Computer simulation studies of self-assembling macromolecules

Self-Assembly of Rhein and Matrine Nanoparticles for Enhanced Wound Healing

Carrier-free self-assembly has gradually shifted the focus of research on natural products, which effectively improve the bioavailability and the drug-loading rate. However, in spite of the existing studies, the development of self-assembled natural phytochemicals that possess pharmacological effects still has scope for further exploration and enhancement. Herein, a nano-delivery system was fabricated through the direct self-assembly of Rhein and Matrine and was identified as a self-assembled Rhein-Matrine nanoparticles (RM NPs). The morphology of RM NPs was characterized by TEM. The molecular mechanisms of self-assembly were explored using FT-IR, 1H NMR, and molecular dynamics simulation analysis. Gelatin methacryloyl (GelMA) hydrogel was used as a drug carrier for controlled release and targeted delivery of RM NPs. The potential wound repair properties of RM NPs were evaluated on a skin wound-healing model. TEM and dynamic light scattering study demonstrated that the RM NPs were close to spherical, and the average size was approximately 75 nm. 1H NMR of RM NPs demonstrated strong and weak changes in the interaction energies during self-assembly. Further molecular dynamics simulation analysis predicted the self-assembly behavior. An in vivo skin wound-healing model demonstrated that RM NPs present better protection effect against skin damages. Taken together, RM NPs are a new self-assembly system; this may provide new directions for natural product applications.

MiMiC: A high-performance framework for multiscale molecular dynamics simulations

MiMiC is a framework for performing multiscale simulations in which loosely coupled external programs describe individual subsystems at different resolutions and levels of theory. To make it highly efficient and flexible, we adopt an interoperable approach based on a multiple-program multiple-data (MPMD) paradigm, serving as an intermediary responsible for fast data exchange and interactions between the subsystems. The main goal of MiMiC is to avoid interfering with the underlying parallelization of the external programs, including the operability on hybrid architectures (e.g., CPU/GPU), and keep their setup and execution as close as possible to the original. At the moment, MiMiC offers an efficient implementation of electrostatic embedding quantum mechanics/molecular mechanics (QM/MM) that has demonstrated unprecedented parallel scaling in simulations of large biomolecules using CPMD and GROMACS as QM and MM engines, respectively. However, as it is designed for high flexibility with general multiscale models in mind, it can be straightforwardly extended beyond QM/MM. In this article, we illustrate the software design and the features of the framework, which make it a compelling choice for multiscale simulations in the upcoming era of exascale high-performance computing.

pSPICA Force Field Extended for Proteins and Peptides

Many coarse-grained (CG) molecular dynamics (MD) studies have been performed to investigate biological processes involving proteins and lipids. CG force fields (FFs) in these MD studies often use implicit or nonpolar water models to reduce computational costs. CG-MD using water models cannot properly describe electrostatic screening effects owing to the hydration of ionic segments and thus cannot appropriately describe molecular events involving water channels and pores through lipid membranes. To overcome this issue, we developed a protein model in the pSPICA FF, in which a polar CG water model showing the proper dielectric response was adopted. The developed CG model greatly improved the transfer free energy profiles of charged side chain analogues across the lipid membrane. Application studies on melittin-induced membrane pores and mechanosensitive channels in lipid membranes demonstrated that CG-MDs using the pSPICA FF correctly reproduced the structure and stability of the pores and channels. Furthermore, the adsorption behavior of the highly charged nona-arginine peptides on lipid membranes changed with salt concentration, indicating the pSPICA FF is also useful for simulating protein adsorption on membrane surfaces.

Improved Protein Model in SPICA Force Field

The previous version of the SPICA coarse-grained (CG) force field (FF) protein model focused primarily on membrane proteins and successfully reproduced the dimerization free energies of several transmembrane helices and the stable structures of various membrane protein assemblies. However, that model had limited accuracy when applied to other proteins, such as intrinsically disordered proteins (IDPs) and peripheral proteins, because the dimensions of the IDPs in an aqueous solution were too compact, and protein binding on the lipid membrane surface was overstabilized. To improve the accuracy of the SPICA FF model for the simulation of such systems, in this study, we introduce protein secondary structure-dependent nonbonded interaction parameters to the backbone segments and reoptimize almost all nonbonded parameters for amino acids. The improved FF proposed here successfully reproduces the radii of gyration of various IDPs, the binding sensitivity of several peripheral membrane proteins, and the dimerization free energies of several transmembrane helices. The new model also shows improved agreement with experiments on the free energy of peptide association in water. In addition, an extensive library of nonbonded interactions between proteins and lipids, including various glycerophospholipids, sphingolipids, and cholesterol, allows the study of specific interactions between lipids and peripheral and transmembrane proteins. Hence, the new SPICA FF (version 2) proposed herein is applicable with high accuracy for simulating a wide range of protein systems.

