We extend the modular AMBER lipid force field to include anionic lipids, polyunsaturated fatty acid (PUFA) lipids, and sphingomyelin, allowing the simulation of realistic cell membrane lipid compositions, including raft-like domains. Head group torsion parameters are revised, resulting in improved agreement with NMR order parameters, and hydrocarbon chain parameters are updated, providing a better match with phase transition temperature. Extensive validation runs (0.9 μs per lipid type) show good agreement with experimental measurements. Furthermore, the simulation of raft-like bilayers demonstrates the perturbing effect of increasing PUFA concentrations on cholesterol molecules. The force field derivation is consistent with the AMBER philosophy, meaning it can be easily mixed with protein, small molecule, nucleic acid, and carbohydrate force fields.

Molecular dynamic simulations of hydrophobins: pure-protein bilayers and lipid-protein interactions

Hydrophobins are a family of proteins characterized by a large exposed hydrophobic region, rendering them highly amphiphilic. Class II hydrophobins such as HFBI self-assemble into monolayers at water-air or water-oil interfaces, revealing long-range ordered hexagonal ‘honeycomb’ structures[1]. This property allows for the preparation of pure-protein bilayers and vesicles [2] with unexpectedly low permeability for water and ions. To provide a molecular explanation for these properties, we carried out atomistic and coarse grained molecular dynamics (MD) simulations of HFBI bilayers.

Developing initial conditions for simulations of asymmetric membranes: a practical recommendation

It has been proposed that the surface tension difference between leaflets (or differential stress) in asymmetric bilayers is generally non-vanishing. This implies that there is no unique approach to generate initial conditions for simulations of asymmetric bilayers in the absence of experimentally derived constraints. Current generation methods include individual area per lipid (APL)-based, leaflet surface area (SA) matching, and zero leaflet tension-based (0-DS). Here, we propose a bilayer-based approach that aims for achieving partial chemical equilibrium by inter-leaflet switching of selected lipids via P21 periodic boundary conditions.

The molecular determinants of membrane viscosity

Lipid membrane viscosity is critical to biological function. Bacterial cells grown in different environments have been shown to alter their lipid composition in order to maintain a specific viscosity, and membrane viscosity has been linked to the rate of cellular respiration. In order to understand the factors which determine the viscosity of a membrane, we ran equilibrium all-atom simulations of single component lipid bilayers and calculated their viscosities. The viscosity was calculated via a Green-Kubo relation, with the stress tensor autocorrelation function fit to a stretched exponential by a maximum-likelihood Markov chain Monte Carlo method.

The effect of different force fields on the ion-membrane interactions

Molecular dynamics (MD) simulations of lipid membranes have been widely used to better understand phenomena at the atomic and molecular level that cannot be observed with conventional experimental methods. This technique is very useful to understand the underlying mechanisms of the most common biological ions, such as K+, Na+, Cl- or Ca2+ when they interact with the lipid bilayer or when they go through the induced pores during electroporation. Lipid bilayer simulations showed that K+ and Cl- interact very little with the lipids, compared to Na+ and Ca2+.

Ripple-like instability in the simulated gel phase of finite size phosphocholine bilayers.

Atomistic molecular dynamics simulations have reached a degree of maturity that makes it possible to investigate the lipid polymorphism of model bilayers over a wide range of temperatures. However if both the fluid Lα and tilted gel [Formula: see text] states are routinely obtained, the [Formula: see text] ripple phase of phosphatidylcholine lipid bilayers is still unsatifactorily described. Performing simulations of lipid bilayers made of different numbers of DPPC (1,2-dipalmitoylphosphatidylcholine) molecules ranging from 32 to 512, we demonstrate that the tilted gel phase [Formula: see text] expected below the pretransition cannot be obtained for large systems (equal or larger than 94 DPPC molecules) through common simulations settings or temperature treatments. Large systems are instead found in a disordered gel phase which display configurations, topography and energies reminiscent from the ripple phase [Formula: see text] observed between the pretransition and the main melting transition. We show how the state of the bilayers below the melting transition can be controlled and depends on thermal history and conditions of preparations. A mechanism for the observed topographic instability is suggested.

Developing initial conditions for simulations of asymmetric membranes: a practical recommendation

It has been proposed that the surface tension difference between leaflets (or differential stress) in asymmetric bilayers is generally nonvanishing. This implies that there is no unique approach to generate initial conditions for simulations of asymmetric bilayers in the absence of experimentally derived constraints. Current generation methods include individual area per lipid (APL) based, leaflet surface area (SA) matching, and zero leaflet tension based (0-DS). This work adds a bilayer-based approach that aims for achieving partial chemical equilibrium by interleaflet switching of selected lipids via P21 periodic boundary conditions. Based on a recently proposed theoretical framework, we obtained expressions for tensions in asymmetric bilayers from both the bending and area strains. We also developed a quantitative measure for the energetic penalty from the differential stress. The impacts of APL-, SA-, and 0-DS-based approaches on mechanical properties are assessed for two different asymmetric bilayers. The lateral pressure profile and its moments differ significantly for each method, whereas the area compressibility modulus is relatively insensitive. Application of P21 periodic boundary conditions (APL/P21, SA/P21, and 0-DS/P21) results in better agreement in mechanical properties between asymmetric bilayers generated by APL-, SA-, and 0-DS-based approaches, in which changes are the smallest for bilayers from the SA-based method. The estimated differential stress from the theory shows good agreement with that from the simulations. These simulation results and the good agreement between the predicted and observed differential stress further support the theoretical framework in which bilayer mechanical properties are outcomes of the interplay between intrinsic bending and asymmetric lipid packing. Based on the simulation results and theoretical predictions, the SA/P21-based, or at least the SA-based (when the differential stress is small), approach is recommended as a practical method for developing initial conditions for asymmetric bilayer simulations.

