Chapter 7 Multiscale Simulation of Membranes and Membrane Proteins: Connecting Molecular Interactions to Mesoscopic Behavior

DOPC versus DOPE as a helper lipid for gene-therapies: molecular dynamics simulations with DLin-MC3-DMA

Ionizable lipids are important compounds of modern therapeutic lipid nano-particles (LNPs). One of the most promising ionizable lipids (or amine lipids) is DLin-MC3-DMA. Depending on their pharmaceutical application these LNPs can also contain various helper lipids, such as phospho- and pegylated lipids, cholesterol and nucleic acids as a cargo. Due to their complex compositions the structures of these therapeutics have not been refined properly. Therefore, the role of each lipid in the pharmacological properties of LNPs has not been determined. In this work an atomistic model for the neutral form of DLin-MC3-DMA was derived and all-atom molecular dynamics (MD) simulations were carried out in order to investigate the effect of the phospholipid headgroup on the possible properties of the shell-membranes of LNPs. Bilayers containing either DOPC or DOPE lipids at two different ratios of DLin-MC3-DMA (5 mol% and 15 mol%) were constructed and simulated at neutral pH 7.4. The results from the analysis of MD trajectories revealed that DOPE lipid headgroups associated strongly with lipid tails and carbonyl oxygens of DLin-MC3-DMA, while for DOPC lipid headgroups no significant associations were observed. Furthermore, the strong associations between DOPE and DLin-MC3-DMA result in the positioning of DLin-MC3-DMA at the surface of the membrane. Such an interplay between the lipids slows down the lateral diffusion of all simulated bilayers, where a more dramatic decrease of the diffusion rate is observed in membranes with DOPE. This can explain the low water penetration of lipid bilayers with phosphatidylethanolamines and, probably, can relate to the bad transfection properties of LNPs with DOPE and DLin-MC3-DMA.

Coarse-grained molecular simulations of large biomolecules

Recently, we saw a dramatic increase in the number of researches that rely on coarse-grained (CG) simulations for large biomolecules. Here, first, we briefly describe recently developed and used CG models for proteins and nucleic acids. Balance between structure-based and physico-chemical terms is a key issue. We also discuss the multiscale algorithms used to derive CG parameters. Next, we comment on the dynamics used in CG simulations with an emphasis on the importance of hydrodynamic interactions. We then discuss the pros and cons of CG simulations. Finally, we overview recent exciting applications of CG simulations. Publicly available tools and software for CG simulations are also summarized.

An NMR database for simulations of membrane dynamics

Computational methods are powerful in capturing the results of experimental studies in terms of force fields that both explain and predict biological structures. Validation of molecular simulations requires comparison with experimental data to test and confirm computational predictions. Here we report a comprehensive database of NMR results for membrane phospholipids with interpretations intended to be accessible by non-NMR specialists. Experimental ¹³C-¹H and ²H NMR segmental order parameters (S(CH) or S(CD)) and spin-lattice (Zeeman) relaxation times (T(1Z)) are summarized in convenient tabular form for various saturated, unsaturated, and biological membrane phospholipids. Segmental order parameters give direct information about bilayer structural properties, including the area per lipid and volumetric hydrocarbon thickness. In addition, relaxation rates provide complementary information about molecular dynamics. Particular attention is paid to the magnetic field dependence (frequency dispersion) of the NMR relaxation rates in terms of various simplified power laws. Model-free reduction of the T(1Z) studies in terms of a power-law formalism shows that the relaxation rates for saturated phosphatidylcholines follow a single frequency-dispersive trend within the MHz regime. We show how analytical models can guide the continued development of atomistic and coarse-grained force fields. Our interpretation suggests that lipid diffusion and collective order fluctuations are implicitly governed by the viscoelastic nature of the liquid-crystalline ensemble. Collective bilayer excitations are emergent over mesoscopic length scales that fall between the molecular and bilayer dimensions, and are important for lipid organization and lipid-protein interactions. Future conceptual advances and theoretical reductions will foster understanding of biomembrane structural dynamics through a synergy of NMR measurements and molecular simulations.