Pragmatic Coarse-Graining of Proteins: Models and Applications

The molecular details involved in the folding, dynamics, organization, and interaction of proteins with other molecules are often difficult to assess by experimental techniques. Consequently, computational models play an ever-increasing role in the field. However, biological processes involving large-scale protein assemblies or long time scale dynamics are still computationally expensive to study in atomistic detail. For these applications, employing coarse-grained (CG) modeling approaches has become a key strategy. In this Review, we provide an overview of what we call pragmatic CG protein models, which are strategies combining, at least in part, a physics-based implementation and a top-down experimental approach to their parametrization. In particular, we focus on CG models in which most protein residues are represented by at least two beads, allowing these models to retain some degree of chemical specificity. A description of the main modern pragmatic protein CG models is provided, including a review of the most recent applications and an outlook on future perspectives in the field.

Development of a coarse-grained model for surface-functionalized gold nanoparticles: towards an accurate description of their aggregation behavior

Understanding the dispersion stability and aggregation propensity of self-assembled monolayer gold NPs at a molecular level is crucial to guide their rational design and to inform about the optimal surface functionalization for specific applications. To reach this goal, in silico modeling via coarse-grained (CG) molecular dynamics (MD) simulations is a fundamental tool to complement the information acquired from experimental studies since CG modeling allows to get a deep knowledge of the molecular interactions that take place at the nanoscale in this kind of systems. Unfortunately, current CG models of monolayer-protected AuNPs present several drawbacks that limit their accuracy in certain scenarios. We here develop a CG model that is fully compatible and extends the SPICA/SDK (Shinoda-DeVane-Klein) force field. Our model allows reproducing the behavior of AuNPs functionalized with hydrophobic as well as charged and more hydrophilic ligands. This model improves upon results obtained with previously derived CG force fields and successfully describes NPs aggregation and self-assembly in aqueous solution.

Endocytosis-Like Vesicle Fission Mediated by a Membrane-Expanding Molecular Machine Enables Virus Encapsulation for In Vivo Delivery

Biological membranes are functionalized by membrane-associated protein machinery. Membrane-associated transport processes, such as endocytosis, represent a fundamental and universal function mediated by membrane-deforming protein machines, by which small biomolecules and even micrometer-size substances can be transported via encapsulation into membrane vesicles. Although synthetic molecules that induce dynamic membrane deformation have been reported, a molecular approach enabling membrane transport in which membrane deformation is coupled with substance binding and transport remains critically lacking. Here, we developed an amphiphilic molecular machine containing a photoresponsive diazocine core (AzoMEx) that localizes in a phospholipid membrane. Upon photoirradiation, AzoMEx expands the liposomal membrane to bias vesicles toward outside-in fission in the membrane deformation process. Cargo components, including micrometer-size M13 bacteriophages that interact with AzoMEx, are efficiently incorporated into the vesicles through the outside-in fission. Encapsulated M13 bacteriophages are transiently protected from the external environment and therefore retain biological activity during distribution throughout the body via the blood following administration. This research developed a molecular approach using synthetic molecular machinery for membrane functionalization to transport micrometer-size substances and objects via vesicle encapsulation. The molecular design demonstrated in this study to expand the membrane for deformation and binding to a cargo component can lead to the development of drug delivery materials and chemical tools for controlling cellular activities.

Coarse-Grained Molecular Dynamics of pH-Sensitive Lipids

pH-sensitive lipids represent a class of lipids that can be protonated and destabilized in acidic environments, as they become positively charged in response to low-pH conditions. They can be incorporated into lipidic nanoparticles such as liposomes, which are able to change their properties and allow specific drug delivery at the acidic conditions encountered in some pathological microenvironments. In this work, we used coarse-grained molecular-dynamic simulations to study the stability of neutral and charged lipid bilayers containing POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) and various kinds of ISUCA ((F)2-(imidazol-1-yl)succinic acid)-derived lipids, which can act as pH-sensitive molecules. In order to explore such systems, we used a MARTINI-derived forcefield, previously parameterized using all-atom simulation results. We calculated the average area per lipid, the second-rank order parameter and the lipid diffusion coefficient of both lipid bilayers made of pure components and mixtures of lipids in different proportions, under neutral or acidic conditions. The results show that the use of ISUCA-derived lipids disturbs the lipid bilayer structure, with the effect being particularly marked under acidic conditions. Although more-in depth studies on these systems must be carried out, these initial results are encouraging and the lipids designed in this research could be a good basis for developing new pH-sensitive liposomes.

A review on microfluidic-assisted nanoparticle synthesis, and their applications using multiscale simulation methods