Nonconverged Constraints Cause Artificial Temperature Gradients in Lipid Bilayer Simulations.

Molecular dynamics (MD) simulations have become an indispensable tool to investigate phase separation in model membrane systems. In particular, simulations based on coarse-grained (CG) models have found widespread use due to their increased computational efficiency, allowing for simulations of multicomponent lipid bilayers undergoing phase separation into liquid-ordered and liquid-disordered domains. Here, we show that a significant temperature difference between molecule types can artificially arise in CG MD membrane simulations with the standard Martini simulation parameters in GROMACS. In particular, the linear constraint solver (LINCS) algorithm does not converge with its default settings, resulting in serious temperature differences between molecules in a time step-dependent manner. We demonstrate that the underlying reason for this behavior is the presence of highly constrained moieties, such as cholesterol. Their presence can critically impact numerous structural and dynamic membrane properties obtained from such simulations. Furthermore, any preference of these molecules toward a certain membrane phase can lead to spatial temperature gradients, which can amplify the degree of phase separation or even induce it in compositions that would otherwise mix well. We systematically investigated the effect of the integration time step and LINCS settings on membrane properties. Our data show that for cholesterol-containing membranes, a time step of 20 fs should be combined with at least lincs_iter = 2 and lincs_order = 12, while using a time step of 30 fs requires at least lincs_iter = 3 and lincs_order = 12 to bring the temperature differences to a level where they do not perturb central membrane properties. Moreover, we show that in cases where stricter LINCS settings are computationally too demanding, coupling the lipids in multiple groups to the temperature bath offers a practical workaround to the problem, although the validity of this approach should be further verified. Finally, we show that similar temperature gradients can also emerge in atomistic simulations using the CHARMM force field in combination with settings that allow for a 5 fs integration step.

Impact of Increased Membrane Realism on Conformational Sampling of Proteins.

The realism and accuracy of lipid bilayer simulations through molecular dynamics (MD) are heavily dependent on the lipid composition. While the field is pushing toward implementing more heterogeneous and realistic membrane compositions, a lack of high-resolution lipidomic data prevents some membrane protein systems from being modeled with the highest level of realism. Given the additional diversity of real-world cellular membranes and protein-lipid interactions, it is still not fully understood how altering membrane complexity affects modeled membrane protein functions or if it matters over long-timescale simulations. This is especially true for organisms whose membrane environments have little to no computational study, such as the plant plasma membrane. Tackling these issues in tandem, a generalized, realistic, and asymmetric plant plasma membrane with more than 10 different lipid species is constructed herein. Classical MD simulations of pure membrane constructs were performed to evaluate how altering the compositional complexity of the membrane impacted the plant membrane properties. The apo form of a plant sugar transporter, OsSWEET2b, was inserted into membrane models where lipid diversity was calculated in either a size-dependent or size-independent manner. An adaptive sampling simulation regime validated by Markov-state models was performed to capture the gating dynamics of OsSWEET2b in each of these membrane constructs. In comparison to previous OsSWEET2b simulations performed in a pure POPC bilayer, we confirm that simulations performed within a native-like membrane composition alter the stabilization of apo OsSWEET2b conformational states by ∼1 kcal/mol. The free-energy barriers of intermediate conformational states decrease when realistic membrane complexity is simplified, albeit roughly within sampling error, suggesting that protein-specific responses to membranes differ due to altered packing caused by compositional fluctuations. This work serves as a case study where a more realistic bilayer composition makes unbiased conformational sampling easier to achieve than with simplified bilayers.

Physical Characterization of Triolein and Implications for Its Role in Lipid Droplet Biogenesis.

Lipid droplets (LDs) are neutral lipid-storing organelles surrounded by a phospholipid (PL) monolayer. At present, how LDs are formed in the endoplasmic reticulum (ER) bilayer is poorly understood. In this study, we present a revised all-atom (AA) triolein (TG) model, the main constituent of the LD core, and characterize its properties in a bilayer membrane to demonstrate the implications of its behavior in LD biogenesis. In bilayer simulations, TG resides at the surface, adopting PL-like conformations (denoted in this work as SURF-TG). Free energy sampling simulation results estimate the barrier for TG relocating from the bilayer surface to the bilayer center to be ∼2 kcal/mol in the absence of an oil lens. SURF-TG is able to modulate membrane properties by increasing PL ordering, decreasing bending modulus, and creating local negative curvature. The other neutral lipid, dioleoyl-glycerol (DAG), also reduces the membrane bending modulus and populates negative curvature regions. A phenomenological coarse-grained (CG) model is also developed to observe larger-scale SURF-TG-mediated membrane deformation. CG simulations confirm that TG nucleates between the bilayer leaflets at a critical concentration when SURF-TG is evenly distributed. However, when one monolayer contains more SURF-TG, the membrane bends toward the other leaflet, followed by TG nucleation if a concentration is higher than the critical threshold. The central conclusion of this study is that SURF-TG is a negative curvature inducer, as well as a membrane modulator. To this end, a model is proposed in which the accumulation of SURF-TG in the luminal leaflet bends the ER bilayer toward the cytosolic side, followed by TG nucleation.