Dissipative particle dynamics simulations of polymer-protected nanoparticle self-assembly

Mechanisms of Scaffold-Mediated Microcompartment Assembly and Size Control

This article describes a theoretical and computational study of the dynamical assembly of a protein shell around a complex consisting of many cargo molecules and long, flexible scaffold molecules. Our study is motivated by bacterial microcompartments, which are proteinaceous organelles that assemble around a condensed droplet of enzymes and reactants. As in many examples of cytoplasmic liquid-liquid phase separation, condensation of the microcompartment interior cargo is driven by flexible scaffold proteins that have weak multivalent interactions with the cargo. Our results predict that the shell size, amount of encapsulated cargo, and assembly pathways depend sensitively on properties of the scaffold, including its length and valency of scaffold-cargo interactions. Moreover, the ability of self-assembling protein shells to change their size to accommodate scaffold molecules of different lengths depends crucially on whether the spontaneous curvature radius of the protein shell is smaller or larger than a characteristic elastic length scale of the shell. Beyond natural microcompartments, these results have important implications for synthetic biology efforts to target alternative molecules for encapsulation by microcompartments or viral shells. More broadly, the results elucidate how cells exploit coupling between self-assembly and liquid-liquid phase separation to organize their interiors.

Computational and Experimental Approaches to Investigate Lipid Nanoparticles as Drug and Gene Delivery Systems

Lipid nanoparticles (LNPs) have been widely applied in drug and gene delivery. More than twenty years ago, DoxilTM was the first LNPs-based drug approved by the US Food and Drug Administration (FDA). Since then, with decades of research and development, more and more LNP-based therapeutics have been used to treat diverse diseases, which often offer the benefits of reduced toxicity and/or enhanced efficacy compared to the active ingredients alone. Here, we provide a review of recent advances in the development of efficient and robust LNPs for drug/gene delivery. We emphasize the importance of rationally combining experimental and computational approaches, especially those providing multiscale structural and functional information of LNPs, to the design of novel and powerful LNP-based delivery systems.

Nanoformulation-by-design: an experimental and molecular dynamics study for polymer coated drug nanoparticles

The formulation of drug compounds into nanoparticles has many potential advantages in enhancing bioavailability and improving therapeutic efficacy. However, few drug molecules will assemble into stable, well-defined nanoparticulate structures. Amphiphilic polymer coatings are able to stabilise nanoparticles, imparting defined surface properties for many possible drug delivery applications. In the present article we explore, both experimentally and in silico, a potential methodology to coat drug nanoparticles with an amphiphilic co-polymer. Monomethoxy polyethylene glycol-polycaprolactone (mPEG-b-PCL) diblock copolymers with different mPEG lengths (M w 350, 550, 750 and 2000), designed to give different levels of colloidal stability, were used to coat the surface of indomethacin nanoparticles. Polymer coating was achieved by a flow nanoprecipitation method that demonstrated excellent batch-to-batch reproducibility and resulted in nanoparticles with high drug loadings (up to 78%). At the same time, in order to understand this modified nanoprecipitation method at an atomistic level, large-scale all-atom molecular dynamics simulations were performed in parallel using the GROMOS53a6 forcefield parameters. It was observed that the mPEG-b-PCL chains act synergistically with the acetone molecules to dissolve the indomethacin nanoparticle while after the removal of the acetone molecules (mimicking the evaporation of the organic solvent) a polymer-drug nanoparticle was formed (yield 99%). This work could facilitate the development of more efficient methodologies for producing nanoparticles of hydrophobic drugs coated with amphiphilic polymers. The atomistic insight from the MD simulations in tandem with the data from the drug encapsulation experiments thus leads the way to a nanoformulation-by-design approach for therapeutic nanoparticles.