Recent years have witnessed an increased interest in the development of nanoparticles (NPs) owing to their potential use in a wide variety of biomedical applications, including drug delivery, imaging agents, gene therapy, and vaccines, where recently, lipid nanoparticle mRNA-based vaccines were developed to prevent SARS-CoV-2 causing COVID-19. NPs typically fall into two broad categories: organic and inorganic. Organic NPs mainly include lipid-based and polymer-based nanoparticles, such as liposomes, solid lipid nanoparticles, polymersomes, dendrimers, and polymer micelles. Gold and silver NPs, iron oxide NPs, quantum dots, and carbon and silica-based nanomaterials make up the bulk of the inorganic NPs. These NPs are prepared using a variety of top-down and bottom-up approaches. Microfluidics provide an attractive synthesis alternative and is advantageous compared to the conventional bulk methods. The microfluidic mixing-based production methods offer better control in achieving the desired size, morphology, shape, size distribution, and surface properties of the synthesized NPs. The technology also exhibits excellent process repeatability, fast handling, less sample usage, and yields greater encapsulation efficiencies. In this article, we provide a comprehensive review of the microfluidic-based passive and active mixing techniques for NP synthesis, and their latest developments. Additionally, a summary of microfluidic devices used for NP production is presented. Nonetheless, despite significant advancements in the experimental procedures, complete details of a nanoparticle-based system cannot be deduced from the experiments alone, and thus, multiscale computer simulations are utilized to perform systematic investigations. The work also details the most common multiscale simulation methods and their advancements in unveiling critical mechanisms involved in nanoparticle synthesis and the interaction of nanoparticles with other entities, especially in biomedical and therapeutic systems. Finally, an analysis is provided on the challenges in microfluidics related to nanoparticle synthesis and applications, and the future perspectives, such as large-scale NP synthesis, and hybrid formulations and devices.

Self-Assembly of Glycerol-Amphiphilic Janus Dendrimers Amplifies and Indicates Principles for the Selection of Stereochemistry by Biological Membranes

The principles for the selection of the stereochemistry of phospholipids of biological membranes remain unclear and continue to be debated. Therefore, any new experiments on this topic may help progress in this field. To address this question, three libraries of constitutional isomeric glycerol-amphiphilic Janus dendrimers (JDs) with nonsymmetric homochiral, racemic, and symmetric achiral branching points were synthesized by an orthogonal-modular-convergent methodology. These JDs amplify self-assembly, and therefore, monodisperse vesicles known as dendrimersomes (DSs) with predictable dimensions programmed by JD concentration were assembled by rapid injection of their ethanol solution into water. DSs of homochiral JD enantiomers, racemic, including mixtures of different enantiomers, and achiral exhibited similar DS size-concentration dependence. However, the number of bilayers of DSs assembled from homochiral, achiral, and racemic JDs determined by cryo-TEM were different. Statistical analysis of the number of bilayers and coarse-grained molecular dynamics simulations demonstrated that homochiral JDs formed predominantly unilamellar DSs. Symmetric achiral JDs assembled only unilamellar DSs while racemic JDs favored multilamellar DSs. Since cell membranes are unilamellar, these results indicate a new rationale for nonsymmetric homochiral vs racemic selection. Simultaneously, these experiments imply that the symmetric achiral lipids forming more stable membrane, probably had been the preferable assemblies of prebiotic cell membranes.

Artificial intelligence aids in development of nanomedicines for cancer management

Over the last decade, the nanomedicine has experienced unprecedented development in diagnosis and management of diseases. A number of nanomedicines have been approved in clinical use, which has demonstrated the potential value of clinical transition of nanotechnology-modified medicines from bench to bedside. The application of artificial intelligence (AI) in development of nanotechnology-based products could transform the healthcare sector by realizing acquisition and analysis of large datasets, and tailoring precision nanomedicines for cancer management. AI-enabled nanotechnology could improve the accuracy of molecular profiling and early diagnosis of patients, and optimize the design pipeline of nanomedicines by tuning the properties of nanomedicines, achieving effective drug synergy, and decreasing the nanotoxicity, thereby, enhancing the targetability, personalized dosing and treatment potency of nanomedicines. Herein, the advances in AI-enabled nanomedicines in cancer management are elaborated and their application in diagnosis, monitoring and therapy as well in precision medicine development is discussed.

Evaluation of Nanoparticle Stability under Blood Flow Shear

The stability of drug-loaded nanoparticles in vivo is related to the success of the drug delivery, which is investigated as a deficiency due to the limitation of traditional experimental methods. In this study, dissipative particle dynamics (DPD), a simulation method suitable for soft matter and fluids, was used to study the stability of amphiphilic nanoparticles in the blood microenvironment. By comparing the morphology alteration of nanoparticles with various molecular topologies in the shear fluid field, we have found that branch degree and geometric symmetry would be the key factors in maintaining the nanoparticle's stability. This research could provide more theoretical guidance for drug delivery system design.

Cooperative antimicrobial action of melittin on lipid membranes: A coarse-grained molecular dynamics study

We conducted a series of coarse-grained molecular dynamics (CG-MD) simulations to investigate the complicated actions of melittin, which is an antimicrobial peptide (AMP) derived from honey bee venom, on a lipid membrane. To accurately simulate the AMP action, we developed and used a protein CG model as an extension of the pSPICA force field (FF), which was designed to reproduce several thermodynamic quantities and structural properties. At a low peptide-to-lipid (P/L) ratio (1/102), no defect was detected. At P/L = 1/51, toroidal pore formation was observed due to collective insertion of multiple melittin peptides from the N-termini. The pore formation was initiated by a local increase in membrane curvature in the vicinity of the peptide aggregate. At a higher P/L ratio (1/26), two more modes were detected, seemingly not controlled by the P/L ratio but by a local arrangement of melittin peptides: 1. Pore formation accompanied by lipid extraction by melittin peptides:a detergent-like mechanism. 2. A rapidly formed large pore in a significantly curved membrane: bursting. Thus, we observed three pore formation modes (toroidal pore formation, lipid extraction, and bursting) depending on the peptide concentration and local arrangement. These observations were consistent with experimental observations and hypothesized melittin modes. Through this study, we found that the local arrangements and population of melittin peptides and the area expansion rate by membrane deformation were key to the initiation of and competition among the multiple pore formation mechanisms.

