Critical size dependence of domain formation observed in coarse-grained simulations of bilayers composed of ternary lipid mixtures

Cholesterol and Lipid Rafts in the Biogenesis of Amyloid-β Protein and Alzheimer's Disease

Cholesterol has been conjectured to be a modulator of the amyloid cascade, the mechanism that produces the amyloid-β (Aβ) peptides implicated in the onset of Alzheimer's disease. We propose that cholesterol impacts the genesis of Aβ not through direct interaction with proteins in the bilayer, but indirectly by inducing the liquid-ordered phase and accompanying liquid-liquid phase separations, which partition proteins in the amyloid cascade to different lipid domains and ultimately to different endocytotic pathways. We explore the full process of Aβ genesis in the context of liquid-ordered phases induced by cholesterol, including protein partitioning into lipid domains, mechanisms of endocytosis experienced by lipid domains and secretases, and pH-controlled activation of amyloid precursor protein secretases in specific endocytotic environments. Outstanding questions on the essential role of cholesterol in the amyloid cascade are identified for future studies.

Binary bilayer simulations for partitioning within membranes

Membrane proteins (MPs) often show preference for one phase over the other, which is characterized by the partition coefficient, Kp. The physical mechanisms underlying Kp have been only inferred indirectly from experiments due to the unavailability of detailed structures and compositions of ordered phases. Molecular dynamics (MD) simulations can complement these details and thus, in principle, provide further insights into the partitioning of MPs between two phases. However, the application of MD has remained difficult due to long time scales required for equilibration and large system size for the phase stability, which have not been fully resolved even in free energy simulations. This chapter describes the recently developed binary bilayer simulation method, where the membrane is composed of two laterally attached membrane patches. The binary bilayer system (BBS) is designed to preserve the lateral packing of both phases in a significantly smaller size compared to that required for macroscopic phase separation. These characteristics are advantageous in partitioning simulations, as the length scale for diffusion across the system can be significantly smaller. Hence the BBS can be efficiently employed in both conventional MD and free energy simulations, though sampling in ordered phases remains difficult due to slow diffusion. Development of efficient lipid swapping methods and its combination with the BBS would be a useful approach for partitioning in coexisting phases.

Ion-Induced PIP2 Clustering with Martini3: Modification of Phosphate-Ion Interactions and Comparison with CHARMM36

Phosphatidylinositol 4,5-bisphosphate (PIP2) is a critical lipid for cellular signaling. The specific phosphorylation of the inositol ring controls protein binding as well as clustering behavior. Two popular models to describe ion-mediated clustering of PIP2 are Martini3 (M3) and CHARMM36 (C36). Molecular dynamics simulations of PIP2-containing bilayers in solutions of potassium chloride, sodium chloride, and calcium chloride, and at two different resolutions are performed to understand the aggregation and the model parameters that drive it. The average M3 clusters of PIP2 in bilayers of 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine and PIP2 bilayers in the presence of K+, Na+, or Ca2+ contained 2.2, 2.6, and 6.4 times more PIP2 than C36 clusters, respectively. Indeed, the Ca2+-containing systems often formed a single large aggregate. Reparametrization of the M3 ion-phosphate Lennard-Jones interaction energies to reproduce experimental osmotic pressure of sodium dimethyl phosphate (DMP), K[DMP], and Ca[DMP]2 solutions, the same experimental target as C36, yielded comparably sized PIP2 clusters for the two models. Furthermore, C36 and the modified M3 predict similar saturation of the phosphate groups with increasing Ca2+, although the coarse-grained model does not capture the cooperativity between K+ and Ca2+. This characterization of the M3 behavior in the presence of monovalent and divalent ions lays a foundation to study cation/protein/PIP2 clustering.

Origin of the nonlinear structural and mechanical properties in oppositely curved lipid mixtures

Structural and mechanical properties of membranes such as thickness, tail order, bending modulus and curvature energetics play crucial role in controlling various cellular functions that depend on the local lipid organization and membrane reshaping. While behavior of these biophysical properties are well understood in single component membranes, very little is known about how do they change in the mixed lipid membranes. Often various properties of the mixed lipid bilayers are assumed to change linearly with the mole fractions of the constituent lipids which, however, is true for "ideal" mixing only. In this study, using molecular dynamics simulations, we show that structural and mechanical properties of binary lipid mixture change nonlinearly with the lipid mole fractions, and the strength of the nonlinearity depends on two factors - spontaneous curvature difference and locally inhomogeneous interactions between the lipid components.