A structurally relevant coarse-grained model for cholesterol

Detailed atomistic computer simulations are now widely used to study biological membranes, including increasingly mixed lipid systems that involve, for example, cholesterol, which is a key membrane lipid. Typically, simulations of these systems start from a preassembled bilayer because the timescale on which self-assembly occurs in mixed lipid systems is beyond the practical abilities of fully atomistic simulations. To overcome this limitation and study bilayer self-assembly, coarse-grained models have been developed. Although there are several coarse-grained models for cholesterol reported in the literature, these generally fail to account explicitly for the unique molecular features of cholesterol that relate to its function and role as a membrane lipid. In this work, we propose a new coarse-grained model for cholesterol that retains the molecule's unique features and, as a result, can be used to study crystalline structures of cholesterol. In the development of the model, two levels of coarse-graining are explored and the importance of retaining key molecular features in the coarse-grained model that are relevant to structural properties is investigated.

Large-scale simulations of fluctuating biological membranes

We present a simple, and physically motivated, coarse-grained model of a lipid bilayer, suited for micron scale computer simulations. Each approximately 25 nm(2) patch of bilayer is represented by a spherical particle. Mimicking forces of hydrophobic association, multiparticle interactions suppress the exposure of each sphere's equator to its implicit solvent surroundings. The requirement of high equatorial density stabilizes two-dimensional structures without necessitating crystalline order, allowing us to match both the elasticity and fluidity of natural lipid membranes. We illustrate the model's versatility and realism by characterizing a membrane's response to a prodding nanorod.

A coarse-grained model for amorphous and crystalline fatty acids

Fatty acids constitute one of the main components of the lipid lamellae in the top layer of the skin, known as the stratum corneum, which acts as a barrier to foreign substances entering the body and to water leaving the body. To better understand the mechanics of the skin, a molecular-level understanding of the structure of the lamellae needs to be investigated. As a first step toward this goal, the current work involves the development of a coarse-grained model for fatty acids in an amorphous and a crystalline state. In order to retain the structural details of the atomistic molecules, radial distribution functions have been used to provide target data against which the coarse-grained force field is optimized. The optimization was achieved using the method developed by Reith, Putz, and Muller-Plathe with a damping factor introduced into the updating scheme to facilitate the convergence against the crystalline radial distribution functions. Using this approach, a transferable force field has been developed for both crystalline and amorphous systems that can be used to describe fatty acids of different chain lengths. We are unaware of any other coarse-grained model in the literature that has been developed to study solid phases. Additionally, the amorphous force field has been shown to accurately model mixtures of different free fatty acids based on the potentials derived from pure lipid systems.

Multiscale simulation of protein mediated membrane remodeling

Proteins interacting with membranes can result in substantial membrane deformations and curvatures. This effect is known in its broadest terms as membrane remodeling. This review article will survey current multiscale simulation methodologies that have been employed to examine protein mediated membrane remodeling.

PX- and FYVE-mediated interactions with membranes: simulation studies

Molecular dynamics simulations have been used to explore the interactions of two PI(3)P-binding domains with their PI ligands and with a phospholipid bilayer. Three simulations each of the EEA1-FYVE domain and the p40(phox)-PX domain have been compared: with the protein in an apo state, with a bound Ins(1,3)P(2) molecule, and bound to a PI(3)P molecule embedded in a lipid bilayer. Two main questions were addressed in analysis of the simulations: (i) the location of these domains relative to the lipid bilayer and (ii) their interactions with the lipids, both specific interactions via bound PI(3)P and nonspecific interactions with bilayer phospholipids. Both domains underwent a decrease in dynamic flexibility on binding to the ligand and to the membrane, this being more pronounced for the FYVE domain. Compared to their starting locations [docked to a membrane-inserted PI(3)P molecule], each of the domains penetrated more deeply into the lipid bilayer. For FYVE, nonspecific protein-lipid interactions were formed mainly by the N-terminal hydrophobic region of the protein. For PX, both the alpha1-alpha2 and the beta1-beta2 regions penetrated the bilayer. There appeared to be more marked dynamic fluctuations in hydrogen bonds between basic side chains and PI(3)P for FYVE than for PX, but for both domains, such interactions were maintained throughout the simulations. The simulations agree well with available biophysical data, suggesting this computational method may be used to predict protein-bilayer interactions for other PI-binding proteins.