Scission energy and topology of micelles controlled by the molecular structure of additives

We employ coarse-grained (CG) molecular dynamics simulations (MD) to investigate the effects of the molecular structure of additives on the scission energy and morphology of charged micelles. Considering sodium dodecyl sulfate (SDS) as a representative charged surfactant and taking trimethylphenylammonium chloride (TMPAC) and octyltrimethylammonium bromide (OTAB) as oppositely charged additives, we show that the scission energy and topology of micelles vary significantly depending on the molecular structure of the hydrophobic part of the additives. The cyclic aromatic tail of the TMPAC disrupts the core structure of the SDS micelle and hence decreases the micelle scission energy, whereas the linear alkyl tail of the OTAB packs very well with the micelle core and increases the scission energy. Although both the additives have similar head structures, they lead to very different micelle morphologies because of the difference in the shape of their tail structures; ring-like or toroidal shaped micelles are formed in SDS/TMPAC solution whereas bicelle-like structures are formed in SDS/OTAB solution when the additive to surfactant ratio is higher than a certain value.

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.

Seipin accumulates and traps diacylglycerols and triglycerides in its ring-like structure

Lipid droplets (LDs) are intracellular organelles responsible for lipid storage, and they emerge from the endoplasmic reticulum (ER) upon the accumulation of neutral lipids, mostly triglycerides (TG), between the two leaflets of the ER membrane. LD biogenesis takes place at ER sites that are marked by the protein seipin, which subsequently recruits additional proteins to catalyze LD formation. Deletion of seipin, however, does not abolish LD biogenesis, and its precise role in controlling LD assembly remains unclear. Here, we use molecular dynamics simulations to investigate the molecular mechanism through which seipin promotes LD formation. We find that seipin clusters TG, as well as its precursor diacylglycerol, inside its unconventional ring-like oligomeric structure and that both its luminal and transmembrane regions contribute to this process. This mechanism is abolished upon mutations of polar residues involved in protein-TG interactions into hydrophobic residues. Our results suggest that seipin remodels the membrane of specific ER sites to prime them for LD biogenesis.

Pivotal Role of Interdigitation in Interleaflet Interactions: Implications from Molecular Dynamics Simulations

The asymmetric lipid composition in plasma membranes within the inner leaflet is not typically suitable for domain formation. Thus elucidation of the likelihood of the formation or stability of a raft-like domain in the inner leaflet is necessary. Herein we investigated the phase behavior of asymmetric membranes using coarse-grained molecular dynamics simulations. The lipid leaflet comprising dioleoylphosphatidylcholine (DOPC) and cholesterol (Chol) does not typically show well-developed domains in symmetric bilayer membranes; however, it does separate into liquid ordered (L_o) and liquid disordered (L_d) phases when the opposing leaflet containing sphingomyelin (SM), DOPC, and Chol demonstrates domain formation. We determine that interdigitated acyl chains modulated the partitioning of Chol in the opposing leaflet, resulting in phase separation. Similarly, the acyl chain length of SM within the opposing leaflet affected the phase behavior of the leaflet. Our results reveal the crucial role of interdigitation in determining the phase status in asymmetric membranes.

Molecular simulation of the shape deformation of a polymersome

Vesicles composed of diblock copolymers, or polymersomes, have proven to possess numerous applications ranging from drug delivery to catalytically driven nano-motors. The shape of a polymersome can be responsive to external stimuli, such as light or solvent. Molecular dynamics simulations reveal that the shape change upon the contraction of the inner volume of a polymersome vesicle occurs in two separate regimes-a stretching regime and a bending regime. The barrier is shown to be dependent on the solvent environment. These results suggest that tailoring the bending modulus of polymer membranes can be used as a design methodology to engineer new stimuli-responsive vesicles.

Self-Assembly of Phosphocholine Derivatives Using the ELBA Coarse-Grained Model: Micelles, Bicelles, and Reverse Micelles