Synergistic computational and experimental studies of a phosphoglycosyl transferase membrane/ligand ensemble

Complex glycans serve essential functions in all living systems. Many of these intricate and byzantine biomolecules are assembled employing biosynthetic pathways wherein the constituent enzymes are membrane-associated. A signature feature of the stepwise assembly processes is the essentiality of unusual linear long-chain polyprenol phosphate-linked substrates of specific isoprene unit geometry, such as undecaprenol phosphate (UndP) in bacteria. How these enzymes and substrates interact within a lipid bilayer needs further investigation. Here, we focus on a small enzyme, PglC from Campylobacter, structurally characterized for the first time in 2018 as a detergent-solubilized construct. PglC is a monotopic phosphoglycosyl transferase that embodies the functional core structure of the entire enzyme superfamily and catalyzes the first membrane-committed step in a glycoprotein assembly pathway. The size of the enzyme is significant as it enables high-level computation and relatively facile, for a membrane protein, experimental analysis. Our ensemble computational and experimental results provided a high-level view of the membrane-embedded PglC/UndP complex. The findings suggested that it is advantageous for the polyprenol phosphate to adopt a conformation in the same leaflet where the monotopic membrane protein resides as opposed to additionally disrupting the opposing leaflet of the bilayer. Further, the analysis showed that electrostatic steering acts as a major driving force contributing to the recognition and binding of both UndP and the soluble nucleotide sugar substrate. Iterative computational and experimental mutagenesis support a specific interaction of UndP with phosphoglycosyl transferase cationic residues and suggest a role for critical conformational transitions in substrate binding and specificity.

Understanding the Free Energy Landscape of Phase Separation in Lipid Bilayers using Molecular Dynamics

Liquid-liquid phase separation (LLPS) inside the cell often results in biological condensates that can critically impact cell homeostasis. Such phase separation events occur in multiple parts of cells, including the cell membranes, where the so-called "lipid raft" hypothesis posits the formation of ordered domains floating in a sea of disordered lipids. The resulting lipid domains often have functional roles. However, the thermodynamics of lipid phase separation and their resulting mechanistic effects on cell function and dysfunction are poorly understood. Understanding such complex phenomena in cell membranes, with their diverse lipid compositions, is exceptionally difficult. For this reasons, simple model systems that can recapitulate similar behavior are widely used to study this phenomenon. Despite these simplifications, the timescale and and length scales of domain formation pose a challenge for molecular dynamics (MD) simulations. Thus, most MD studies focus on spontaneous lipid phase separation - essentially measuring the sign (but not the amplitude) of the free energy change upon separation - rather than directly interrogating the thermodynamics. Here, we propose a proof-of-concept pipeline that can directly measure this free energy by combining coarse-grained MD with enhanced sampling protocols using a novel collective variable. This approach will be a useful tool to help connect the thermodynamics of phase separation with the mechanistic insights already available from molecular dynamics simulations.

SIGNIFICANCE

Standard molecular dynamics simulations can determine the sign the free energy change upon phase separation, but not the amplitude. We present a new method to determine the phase separation free energy for lipid membranes, based on a enhanced sampling using the weighted ensemble method combined with a novel collective variable, validated using coarse-grained simulations applied to several simple systems. The new method will be valuable as a way to develop models that connect molecular-level structural features to the thermodynamics of phase separation.

Unsaturated Lipids Facilitate Partitioning of Transmembrane Peptides into the Liquid Ordered Phase

The affinity of single-pass transmembrane (TM) proteins for ordered membrane phases has been reported to depend on their lipidation, TM length, and lipid accessible surface area. In this work, the raft affinities of the TM domain of the linker for activation of T cells and its depalmitoylated variant are assessed using free energy simulations in a binary bilayer system composed of two laterally patched bilayers of ternary liquid ordered (Lo) and liquid disordered (Ld) phases. These phases are modeled by distinct compositions of distearoylphosphatidylcholine, palmitoyloleoylphosphatidylcholine (POPC), and cholesterol, and the simulations were carried out for 4.5 μs/window. Both peptides are shown to preferentially partition into the Ld phase in agreement with model membrane experiments and previous simulations on ternary lipid mixtures but not with measurements on giant plasma membrane vesicles where the Lo is slightly preferred. However, the 500 ns average relaxation time of lipid rearrangement around the peptide precluded a quantitative analysis of free energy differences arising from peptide palmitoylation and two different lipid compositions. When in the Lo phase, peptides reside in regions rich in POPC and interact preferentially with its unsaturated tail. Hence, the detailed substructure of the Lo phase is an important modulator of peptide partitioning, in addition to the inherent properties of the peptide.

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.

Coarse-grained molecular dynamics simulation of cation distribution profiles on negatively charged lipid membranes during phase separation

Revealing the ion distributions on a charged lipid membrane in aqueous solution under the influence of long-range interactions is essential for understanding the origin of the stability of the bilayer structure and the interaction between biomembranes and various electrolytes. However, the ion distributions and their dynamics associated with the phase separation process of the lipid bilayer membrane are still unclear. We perform coarse-grained molecular dynamics simulations to reveal the Na⁺ and Cl^- distributions on charged phospholipid bilayer membranes during phase separation. During the phase separation, cations closely follow the position of negatively charged lipids on a microsecond timescale and are rapidly redistributed parallel to the lipid bilayer. In the homogenous mixture of zwitterionic and negatively charged lipids, cations weakly follow negatively charged lipids, indicating the strong interaction between cations and negatively charged lipids. We also compare cation concentrations as a function of surface charge density obtained by our simulation with those obtained by a modified Poisson-Boltzmann theory. Including the ion finite size makes the statistical results consistent, suggesting the importance of the ion-ion interactions in aqueous solution. Our simulation results advance our understanding of ion distribution during phase separation.