Molecular dynamics simulation study of linear, bottlebrush, and star-like amphiphilic block polymer assembly in solution

In this study we investigate the effect of varying branched polymer architectures on the assembly of amphiphilic block polymers in solution using coarse-grained molecular dynamics simulations. We quantify assembly structure (e.g., aggregation number, assembly morphology, and micelle core size) and thermodynamics (e.g., unimer to micelle transition conditions) as a function of increasing solvophobicity of the solvophobic block in the copolymer for three broad categories of polymer architectures: linear, 'bottlebrush' (with many short side chains on a long backbone), and 'star-like' (with few long side chains on a short backbone). Keeping the total number of coarse-grained beads in each polymer (or polymer molecular weight) constant, as we go from either linear or 'star-like' to 'bottlebrush' polymer architectures, the micelle aggregation number and micelle core size decrease, and the solvophobicity required for assembly (i.e., transition solvophobicity) increases. This trend is linked to the topological/steric hinderance for making solvophobic bead contacts between neighboring polymers for the 'bottlebrush' polymer architecture compared to the linear or 'star-like' architectures. We are able to identify some universal trends in assembly by plotting the assembly structure and thermodynamics data as a function of branching parameter defined as the ratio of the branched chain to the linear chain radius of gyration in the unimer state, and the relative lengths of the backbone versus side chain. The results in this paper guide how one could manipulate the amphiphilic block polymer assembly structure and thermodynamics by choosing appropriate polymer architecture, block sequence, and composition.

Relationship between water permeation and flip-flop motion in a bilayer membrane

The lipid bilayer membrane facilitates various biological reactions and is thus an essential structure that sustains all higher forms of life. The unique local environment of the lipid bilayer plays critical roles for the diffusion of biomolecules as well as water molecules in biological reactions. Although fluctuation of the cell membrane is expected to allow for the transport of some water molecules, the flip-flop of lipid molecules corresponds to lipid transport between membrane leaflets, and is considered to be an important process to regulate the lipid composition of biological membranes. However, the relationship between these flip-flop phenomena and surrounding water molecules remains poorly understood. We hypothesized that the flip-flop is caused by water molecules permeating through the cell membrane. To test this hypothesis, we used millisecond-order coarse-grained molecular simulations (dissipative particle dynamics) to investigate the distance between water molecules and lipid molecules depending on the position of the lipid molecule. The results clearly showed that water molecules affect the flip-flop motion in the early stage, but have minimal contribution to the subsequent behavior. Moreover, based on the results of dissipative particle dynamics simulation, we computed several first-passage-time (FPT) quantities to describe the detailed dynamics of water permeation. We modeled arrangements in the middle of the flip-flop process, which were compared with the arrangement without lipid molecules. Overall, our results indicate that lipid molecules located both in perpendicular and parallel arrangements largely affect water permeation. These findings provide new insight into the detailed relationship between water permeation and the flip-flop motion.

Controlling and Predicting Nanoparticle Formation by Block Copolymer Directed Rapid Precipitations

Nanoparticles have shown promise in several biomedical applications, including drug delivery and medical imaging; however, quantitative prediction of nanoparticle formation processes that scale from laboratory to commercial production has been lacking. Flash NanoPrecipitation (FNP) is a scalable technique to form highly loaded, block copolymer protected nanoparticles. Here, the FNP process is shown to strictly obey diffusion-limited aggregation assembly kinetics, and the parameters that control the nanoparticle size and the polymer brush density on the nanoparticle surface are shown. The particle size, ranging from 40 to 200 nm, is insensitive to the molecular weight and chemical composition of the hydrophobic encapsulated material, which is shown to be a consequence of the diffusion-limited growth kinetics. In a simple model derived from these kinetics, a single constant describes the 46 unique nanoparticle formulations produced here. The polymer brush densities on the nanoparticle surface are weakly dependent on the process parameters and are among the densest reported in the literature. Though modest differences in brush densities are observed, there is no measurable difference in the amount of protein adsorbed within this range. This work highlights the material-independent and universal nature of the Flash NanoPrecipitation process, allowing for the rapid translation of formulations to different stabilizing polymers and therapeutic loads.