The ELBA coarse-grained force field was originally developed for lipids, and its water model is described as a single-site Lennard-Jones particle with electrostatics modeled by an embedded point-dipole, while other molecules in this force field have a three (or four)-to-one mapping scheme. Here, ELBA was applied to investigate the self-assembly processes of dodecyl-phosphocholine (DPC) micelle, 1,2-dipalmitoyl-sn-glycero-3-phosphocholine/1,2-dihexaoyl-sn-glycero-3-phosphocholine (DPPC/DHPC) bicelles, and DPPC/cyclohexane/water reverse micelles through coarse-grained molecular dynamics (MD) simulations. New parameters were obtained using a simplex algorithm-based calibration procedure to determine the Lennard-Jones parameters for cyclohexane, dodecane, and cyclohexane-dodecane cross-interactions. Density, self-diffusion coefficient, surface tension, and mixture excess volume were found to be in fair agreement with experimental data. These new parameters were used in the simulations, and the obtained structures were analyzed for shape, size, volume, and surface area. Except for the shape of DPC micelles, all other properties match well with available experimental data and all-atom simulations. Remarkably, in agreement with experiments the rodlike shape of the DPPC reverse micelle is well described by ELBA, while all-atom data in the literature predicts a disclike shape. To further check the consistency of the force field in reproducing the correct shapes of reverse micelles, additional simulations were performed doubling the system size. Two distinct reverse micelles were obtained both presenting the rodlike shape and correct aggregation number.

Study of Structural stability and formation mechanisms in DSPC and DPSM liposomes: A coarse-grained molecular dynamics simulation

Liposomes or biological vesicles can be created from cholesterol, phospholipid, and water. Their stability is affected by their phospholipid composition which can influence disease treatment and drug delivery efficacy. In this study, the effect of phospholipid type on the formation and stability of liposomes using coarse-grained molecular dynamics simulations is investigated. For this purpose, the simulation study of the DSPC (1,2-distearoyl-sn-glycero-3-phosphocholine) and DPSM (Egg sphingomyelin) lipids were considered. All simulations were carried out using the Gromacs software and Martini force field 2.2. Energy minimization (3000 steps) model, equilibrium at constant volume to adjust the temperature at 400 Kelvin and equilibrium at constant pressure to adjust the pressure, at atmospheric pressure (1 bar) have been validated. Microsecond simulations, as well as formation analysis including density, radial distribution function, and solvent accessible surface area, demonstrated spherical nanodisc structures for the DPSM and DSPC liposomes. The results revealed that due to the cylindrical geometric structure and small-size head group, the DSPC lipid maintained its perfectly spherical structure. However, the DPSM lipid showed a conical geometric structure with larger head group than other lipids, which allows the liposome to form a micelle structure. Although the DSPC and DPSM lipids used in the laboratory tests exhibit liposome and micelle behaviors, the simulation results revealed their nanodisc structures. Energy analysis including overall energy, Van der Waals interaction energy, and electrostatic interaction energy showed that DPSM liposome is more stable than DSPC liposome.

A coarse-grain model for entangled polyethylene melts and polyethylene crystallization

The Shinoda-DeVane-Klein (SDK) model is herein demonstrated to be a viable coarse-grain model for performing molecular simulations of polyethylene (PE), affording new opportunities to advance molecular-level, scientific understanding of PE materials and processes. Both structural and dynamical properties of entangled PE melts are captured by the SDK model, which also recovers important aspects of PE crystallization phenomenology. Importantly, the SDK model can be used to represent a variety of materials beyond PE and has a simple functional form, making it unique among coarse-grain PE models. This study expands the suite of tools for studying PE in silico and paves the way for future work probing PE and PE-based composites at the molecular level.

Computational Modeling of Realistic Cell Membranes

Cell membranes contain a large variety of lipid types and are crowded with proteins, endowing them with the plasticity needed to fulfill their key roles in cell functioning. The compositional complexity of cellular membranes gives rise to a heterogeneous lateral organization, which is still poorly understood. Computational models, in particular molecular dynamics simulations and related techniques, have provided important insight into the organizational principles of cell membranes over the past decades. Now, we are witnessing a transition from simulations of simpler membrane models to multicomponent systems, culminating in realistic models of an increasing variety of cell types and organelles. Here, we review the state of the art in the field of realistic membrane simulations and discuss the current limitations and challenges ahead.

Following the nucleation pathway from disordered liquid to gyroid mesophase

Mesophases have order intermediate between liquids and crystals and arise in systems with frustration, such as surfactants, block copolymers, and Janus nanoparticles. The gyroid mesophase contains two interpenetrated, nonintersecting chiral networks that give it properties useful for photonics. It is challenging to nucleate a gyroid from the liquid. Elucidating the reaction coordinate for gyroid nucleation could assist in designing additives that facilitate the formation of the mesophase. However, the complexity of the gyroid structure and the extreme weakness of the first-order liquid to gyroid transition make this a challenging quest. Here, we investigate the pathway and transition states for the nucleation of a gyroid from the liquid in molecular simulations with a mesogenic binary mixture. We find that the gyroid nuclei at the transition states have a large degree of positional disorder and are not compact, consistent with the low surface free energy of the liquid-gyroid interface. A combination of bond-order parameters for the minor component is best to describe the passage from liquid to gyroid, among those we consider. The committor analyses, however, show that this best coordinate is not perfect and suggests that accounting for the relative ordering of the two interpenetrated networks in infant nuclei, as well as for signatures of ordering in the major component of the mesophase, would improve the accuracy of the reaction coordinate for gyroid formation and its use to evaluate nucleation barriers. To our knowledge, this study is the first to investigate the reaction coordinate and critical nuclei for the formation of any mesophase from an amorphous phase.