CHARMM-GUI Membrane Builder: Past, Current, and Future Developments and Applications

Molecular dynamics simulations of membranes and membrane proteins serve as computational microscopes, revealing coordinated events at the membrane interface. As G protein-coupled receptors, ion channels, transporters, and membrane-bound enzymes are important drug targets, understanding their drug binding and action mechanisms in a realistic membrane becomes critical. Advances in materials science and physical chemistry further demand an atomistic understanding of lipid domains and interactions between materials and membranes. Despite a wide range of membrane simulation studies, generating a complex membrane assembly remains challenging. Here, we review the capability of CHARMM-GUI Membrane Builder in the context of emerging research demands, as well as the application examples from the CHARMM-GUI user community, including membrane biophysics, membrane protein drug-binding and dynamics, protein-lipid interactions, and nano-bio interface. We also provide our perspective on future Membrane Builder development.

A lattice model of ternary mixtures of lipids and cholesterol with tunable domain sizes

Much of our understanding of the physical properties of raft domains in biological membranes, and some insight into the mechanisms underlying their formation stem from atomistic simulations of simple model systems, especially ternary mixtures consisting of saturated and unsaturated lipids, and cholesterol (Chol). To explore the properties of such systems at large spatial scales, we here present a simple ternary mixture lattice model, involving a small number of nearest neighbor interaction terms. Monte Carlo simulations of mixtures with different compositions show excellent agreement with experimental and atomistic simulation observations across multiple scales, ranging from the local distributions of lipids to the phase diagram of the system. The simplicity of the model allows us to identify the roles played by the different interactions between components, and the interplay between them. Importantly, by changing the value of one of the model parameters, we can tune the size of the liquid-ordered domains, thereby simulating both Type II mixtures exhibiting macroscopic phase separation and Type I mixtures with nanoscopic domains. The Type II mixture simulation results fit well to the experimentally determined phase diagram of mixtures containing saturated DPPC/unsaturated DOPC/Chol. When the tunable parameter is changed, we obtain the Type I version of DPPC/DOPC/Chol, i.e., a mixture not showing thermodynamic phase transitions but one that may be fitted to the same phase diagram if local measures are used to distinguish between the different states. Our model results suggest that short range packing is likely to be a key regulator of the stability and size distribution of biological rafts.

Nanodisc Lipids Exhibit Singular Behaviors Implying Critical Phenomena

Nanodiscs are broadly used for characterization of membrane proteins as they are generally assumed to provide a near-native environment. In fact, it is an open question whether the physical properties of lipids in nanodiscs and membrane vesicles of the same lipid composition are identical. Here, we investigate the properties of lipids (1,2-dipalmitoyl-sn-glycero-3-phosphocholine, 1,2-dilauroyl-sn-glycero-3-phosphocholine, and their mixtures) in two different sample types, nanodiscs and multilamellar vesicles, by means of spin-label electron spin resonance techniques. Our results provide a quantitative description of lipid dynamics and ordering, elucidating the molecular details of how lipids in the two sample types behave differently in response to temperature and lipid composition. We show that the properties of lipids are altered in nanodiscs such that the dissimilarity of the fluid and gel lipid phases is reduced, and the first-order phase transitions are largely abolished in nanodiscs. We unveil that the ensemble of lipids in the middle of a nanodisc bilayer, as probed by the end-chain spin-label 16-PC, is promoted to a state close to a miscibility critical point, thereby rendering the phase transitions continuous. Critical phenomena have recently been proposed to explain features of the heterogeneity in native cell membranes. Our results lay the groundwork for how to establish a near-native environment in nanodiscs with simple organization of lipid components.

Phase Behavior and Miscibility in Two-Component Glycolipid Monolayers

Glycolipids are known to be involved in the formation of ordered functional domains in biological membranes. Since the structural characterization of such domains is difficult, most studies have so far dealt with lipid mixtures containing only one glycolipid component at a time, although biological membranes usually contain several glycolipid species, which can result in more complex structures and phase behavior. Here, we combine classical isotherm measurements with surface-sensitive grazing-incidence X-ray diffraction to investigate the phase behavior and miscibility in Langmuir monolayers of binary glycolipid mixtures. We find that the phase behavior has a subtle dependence on the saccharide headgroup chemistry. For compatible chemistries, molecular superlattice structures formed by one of the glycolipid species are conserved and can host foreign glycolipids up to a defined stoichiometry. In contrast, for sterically incompatible saccharide chemistries, the superlattice is lost even if both species are able to form such structures in their pure forms. Our results suggest that related phenomena may play important roles also in biological contexts.