Controllable multicompartment morphologies from cooperative self-assembly of copolymer-copolymer blends

Multicompartment nanostructures, such as microcapsules with clearly separated shell and core, are not easily accessible by conventional block copolymer self-assembly. We assess a versatile computational strategy through cooperative assembly of diblock copolymer blends to generate spherical and cylindrical compartmentalized micelles with intricate structures and morphologies. The co-assembly strategy combines the advantages of polymer blending and incompatibility-induced phase separation. Following this strategy, various nanoassemblies of pure AB, binary AB/AC and ternary AB/AC/AD systems such as compartmentalized micelles with sponge-like, Janus, capsule-like and onion-like morphologies can be obtained. The formation and structural adjustment of microcapsule micelles, in which the shell or core can be occupied by either pure or mixed diblock copolymers, were explored. The mechanism involving the separation of shell and core copolymers is attributed to the stretching force differences of copolymers which drive the arrangement of different copolymers in a pathway to minimize the total interfacial energy. Moreover, by adjusting block interactions, an efficient approach is exhibited for regulating the shell or core composition and morphology in microcapsule micelles, such as the transition from the "pure shell/mixed core" morphology to the "mixed shell/pure core" morphology in the AB/AC/AD micelle. This mesoscale simulation study identifies the key factors governing co-assembly of diblock copolymer blends and provides bottom-up insights towards the design and optimization of new multicompartment micelles.

Self-assembled polypeptide nanoparticles for intracellular irinotecan delivery

In this research poly(l-lysine)-b-poly(l-leucine) (PLys-b-PLeu) polymersomes were developed. It was shown that the size of nanoparticles depended on pH of self-assembly process and varied from 180 to 650nm. The biodegradation of PLys-b-PLeu nanoparticles was evaluated using in vitro polypeptide hydrolysis in two model enzymatic systems, as well as in human blood plasma. The experiments on the visualization of cellular uptake of rhodamine 6g-loaded and fluorescein-labeled nanoparticles were carried out and the possibility of their penetration into the cells was approved. The cytotoxicity of polymersomes obtained was tested using three cell lines, namely, HEK, NIH-3T3 and A549. It was shown that tested nanoparticles did not demonstrate any cytotoxicity in the concentrations up to 2mg/mL. The encapsulation of specific to colorectal cancer anti-tumor drug irinotecan into developed nanocontainers was performed by means of pH gradient method. The dispersion of drug-loaded polymersomes in PBS was stable at 4°C for a long time (at least 1month) without considerable drug leakage. The kinetics of drug release was thoroughly studied using two model enzymatic systems, human blood serum and PBS solution. The approximation of irinotecan release profiles with different mathematical drug release models was carried out and allowed identification of the release mechanism, as well as the morphological peculiarities of developed particles. The dependence of encapsulation efficiency, as well as maximal loading capacity, on initial drug concentration was studied. The maximal drug loading was found as 320±55μg/mg of polymersomes. In vitro anti-tumoral activity of irinotecan-loaded polymersomes on a colon cancer cell line (Caco-2) was measured and compared to that for free drug.

Directed assembly of functionalized nanoparticles with amphiphilic diblock copolymers

We theoretically propose a simple approach to achieve soft nanoparticles with a self-patchiness nature, which are further directed to assemble into a rich variety of highly ordered superstructures.

Encapsulation of Nanoparticles During Polymer Micelle Formation: A Dissipative Particle Dynamics Study

The formation of block copolymer micelles with and without hydrophobic nanoparticles is simulated using dissipative particle dynamics. We use the model developed by Spaeth et al. [ Spaeth , J. R. , Kevrekidis , I. G. , and Panagiotopoulos , A. Z. J. Chem. Phys. 2011 , 134 ( (16) ) 164902 ], and drive micelle formation by adjusting the interaction parameters linearly over time to represent a rapid change from organic solvent to water. For different concentrations of added nanoparticles, we determine characteristic times for micelle formation and coagulation, and characterize micelles with respect to size, polydispersity, and nanoparticle loading. Four block copolymers with different numbers of hydrophobic and hydrophilic polymer beads, are examined. We find that increasing the number of hydrophobic beads on the polymer decreases the micelle formation time and lowers polydispersity in the final micelle distribution. Adding more nanoparticles to the simulation has a negligible effect on micelle formation and coagulation times, and monotonically increases the polydispersity of the micelles for a given polymer system. The presence of relatively stable free polymer in one system decreases the amount of polymer encapsulating the nanoparticles, and results in an increase in polydispersity and the number of nanoparticles per micelle for that system, especially at high nanoparticle concentration. Longer polymers lead to micelles with a more uniform nanoparticle loading.