SPICA Force Field for Lipid Membranes: Domain Formation Induced by Cholesterol

Heterogeneity is essential for multicomponent lipid membranes. Especially, sterol-induced domain formation in membranes has recently attracted attention because of its biological importance. To investigate such membrane domains at the molecular level, coarse-grained molecular dynamics (CG-MD) simulations are a promising approach since they allow one to consider the temporal and spatial scales involved in domain formation. In this work, we present a new CG force field, named SPICA, which can accurately predict domain formation within various lipids in membranes. The SPICA force field was developed as an extension of a previous CG model, known as SDK (Shinoda-DeVane-Klein), in which membrane properties such as tension, elasticity, and structure are well reproduced. By examining domain formation in a series of ternary lipid bilayers, we observed a separation into liquid-ordered and liquid-disordered phases fully consistent with experimental observations. Importantly, it is shown that the SPICA force field can detect the different phase behavior that results from subtle differences in the lipid composition of the bilayer.

Stretch and Breakage of Wormlike Micelles under Uniaxial Strain: A Simulation Study and Comparison with Experimental Results

We use coarse-grained (CG) molecular dynamics simulations to determine the effect of uniaxial strain on the stress, scission stress, and scission energy of solutions of wormlike micelles of cetyltrimethylammonium chloride/sodium salicylate (NaSal). We find that the breaking stress, stretch modulus, and scission energy of the charged micelles are nonmonotonic functions of oppositely charged hydrotrope (NaSal) concentration. While the stretch modulus shows a peak at a value of surfactant-to-hydrotrope concentration ratio ( R) close to unity as expected due to neutralization of head-group charge at R = 1, the breaking stress and scission energy produce a peak at R < 1.0 because of thinning of the micelle diameter with increased R. The breaking stress from the simulations depends on the rate of deformation and roughly agrees with the experimental values of Rothstein ( J. Rheol. 2003 , 47 , 1227 ) after extrapolation to the much lower experimental rates. The method and results can be used to predict the effects of flow and mechanical stress on rates of micellar breakage, which is important in the rheology of wormlike micellar solutions.

Why Is Gyroid More Difficult to Nucleate from Disordered Liquids than Lamellar and Hexagonal Mesophases?

Block copolymers, surfactants, and biomolecules form lamellar, hexagonal, and gyroid mesophases. Across these systems, the nucleation of lamellar from the disordered liquid is the easiest and the nucleation of gyroid the most challenging. This poses the question of what are the factors that determine the rates of nucleation of the mesophases and whether they are controlled by the complexity of the structures or the thermodynamics of nucleation. Here, we use molecular simulations to investigate the nucleation and thermodynamics of lamellar, hexagonal, and gyroid in a binary mixture of particles that produces the same mesophases as those of surfactants and block copolymers. We demonstrate that a combination of averaged bond-order parameters q̅₂ and q̅₈ identifies and distinguishes the three mesophases. We use these parameters to track the microscopic process of nucleation of each mesophase and investigate the existence of heterogeneous nucleation (cross-nucleation) between mesophases. We estimate the surface tensions of the liquid/mesophase interfaces from nucleation rates using classical nucleation theory and find that they are comparable for the three mesophases with values that are about a third of those expected for liquid-crystal interfaces. The driving forces for nucleation, on the other hand, are quite different and increase in the order gyroid < hexagonal < lamellar at any temperature. We find that the nucleation rates of the mesophases follow the order of their driving forces. We conclude that the difficulty to nucleate the gyroid originates in its lower temperature of melting and extremely low entropy of melting compared to those of the hexagonal and lamellar mesophases.

Computational and theoretical approaches for studies of a lipid recognition protein on biological membranes

Many cellular functions, including cell signaling and related events, are regulated by the association of peripheral membrane proteins (PMPs) with biological membranes containing anionic lipids, e.g., phosphatidylinositol phosphate (PIP). This association is often mediated by lipid recognition modules present in many PMPs. Here, I summarize computational and theoretical approaches to investigate the molecular details of the interactions and dynamics of a lipid recognition module, the pleckstrin homology (PH) domain, on biological membranes. Multiscale molecular dynamics simulations using combinations of atomistic and coarse-grained models yielded results comparable to those of actual experiments and could be used to elucidate the molecular mechanisms of the formation of protein/lipid complexes on membrane surfaces, which are often difficult to obtain using experimental techniques. Simulations revealed some modes of membrane localization and interactions of PH domains with membranes in addition to the canonical binding mode. In the last part of this review, I address the dynamics of PH domains on the membrane surface. Local PIP clusters formed around the proteins exhibit anomalous fluctuations. This dynamic change in protein-lipid interactions cause temporally fluctuating diffusivity of proteins, i.e., the short-term diffusivity of the bound protein changes substantially with time, and may in turn contribute to the formation/dissolution of protein complexes in membranes.