Simulation study of domain formation in a model bacterial membrane

Recent experimental studies revealed that functional membrane microdomains (FMMs) are formed in prokaryotic cells which are structurally and functionally similar to the lipid rafts formed in eukaryotic cells. In this study, we employ coarse-grained molecular dynamics simulations to investigate the mechanism of domain formation and its physiochemical properties in a model methicillin-resistant staphylococcus aureus (MRSA) cell membrane. We find that domains are formed through lateral segregation of staphyloxanthin (STX), a carotenoid which shields the bacteria from the host's immune because of its antioxidant nature. Simulation results suggest that membrane integrity increases with the size of the domain, which is assessed by computing bond order parameter of the lipid tails, membrane expansion modulus and water permeability across the membrane. Various membrane domain proteins such as flotillin-like protein floA and penicillin binding protein (PBP2a) preferentially bind with the STX and accumulate in the membrane domain which is consistent with the recent experimental results.

On Computing Equilibrium Binding Constants for Protein-Protein Association in Membranes

Protein association in lipid membranes is fundamental to membrane protein function and of great biomedical relevance. All-atom and coarse-grained models have been extensively used to understand the protein-protein interactions in the membrane and to compute equilibrium association constants. However, slow translational and rotational diffusion of protein in membrane presents challenges to the effective sampling of conformations defining the ensembles of free and bound states contributing to the association equilibrium and the free energy of dimerization. We revisit the homodimerization equilibrium of the TM region of glycophorin A. Conformational sampling is performed using umbrella sampling along previously proposed one-dimensional collective variables and compared with sampling over a two-dimensional collective variable space using the MARTINI v2.2 force field. We demonstrate that the one-dimensional collective variables suffer from restricted sampling of the native homodimer conformations leading to a biased free energy landscape. Conversely, simulations along the two-dimensional collective variable effectively characterize the thermodynamically relevant native and non-native interactions contributing to the association equilibrium. These results demonstrate the challenges associated with accurately characterizing binding equilibria when multiple poses contribute to the bound state ensemble.

Interdomain exchange and the flip-flop of cholesterol in ternary component lipid membranes and their effects on heterogeneous cholesterol diffusion

Cell membranes are heterogeneous with a variety of lipids, cholesterol, and proteins and are composed of domains of different compositions. Such heterogeneous environments make the transport of cholesterol complicated: cholesterol not only diffuses within a particular domain but also travels between domains. Cholesterol also flip-flops between upper and lower leaflets such that cholesterol may reside both within leaflets and in the central region between two leaflets. How the presence of multiple domains and the interdomain exchange of cholesterol would affect the cholesterol transport, however, remains elusive. In this study, therefore, we perform molecular dynamics simulations up to 100μs for ternary component lipid membranes, which consist of saturated lipids (dipalmitoylphosphatidylcholine, DPPC), unsaturated lipids (dilinoleylphosphatidylcholine, DIPC), and cholesterol. The ternary component membranes in our simulations form two domains readily: DPPC and DIPC domains. We find that the diffusion of cholesterol molecules is much more heterogeneous and non-Gaussian than expected for binary component lipid membranes of lipids and cholesterol. The non-Gaussian parameter of the cholesterol molecules is about four times larger in the ternary component lipid membranes than in the binary component lipid membranes. Such non-Gaussian and heterogeneous transport of cholesterol arises from the interplay among the interdomain kinetics, the different diffusivity of cholesterol in different domains, and the flip-flop of cholesterol. This suggests that in cell membranes that consist of various domains and proteins, the cholesterol transport can be very heterogeneous. We also find that the mechanism of the interdomain exchange differs for different domains: cholesterol tends to exit the DIPC domain along the central region of the membrane for the DIPC-to-DPPC transition, while the cholesterol is likely to exit the DPPC domain within the membrane leaflet for the DPPC-to-DIPC transition. Also, the interdomain exchange kinetics of cholesterol for the DPPC-to-DIPC transition is up to 7.9 times slower than the DIPC-to-DPPC transition.

Capturing Membrane Phase Separation by Dual Resolution Molecular Dynamics Simulations

Understanding the lateral organization in plasma membranes remains an open problem and is of great interest to many researchers. Model membranes consisting of coexisting domains are commonly used as simplified models of plasma membranes. The coarse-grained (CG) Martini force field has successfully captured spontaneous separation of ternary membranes into a liquid-disordered and a liquid-ordered domain. With all-atom (AA) models, however, phase separation is much harder to achieve due to the slow underlying dynamics. To remedy this problem, here, we apply the virtual site (VS) hybrid method on a ternary membrane composed of saturated lipids, unsaturated lipids, and cholesterol to investigate the phase separation. The VS scheme couples the two membrane leaflets at CG and AA resolution. We found that the rapid phase separation reached by the CG leaflet can accelerate and guide this process in the AA leaflet.