Modeling size controlled nanoparticle precipitation with the co-solvency method by spinodal decomposition

The co-solvency method is a method for the size controlled preparation of nanoparticles like polymersomes, where a poor co-solvent is mixed into a homogeneous copolymer solution to trigger precipitation of the polymer. The size of the resulting particles is determined by the rate of co-solvent addition. We use the Cahn-Hilliard equation with a Flory-Huggins free energy model to describe the precipitation of a polymer under changing solvent quality by applying a time dependent Flory-Huggins interaction parameter. The analysis focuses on the characteristic size R of polymer aggregates that form during the initial spinodal decomposition stage, and especially on how R depends on the rate s of solvent quality change. Both numerical results and a perturbation analysis predict a power law dependence R∼s(-⅙), which is in agreement with power laws for the final particle sizes that have been reported from experiments and molecular dynamics simulations. Hence, our model results suggest that the nanoparticle size in size-controlled precipitation is essentially determined during the spinodal decomposition stage.

Preparation, Characterization, and Biological Evaluation of Poly(Glutamic Acid)-b-Polyphenylalanine Polymersomes

Different types of amphiphilic macromolecular structures have been developed within recent decades to prepare the polymer particles considered as drug delivery systems. In the present research the series of amphiphilic block-copolymers containing poly(glutamatic acid) as hydrophilic, and polyphenylalanine as hydrophobic blocks was synthesized and characterized. Molecular weights for homo- and copolymers were determined by gel-permeation chromatography (GPC) and amino acid analysis, respectively. The copolymers obtained were applied for preparation of polymer particles. The specific morphology of prepared polymerosomes was proved using transmission electron microscopy (TEM). The influence on particle size of polymer concentration and pH used for self-assembly, as well as on the length of hydrophobic and hydrophilic blocks of applied copolymers, was studied by dynamic light scattering (DLS). Depending on different experimental conditions, the formation of nanoparticles with sizes from 60 to 350 nm was observed. The surface of polymersomes was modified with model protein (enzyme). No loss in biocatalytic activity was detected. Additionally, the process of encapsulation of model dyes was developed and the possibility of intracellular delivery of the dye-loaded nanoparticles was proved. Thus, the nanoparticles discussed can be considered for the creation of modern drug delivery systems.

Highly grafted polystyrene/polyvinylpyridine polymer gold nanoparticles in a good solvent: effects of chain length and composition

In this work, the structural features of spherical gold nanoparticles (NPs) decorated with highly grafted poly(styrene) (PS), poly(vinylpyridine) (PVP) and PS-PVP diblock copolymer brushes immersed in a good solvent are investigated by means of Dissipative Particle Dynamics (DPD) simulations as a function of grafted chain length and of homopolymer and copolymer chain composition. For NPs grafted either by PS or PVP homopolymer brushes (selected as a proof of concept), good agreement between the Daoud-Cotton theory, experimental evidence, and our DPD simulations is observed in the scaling behavior of single chain properties, especially for longer grafted chains, and in brush thickness prediction. On the other hand, for grafted chain lengths comparable to NP dimensions parabolic-like profiles of the end-monomer distributions are obtained. Furthermore, a region of high concentration of polymer segments is observed in the monomer density distribution for long homopolymers. In the case of copolymer-decorated NPs, the repulsion between PS and PVP blocks is found to substantially influence the radius of gyration and the shape of the end-monomer distribution of the relevant polymer shell. Moreover, for diblock chains, the un-swollen region is observed to be thinner (and, correspondingly, the swollen layer thicker) than that of a NP modified with a homopolymer of the same length. Finally, the lateral segregation of PS and PVP blocks is evidenced by our calculations and a detailed analysis of the corona behavior is reported, thus revealing the key parameters in controlling the surface properties and the response of diblock copolymer modified nanoparticles.

Directed Assembly of Soft Colloids through Rapid Solvent Exchange

We studied the directed assembly of soft nanoparticles through rapid micromixing of polymers in solution with a nonsolvent. Both experiments and computer simulations were performed to elucidate the underlying physics and to investigate the role of various process parameters. In particular, we discovered that no external stabilizing agents or charged end groups are required to keep the colloids separated from each other when water is used as the nonsolvent. Furthermore, the size of the nanoparticles can be reliably tuned through the mixing rate and the ratio between polymer solution and nonsolvent. Our results demonstrate that this mechanism is highly promising for the mass fabrication of uniformly sized colloidal particles, using a wide variety of polymeric feed materials.