Simulating Bilayers of Nonionic Surfactants with the GROMOS-Compatible 2016H66 Force Field

Polyoxyethylene glycol alkyl ether amphiphiles (C_iE_j) are important nonionic surfactants, often used for biophysical and membrane protein studies. In this work, we extensively test the GROMOS-compatible 2016H66 force field in molecular dynamics simulations involving the lamellar phase of a series of C_iE_j surfactants, namely C₁₂E₂, C₁₂E₃, C₁₂E₄, C₁₂E₅, and C₁₄E₄. The simulations reproduce qualitatively well the monitored structural properties and their experimental trends along the surfactant series, although some discrepancies remain, in particular in terms of the area per surfactant, the equilibrium phase of C₁₂E₅, and the order parameters of C₁₂E₃, C₁₂E₄, and C₁₂E₅. The polar head of the C_iE_j surfactants is highly hydrated, almost like a single polyethyleneoxide (PEO) molecule at full hydration, resulting in very compact conformations. Within the bilayer, all C_iE_j surfactants flip-flop spontaneously within tens of nanoseconds. Water-permeation is facilitated, and the bending rigidity is 4 to 5 times lower than that of typical phospholipid bilayers. In line with another recent theoretical study, the simulations show that the lamellar phase of C_iE_j contains large hydrophilic pores. These pores should be abundant in order to reproduce the comparatively low NMR order parameters. We show that their contour length is directly correlated to the order parameters, and we estimate that they should occupy approximately 7-10% of the total membrane area. Due to their highly dynamic nature (rapid flip-flops, high water permeability, observed pore formation), C_iE_j surfactant bilayers are found to represent surprisingly challenging systems in terms of modeling. Given this difficulty, the results presented here show that the 2016H66 parameters, optimized independently considering pure-liquid as well as polar and nonpolar solvation properties of small organic molecules, represent a good starting point for simulating these systems.

A New Mixed All-Atom/Coarse-Grained Model: Application to Melittin Aggregation in Aqueous Solution

We introduce a new mixed resolution, all-atom/coarse-grained approach (AACG), for modeling peptides in aqueous solution and apply it to characterizing the aggregation of melittin. All of the atoms in peptidic components are represented, while a single site is used for each water molecule. With the full flexibility of the peptide retained, our AACG method achieves speedups by a factor of 3-4 for CPU time reduction and another factor of roughly 7 for diffusion. An Ewald treatment permits the inclusion of long-range electrostatic interactions. These characteristics fit well with the requirements for studying peptide association and aggregation, where the system sizes and time scales require considerable computational resources with all-atom models. In particular, AACG is well suited for biologics since changes in peptide shape and long-range electrostatics may play an important role. The application of AACG to melittin, a 26-residue peptide with a well-known propensity to aggregate in solution, serves as an initial demonstration of this technology for studying peptide aggregation. We observed the formation of melittin aggregates during our simulations and characterized the time-evolution of aggregate size distribution, buried surface areas, and residue contacts. Key interactions including π-cation and π-stacking involving TRP19 were also examined. Our AACG simulations demonstrated a clear salt effect and a moderate temperature effect on aggregation and support the molten globule model of melittin aggregates. As a showcase, this work illustrates the useful role for AACG in investigations of peptide aggregation and its potential to guide formulation and design of biologics.

Vesicles from Amphiphilic Dumbbells and Janus Dendrimers: Bioinspired Self-Assembled Structures for Biomedical Applications

The current review focuses on vesicles obtained from the self-assembly of two types of dendritic macromolecules, namely amphiphilic Janus dendrimers (forming dendrimersomes) and amphiphilic dumbbells. In the first part, we will present some synthetic strategies and the various building blocks that can be used to obtain dendritic-based macromolecules, thereby showing their structural versatility. We put our focus on amphiphilic Janus dendrimers and amphiphilic dumbbells that form vesicles in water but we also encompass vesicles formed thereof in organic solvents. The second part of this review deals with the production methods of these vesicles at the nanoscale but also at the microscale. Furthermore, the influence of various parameters (intrinsic to the amphiphilic JD and extrinsic-from the environment) on the type of vesicle formed will be discussed. In the third part, we will review the numerous biomedical applications of these vesicles of nano- or micron-size.

Molecular dynamics simulations of membrane proteins and their interactions: from nanoscale to mesoscale

Molecular dynamics simulations provide a computational tool to probe membrane proteins and systems at length scales ranging from nanometers to close to a micrometer, and on microsecond timescales. All atom and coarse-grained simulations may be used to explore in detail the interactions of membrane proteins and specific lipids, yielding predictions of lipid binding sites in good agreement with available structural data. Building on the success of protein-lipid interaction simulations, larger scale simulations reveal crowding and clustering of proteins, resulting in slow and anomalous diffusional dynamics, within realistic models of cell membranes. Current methods allow near atomic resolution simulations of small membrane organelles, and of enveloped viruses to be performed, revealing key aspects of their structure and functionally important dynamics.