Interfacial hydration determines orientational and functional dimorphism of sterol-derived Raman tags in lipid-coated nanoparticles

Lipid-coated noble metal nanoparticles (L-NPs) combine the biomimetic surface properties of a self-assembled lipid membrane with the plasmonic properties of a nanoparticle (NP) core. In this work, we investigate derivatives of cholesterol, which can be found in high concentrations in biological membranes, and other terpenoids, as tunable, synthetic platforms to functionalize L-NPs. Side chains of different length and polarity, with a terminal alkyne group as Raman label, are introduced into cholesterol and betulin frameworks. The synthesized tags are shown to coexist in two conformations in the lipid layer of the L-NPs, identified as "head-out" and "head-in" orientations, whose relative ratio is determined by their interactions with the lipid-water hydrogen-bonding network. The orientational dimorphism of the tags introduces orthogonal functionalities into the NP surface for selective targeting and plasmon-enhanced Raman sensing, which is utilized for the identification and Raman imaging of epidermal growth factor receptor-overexpressing cancer cells.

The effects of the lipid type on the spatial arrangement and dynamics of cholesterol in binary component lipid membranes

Intermolecular interactions between cholesterol and lipids in cell membranes, which play critical roles in cellular processes such as the formation of nano-domains, depend on the molecular structure of the lipids. The diffusion and the spatial arrangement of cholesterol within the lipid membranes also change with the type of lipids. For example, the flip-flop, an important transport mechanism for cholesterol in the membranes, can be facilitated significantly by the presence of unsaturated lipids. However, how the structure of lipids affects the spatial arrangement and the dynamics of cholesterol remains elusive at a molecular level. In this study, we investigate the effects of lipid-cholesterol interactions on the spatial arrangement and the dynamics of cholesterol. We perform molecular dynamics simulations for the binary component membranes of lipids and cholesterol. We employ seven different kinds of lipids by changing either the degree of a saturation level or the length of lipid tails. We find from our simulations that the rate of cholesterol flip-flop is enhanced as the lipids are either less saturated or shorter, which is consistent with previous studies. Interestingly, when the lipid tails are fully saturated and sufficiently long, the center in between two leaflets becomes metastable for cholesterol to stay at. Because the cholesterol at the membrane center diffuses faster than that within leaflets, regardless of the lipid type, such an emergence of the metastable state (in terms of the cholesterol position) complicates the cholesterol diffusion significantly.

Finite-Size Effects and Optimal System Sizes in Simulations of Surfactant Micelle Self-Assembly

The spontaneous formation of micelles in aqueous solutions is governed by the amphipathic nature of surfactants and is practically interesting due to the regular use of micelles as membrane mimics, for the characterization of protein structure, and for drug design and delivery. We performed a systematic characterization of the finite-size effect observed in single-component dodecylphosphocholine (DPC) micelles with the coarse-grained MARTINI model. Of multiple coarse-grained solvent models investigated using large system sizes, the nonpolarizable solvent model was found to most accurately reproduce SANS spectra of 100 mM DPC in aqueous solution. We systematically investigated the finite-size effect at constant 100 mM concentration in 23 systems of sizes 40-150 DPC, confirming the finite-size effect to manifest as an oscillation in the mean micelle aggregation number about the thermodynamic aggregation number as the system size increases. The oscillations in aggregation number mostly diminish once the system supports the formation of three micelles. Similar oscillations were observed in the estimated critical micelle concentration with a mean value of 1.10 mM, which is in agreement with experiment to 0.1 mM. The accuracy of using a multiscale simulation approach to avoid finite-size effects in the micelle size distribution and SANS spectra using MARTINI and CHARMM36 was explored using multiple long time scale 500 DPC coarse-grained simulations, which were back-mapped to CHARMM36 all-atom systems. It was found that the MARTINI model generally occupies more volume than the all-atom model, leading to the formation of micelles that are of a reasonable radius of gyration but are smaller in aggregation number. The systematic characterization of the finite-size effect and exploration of multiscale modeling presented in this work provide guidance for the accurate modeling of micelles in simulations.

Addressing the Excessive Aggregation of Membrane Proteins in the MARTINI Model

The MARTINI model is a widely used coarse-grained force field popular for its capacity to represent a diverse array of complex biomolecules. However, efforts to simulate increasingly realistic models of membranes, involving complex lipid mixtures and multiple proteins, suggest that membrane protein aggregates are overstabilized by the MARTINI v2.2 force field. In this study, we address this shortcoming of the MARTINI model. We determined the free energy of dimerization of four transmembrane protein systems using the nonpolarizable MARTINI model. Comparison with experimental FRET-based estimates of the dimerization free energy was used to quantify the significant overstabilization of each protein homodimer studied. To improve the agreement between simulation and experiment, a single uniform scaling factor, α, was used to enhance the protein-lipid Lennard-Jones interaction. A value of α = 1.04-1.045 was found to provide the best fit to the dimerization free energies for the proteins studied while maintaining the specificity of contacts at the dimer interface. To further validate the modified force field, we performed a multiprotein simulation using both MARTINI v2.2 and the reparameterized MARTINI model. While the original MARTINI model predicts oligomerization of protein into a single aggregate, the reparameterized MARTINI model maintains a dynamic equilibrium between monomers and dimers as predicted by experimental studies. The proposed reparameterization is an alternative to the standard MARTINI model for use in simulations of realistic models of a biological membrane containing diverse lipids and proteins.