Modeling Nanoparticle Targeting to a Vascular Surface in Shear Flow Through Diffusive Particle Dynamics

Nanoparticles are regarded as promising carriers for targeted drug delivery and imaging probes. A fundamental understanding of the dynamics of polymeric nanoparticle targeting to receptor-coated vascular surfaces is therefore of great importance to enhance the design of nanoparticles toward improving binding ability. Although the effects of particle size and shear flow on the binding of nanoparticles to a vessel wall have been studied at the particulate level, a computational model to investigate the details of the binding process at the molecular level has not been developed. In this research, dissipative particle dynamics simulations are used to study nanoparticles with diameters of several nanometers binding to receptors on vascular surfaces under shear flow. Interestingly, shear flow velocities ranging from 0 to 2000 s(-1) had no effect on the attachment process of nanoparticles very close to the capillary wall. Increased binding energy between the ligands and wall caused a corresponding linear increase in bonding ability. Our simulations also indicated that larger nanoparticles and those of rod shape with a higher aspect ratio have better binding ability than those of smaller size or rounder shape.

Polymer directed self-assembly of pH-responsive antioxidant nanoparticles

We have developed pH-responsive, multifunctional nanoparticles based on encapsulation of an antioxidant, tannic acid (TA), using flash nanoprecipitation, a polymer directed self-assembly method. Formation of insoluble coordination complexes of tannic acid and iron during mixing drives nanoparticle assembly. Tuning the core material to polymer ratio, the size of the nanoparticles can be readily tuned between 50 and 265 nm. The resulting nanoparticle is pH-responsive, i.e., stable at pH 7.4 and soluble under acidic conditions due to the nature of the coordination complex. Further, the coordination complex can be coprecipitated with other hydrophobic materials such as therapeutics or imaging agents. For example, coprecipitation with a hydrophobic fluorescent dye creates fluorescent nanoparticles. In vitro, the nanoparticles have low cytotoxicity and show antioxidant activity. Therefore, these particles may facilitate intracellular delivery of antioxidants.

Hierarchical self-assembly: Self-organized nanostructures in a nematically ordered matrix of self-assembled polymeric chains

We report many different nanostructures which are formed when model nanoparticles of different sizes (diameter σn) are allowed to aggregate in a background matrix of semiflexible self-assembled polymeric wormlike micellar chains. The different nanostructures are formed by the dynamical arrest of phase-separating mixtures of micellar monomers and nanoparticles. The different morphologies obtained are the result of an interplay of the available free volume, the elastic energy of deformation of polymers, the density (chemical potential) of the nanoparticles in the polymer matrix, and, of course, the ratio of the size of self-assembling nanoparticles and self-avoidance diameter of polymeric chains. We have used a hybrid semi-grand-canonical Monte Carlo simulation scheme to obtain the (nonequilibrium) phase diagram of the self-assembled nanostructures. We observe rodlike structures of nanoparticles which get self-assembled in the gaps between the nematically ordered chains, as well as percolating gel-like network of conjoined nanotubes. We also find a totally unexpected interlocked crystalline phase of nanoparticles and monomers, in which each crystal plane of nanoparticles is separated by planes of perfectly organized polymer chains. We identified the condition which leads to such interlocked crystal structure. We suggest experimental possibilities of how the results presented in this paper could be used to obtain different nanostructures in the laboratory.

Parametric study of particle sedimentation by dissipative particle dynamics simulation

A parametric study on the simulation of a single aluminum (Al) particle settling in water is conducted using various sets of interactive parameters between Al and water particles, so that a systematic method can be established to describe the hydrodynamic interaction between an Al particle and the fluid in a large range of particle sizes. The force parameters and the cutoff have been correlated to the terminal settling velocity of the Al particle in the dissipative particle dynamics simulation, so that the classic Stokes' law can be used to determine those parameters. Two empirical equations are developed to calculate the minimum repulsive force parameter in terms of the number density and radius, respectively. In addition, the correlation between the cutoff and the Al particle radius has been obtained by linear curve fitting. The radial distribution functions of Al and water particles are computed to examine the relative spacing among solid and fluid particles. The present approach is general and can also be extended to study particle motion of other types of particles and fluids. This study will be a baseline for the investigation of multiple particles settling in a viscous fluid.