Molecular dynamics simulations of cholesterol-rich membranes using a coarse-grained force field for cyclic alkanes

The architecture of a biological membrane hinges upon the fundamental fact that its properties are determined by more than the sum of its individual components. Studies on model membranes have shown the need to characterize in molecular detail how properties such as thickness, fluidity, and macroscopic bending rigidity are regulated by the interactions between individual molecules in a non-trivial fashion. Simulation-based approaches are invaluable to this purpose but are typically limited to short sampling times and model systems that are often smaller than the required properties. To alleviate both limitations, the use of coarse-grained (CG) models is nowadays an established computational strategy. We here present a new CG force field for cholesterol, which was developed by using measured properties of small molecules, and can be used in combination with our previously developed force field for phospholipids. The new model performs with precision comparable to atomistic force fields in predicting the properties of cholesterol-rich phospholipid bilayers, including area per lipid, bilayer thickness, tail order parameter, increase in bending rigidity, and propensity to form liquid-ordered domains in ternary mixtures. We suggest the use of this model to quantify the impact of cholesterol on macroscopic properties and on microscopic phenomena involving localization and trafficking of lipids and proteins on cellular membranes.

Coarse-grained molecular dynamics study of membrane fusion: Curvature effects on free energy barriers along the stalk mechanism

The effects of membrane curvature on the free energy barrier for membrane fusion have been investigated using coarse-grained molecular dynamics (CG-MD) simulations, assuming that fusion takes place through a stalk intermediate. Free energy barriers were estimated for stalk formation as well as for fusion pore formation using the guiding potential method. Specifically, the three different geometries of two apposed membranes were considered: vesicle-vesicle, vesicle-planar, and planar-planar membranes. The free energy barriers for the resulting fusion were found to depend importantly on the fusing membrane geometries; the lowest barrier was obtained for vesicular membranes. Further, lipid sorting was observed in fusion of the mixed membranes of dimyristoyl phosphatidylcholine and dioleoyl phosphatidylethanolamine (DOPE). Specifically, DOPE molecules were found to assemble around the stalk to support the highly negative curved membrane surface. A consistent result for lipid sorting was observed when a simple continuum model (CM) was used, where the Helfrich energy and mixing entropy of the lipids were taken into account. However, the CM predicts a much higher free energy barrier than found using CG-MD. This discrepancy originates from the conformational changes of lipids, which were not considered in the CM. The results of the CG-MD simulations reveal that a large conformational change in the lipid takes place around the stalk region, which results in a reduction of free energy barriers along the stalk mechanism of membrane fusion.

Molecular dynamics simulations in drug delivery research: Calcium chelation of G3.5 PAMAM dendrimers

Poly(amido amine) (PAMAM) dendrimers have been considered as possible delivery systems for anticancer drugs. One potential advantage of these carriers would be their use in oral formulations, which will require absorption in the intestinal lumen. This may require the opening of tight junctions which may be enabled by reducing the Ca2+ concentration in the intestinal lumen, which has been shown as an absorption mechanism for EDTA (ethylenediaminetetraacetic acid). Using molecular dynamics simulations, we show that the G3.5 PAMAM dendrimers are able to chelate Ca2+ at similar proportions to EDTA, providing support to the hypothesis that oral formulations of PAMAM dendrimers could use this high chelating efficiency as a potential mechanism for permeating the tight junctions of the intestines if other formulation barriers could be overcome.

Thermodynamic free energy methods to investigate shape transitions in bilayer membranes

The conformational free energy landscape of a system is a fundamental thermodynamic quantity of importance particularly in the study of soft matter and biological systems, in which the entropic contributions play a dominant role. While computational methods to delineate the free energy landscape are routinely used to analyze the relative stability of conformational states, to determine phase boundaries, and to compute ligand-receptor binding energies its use in problems involving the cell membrane is limited. Here, we present an overview of four different free energy methods to study morphological transitions in bilayer membranes, induced either by the action of curvature remodeling proteins or due to the application of external forces. Using a triangulated surface as a model for the cell membrane and using the framework of dynamical triangulation Monte Carlo, we have focused on the methods of Widom insertion, thermodynamic integration, Bennett acceptance scheme, and umbrella sampling and weighted histogram analysis. We have demonstrated how these methods can be employed in a variety of problems involving the cell membrane. Specifically, we have shown that the chemical potential, computed using Widom insertion, and the relative free energies, computed using thermodynamic integration and Bennett acceptance method, are excellent measures to study the transition from curvature sensing to curvature inducing behavior of membrane associated proteins. The umbrella sampling and WHAM analysis has been used to study the thermodynamics of tether formation in cell membranes and the quantitative predictions of the computational model are in excellent agreement with experimental measurements. Furthermore, we also present a method based on WHAM and thermodynamic integration to handle problems related to end-point-catastrophe that are common in most free energy methods.

Permeability across lipid membranes

Molecular permeation through lipid membranes is a fundamental biological process that is important for small neutral molecules and drug molecules. Precise characterization of free energy surface and diffusion coefficients along the permeation pathway is required in order to predict molecular permeability and elucidate the molecular mechanisms of permeation. Several recent technical developments, including improved molecular models and efficient sampling schemes, are illustrated in this review. For larger penetrants, explicit consideration of multiple collective variables, including orientational, conformational degrees of freedom, are required to be considered in addition to the distance from the membrane center along the membrane normal. Although computationally demanding, this method can provide significant insights into the molecular mechanisms of permeation for molecules of medical and pharmaceutical importance. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.