Modulated and spiral surface patterns on deformable lipid vesicles

We investigate the behavior of two-dimensional systems that exhibit a transition between homogeneous and spatially inhomogeneous phases, which have spherical topology, and whose mechanical properties depend on the local value of the order parameter. One example of such a system is multicomponent lipid bilayer vesicles, which serve as a model to study cellular membranes. Under certain conditions, such bilayers separate into coexisting liquid-ordered and liquid-disordered regions. When arranged into the shape of small vesicles, this phase coexistence can result in spatial patterns that are more complex than the basic two-domain configuration encountered in typical bulk systems. The difference in bending rigidity between the liquid-ordered and liquid-disordered regions couples the shape of the vesicle to the local composition. We show that this interplay gives rise to a rich phase diagram that includes homogeneous, separated, and axisymmetric modulated phases that are divided by regions of spiral patterns in the surface morphology.

Pollen wall patterns as a model for biological self-assembly

We are still far from being able to predict organisms' shapes purely from their genetic codes. While it is imperative to identify which encoded macromolecules contribute to a phenotype, determining how macromolecules self-assemble independently of the genetic code may be equally crucial for understanding shape development. Pollen grains are typically single-celled microgametophytes that have decorated walls of various shapes and patterns. The accumulation of morphological data and a comprehensive understanding of the wall development makes this system ripe for mathematical and physical modeling. Therefore, pollen walls are an excellent system for identifying both the genetic products and the physical processes that result in a huge diversity of extracellular morphologies. In this piece, I highlight the current understanding of pollen wall biology relevant for quantification studies and enumerate the modellable aspects of pollen wall patterning and specific approaches that one may take to elucidate how pollen grains build their beautifully patterned walls.

Lateral heterogeneity and domain formation in cellular membranes

•

Review article describing recent experimental and theoretical membrane lateral heterogeneity research.

•

Describes the static and dynamic physical concepts behind domain formation in model membranes.

•

Describes coarse-grained, phenomenological approaches that result in phases associated with lipid lateral heterogeneity.

As early as the development of the fluid mosaic model for cellular membranes, researchers began observing the telltale signs of lateral heterogeneity. Over the decades this has led to the development of the lipid raft hypothesis and the ensuing controversy that has unfolded, as a result. Here, we review the physical concepts behind domain formation in lipid membranes, both of their structural and dynamic origins. This, then leads into a discussion of coarse-grained, phenomenological approaches that describe the wide range of phases associated with lipid lateral heterogeneity. We use these physical concepts to describe the interaction between raft-lipid species, such as long-chain saturated lipids, sphingomyelin, and cholesterol, and non-raft forming lipids, such as those with short acyl chains or unsaturated fatty acids. While debate has persisted on the biological relevance of lipid domains, recent research, described here, continues to identify biological roles for rafts and new experimental approaches have revealed the existence of lipid domains in living systems. Given the recent progress on both the biological and structural aspects of raft formation, the research area of membrane lateral heterogeneity will not only expand, but will continue to produce exciting results.

Phase Transition in a Heterogeneous Membrane: Atomically Detailed Picture

Membranes serve diverse functions in biological systems. Variations in their molecular compositions impact their physical properties and lead to rich phase behavior such as switching from the gel to fluid phase and/or separation to micro- and macrodomains with different molecular compositions. We present a combined computational and experimental study of the phase behavior of a mixed membrane of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) molecules. This heterogeneous membrane changes from gel to fluid and shows separate domains as a function of temperature. Atomically detailed simulations provide microscopic information about these molecular assemblies. However, these systems are challenging for computations since approaching equilibrium necessitates exceptionally long molecular dynamics trajectories. We use the simulation method of MDAS (Molecular Dynamics with Alchemical Steps) to generate adequate statistics. Isotope-edited IR spectroscopy of the lipids was used to benchmark the simulations. Together, simulations and experiments provide insight into the structural and dynamical features of the phase diagram.

Twisting and tilting of a mechanosensitive molecular probe detects order in membranes

Lateral forces in biological membranes affect a variety of dynamic cellular processes. Recent synthetic efforts have introduced fluorescent "flippers" as environment-sensitive planarizable push-pull probes that can detect lipid packing and membrane tension, and respond to lipid-induced mechanical forces by a shift in their spectroscopic properties. Herein, we investigate the molecular origin of the mechanosensitivity of the best known flipper, Flipper-TR, by an extended set of molecular dynamics (MD) simulations in membranes of increasing complexity and under different physicochemical conditions, revealing unprecedented details of the sensing process. Simulations enabled by accurate refinement of Flipper-TR force field using quantum mechanical calculations allowed us to unambiguously correlate the planarization of the two fluorescent flippers to spectroscopic response. In particular, Flipper-TR conformation exhibits bimodal distribution in disordered membranes and a unimodal distribution in highly ordered membranes. Such dramatic change was associated with a shift in Flipper-TR excitation spectra, as supported both by our simulated and experimentally-measured spectra. Flipper-TR sensitivity to phase-transition is confirmed by a temperature-jump protocol that alters the lipid phase of an ordered membrane, triggering an instantaneous mechanical twisting of the probe. Simulations show that the probe is also sensitive to surface tension, since even in a naturally disordered membrane, the unimodal distribution of coplanar flippers can be achieved if a sufficiently negative surface tension is applied to the membrane. MD simulations in ternary mixtures containing raft-like nanodomains show that the probe can discriminate lipid domains in phase-separated complex bilayers. A histogram-based approach, called DOB-phase classification, is introduced that can differentiate regions of disordered and ordered lipid phases by comparing dihedral distributions of Flipper-TR. Moreover, a new sensing mechanism involving the orientation of Flipper-TR is elucidated, corroborating experimental evidence that the probe tilt angle is strongly dependent on lipid ordering. The obtained atomic-resolution description of Flipper-TR mechanosensitivity is key to the interpretation of experimental data and to the design of novel mechanosensors with improved spectroscopic properties.

The aggregation of striped nanoparticles in mixed phospholipid bilayers

The unique and adjustable properties of nanoparticles present enormous opportunities for their use as targeted drug delivery vectors. For example, nanoparticles functionalized with key surface ligands have been shown to pass through phospholipid bilayers without causing localised disruption. However, the further effects nanoparticles have on multi-component phospholipid bilayers remain unclear. We use coarse-grained computational models to investigate the structural properties of mixed phospholipid bilayers in the presence of ligand-functionalized nanoparticles. Model bilayers are composed of DPPC, DUPC, DFPC and cholesterol, and the nanoparticles are striped with a hydrophobic-ligand band and charged-ligand spherical caps. Our results show that nanoparticles aggregate near unsaturated phospholipid regions, phospholipid bilayer phase-separation is promoted in the presence of nanoparticles, and the heterogeneous components of a phospholipid bilayer play a significant role in the lateral organization of nanoparticles. This study highlights the need for considering the complexity of realistic phospholipid bilayers when optimising ligand functionalized nanoparticles for efficient drug delivery vectors.

Exploring the impact of proteins on the line tension of a phase-separating ternary lipid mixture

The separation of lipid mixtures into thermodynamically stable phase-separated domains is dependent on lipid composition, temperature, and system size. Using molecular dynamics simulations, the line tension between thermodynamically stable lipid domains formed from ternary mixtures of di-C16:0 PC:di-C18:2 PC:cholesterol at 40:40:20 mol. % ratio was investigated via two theoretical approaches. The line tension was found to be 3.1 ± 0.2 pN by capillary wave theory and 4.7 ± 3.7 pN by pressure tensor anisotropy approaches for coarse-grained models based on the Martini force field. Using an all-atom model of the lipid membrane based on the CHARMM36 force field, the line tension was found to be 3.6 ± 0.9 pN using capillary wave theory and 1.8 ± 2.2 pN using pressure anisotropy approaches. The discrepancy between estimates of the line tension based on capillary wave theory and pressure tensor anisotropy methods is discussed. Inclusion of protein in Martini membrane lipid mixtures was found to reduce the line tension by 25%-35% as calculated by the capillary wave theory approach. To further understand and predict the behavior of proteins in phase-separated membranes, we have formulated an analytical Flory-Huggins model and parameterized it against the simulation results. Taken together these results suggest a general role for proteins in reducing the thermodynamic cost associated with domain formation in lipid mixtures and quantifies the thermodynamic driving force promoting the association of proteins to domain interfaces.

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.

Structure of lateral heterogeneities in a coarse-grained model for multicomponent membranes

We study the lateral domain structure in a coarse-grained molecular model for multicomponent lipid bilayers by semi-grandcanonical Monte Carlo simulations. The membranes are filled with liquid ordered (lo) domains surrounded by a liquid disordered (ld) matrix. Depending on the membrane composition and temperature, we identify different morphological regimes: one regime (I) where the lo domains are small and relatively compact, and two regimes (II, II') where they are larger and often interconnected. In the latter two regimes, the ld matrix forms a network of disordered trenches separating the lo domains, with a relatively high content of interdigitated line defects. Since such defects are also a structural element of the modulated ripple phase in one component membranes, we argue that the regimes II, II' may be amorphous equivalents of the ripple phase in multicomponent membranes. We also analyze the local structure and provide evidence that the domains in regime I are stabilized by a monolayer curvature mechanism postulated in earlier work [S. Meinhardt et al., PNAS, 2013, 110, 4476].

Facilitated and Non-Gaussian Diffusion of Cholesterol in Liquid Ordered Phase Bilayers Depends on the Flip-Flop and Spatial Arrangement of Cholesterol

The diffusion of cholesterol in biological membranes is critical to cellular processes such as the formation of cholesterol-enriched domains. The cholesterol diffusion may be complicated especially when cholesterol flip-flops and/or stays at the membrane center. Understanding the diffusion mechanism of cholesterol at a molecular level should be, therefore, a topic of interest. We perform molecular dynamics simulations up to 100 μs for lipid bilayers with various concentrations of cholesterol. We find that cholesterol diffusion in the liquid ordered phase depends on whether it is within leaflets or at the bilayer center, is non-Gaussian for several microseconds, and is enhanced significantly compared to that of lipids. Cholesterol at the bilayer center diffuses fast, while cholesterol in the hydrocarbon region with upright orientation diffuses relatively slowly. Such position-dependent dynamics of cholesterol leads to facilitated and non-Gaussian diffusion.

A simple model of planar membrane: An integral equation investigation

A simple model of a lipid membrane, a binary mixture of saturated lipids and unsaturated lipids, was studied using an integral equation theory. The planar membrane is modeled as mixture of linear and bent molecules in two-dimensional space, and site-site radial distribution function, Kirkwood-Buff (KB) integral and related quantities were computed over the whole range of the molar fraction to understand their mixing behavior. We found that a close packing of linear molecules is enhanced as the fraction of bent molecules increases, but a long range correlation between the linear molecules is weakened. A high concentration of linear molecules promotes the demixing of linear molecules and bent molecules, and enhances the long range correlation between molecules. This implies that, the higher the concentration of linear molecules, the larger clusters tend to be formed. © 2018 Wiley Periodicals, Inc.

Membrane Lipid Nanodomains

Lipid membranes can spontaneously organize their components into domains of different sizes and properties. The organization of membrane lipids into nanodomains might potentially play a role in vital functions of cells and organisms. Model membranes represent attractive systems to study lipid nanodomains, which cannot be directly addressed in living cells with the currently available methods. This review summarizes the knowledge on lipid nanodomains in model membranes and exposes how their specific character contrasts with large-scale phase separation. The overview on lipid nanodomains in membranes composed of diverse lipids (e.g., zwitterionic and anionic glycerophospholipids, ceramides, glycosphingolipids) and cholesterol aims to evidence the impact of chemical, electrostatic, and geometric properties of lipids on nanodomain formation. Furthermore, the effects of curvature, asymmetry, and ions on membrane nanodomains are shown to be highly relevant aspects that may also modulate lipid nanodomains in cellular membranes. Potential mechanisms responsible for the formation and dynamics of nanodomains are discussed with support from available theories and computational studies. A brief description of current fluorescence techniques and analytical tools that enabled progress in lipid nanodomain studies is also included. Further directions are proposed to successfully extend this research to cells.

Regimes of Complex Lipid Bilayer Phases Induced by Cholesterol Concentration in MD Simulation

Cholesterol is essential to the formation of phase-separated lipid domains in membranes. Lipid domains can exist in different thermodynamic phases depending on the molecular composition and play significant roles in determining structure and function of membrane proteins. We investigate the role of cholesterol in the structure and dynamics of ternary lipid mixtures displaying phase separation using molecular dynamics simulations, employing a physiologically relevant span of cholesterol concentration. We find that cholesterol can induce formation of three regimes of phase behavior: 1) miscible liquid-disordered bulk, 2) phase-separated, domain-registered coexistence of liquid-disordered and liquid-ordered domains, and 3) phase-separated, domain-antiregistered coexistence of liquid-disordered and newly identified nanoscopic gel domains composed of cholesterol threads we name "cholesterolic gel" domains. These findings are validated and discussed in the context of current experimental knowledge, models of cholesterol spatial distributions, and models of ternary lipid-mixture phase separation.

A mixed alchemical and equilibrium dynamics to simulate heterogeneous dense fluids: Illustrations for Lennard-Jones mixtures and phospholipid membranes

An algorithm to efficiently simulate multi-component fluids is proposed and illustrated. The focus is on biological membranes that are heterogeneous and challenging to investigate quantitatively. To achieve rapid equilibration of spatially inhomogeneous fluids, we mix conventional molecular dynamics simulations with alchemical trajectories. The alchemical trajectory switches the positions of randomly selected pairs of molecules and plays the role of an efficient Monte Carlo move. It assists in accomplishing rapid spatial de-correlations. Examples of phase separation and mixing are given in two-dimensional binary Lennard-Jones fluid and a DOPC-POPC membrane. The performance of the algorithm is analyzed, and tools to maximize its efficiency are provided. It is concluded that the algorithm is vastly superior to conventional molecular dynamics for the equilibrium study of biological membranes.