Computer simulation of architectural and molecular weight effects on the assembly of amphiphilic linear-dendritic block copolymers in solution

Impact of Copolymer Architecture on Demicellization and Cargo Release via Head-to-Tail Depolymerization of Hydrophobic Blocks or Branches

Utilizing molecular dynamics simulations, we explored the demicellization and cargo release dynamics of linear and miktoarm copolymers, featuring one, two, and three hydrophobic blocks or branches, each capable of head-to-tail depolymerization. Our findings revealed that, under stoichiometric trigger molecule concentrations, miktoarms with three branches exhibited consistently faster depolymerization rates than those with two branches and linear copolymers. Conversely, at constant trigger molecule concentrations, the depolymerization rates of copolymers exhibited more complex behaviors influenced by two opposing factors: the excess of trigger molecules, which increased with a decrease in the number of hydrophobic branches or blocks, and simultaneous head-to-tail depolymerization, which intensified with an increasing number of branches. Our study elucidates the intricate interplay between copolymer architecture, trigger molecule concentrations, and depolymerization dynamics, providing valuable insights for the rational design of amphiphilic copolymers with tunable demicellization and cargo release properties.

Chemical Feedback in Templated Reaction-Assembly of Polyelectrolyte Complex Micelles: A Molecular Simulation Study of the Kinetics and Clustering

The chemical feedback between building blocks in templated polymerization of diblock copolymers and their consecutive micellization was studied for the first time by means of coarse-grained molecular dynamics simulations. Using a stochastic polymerization model, we were able to reproduce the experimental findings on the effect of chemical feedback on the polymerization rates at low and high solution concentrations. The size and shape of micelles were computed using a newly developed software in Python conjugated with graph theory. In full agreement with the experiments, our simulations revealed that micelles formed by the templated micellization are more spherical and have a lower radius of gyration than those formed by the traditional two-step micellization method. The advantage of molecular simulation over the traditional kinetic models is that with the simulation, one studies in detail the heterogeneous polymerization in the presence of the oppositely charged template while also accounting for the incompatibility between reacted species, which significantly influences the reaction process.

Implicit-Solvent Coarse-Grained Simulations of Linear-Dendritic Block Copolymer Micelles

The design of nanoassemblies can be conveniently achieved by tuning the strength of the hydrophobic interactions of block copolymers in selective solvents. These block copolymer micelles form supramolecular aggregates, which have attracted great attention in the area of drug delivery and imaging in biomedicine due to their easy-to-tune properties and straightforward large-scale production. In the present work, we have investigated the micellization process of linear-dendritic block copolymers in order to elucidate the effect of branching on the micellar properties. We focus on block copolymers formed by linear hydrophobic blocks attached to either dendritic neutral or charged hydrophilic blocks. We have implemented a simple protocol for determining the equilibrium micellar size, which permits the study of linear-dendritic block copolymers in a wide range of block morphologies in an efficient and parallelizable manner. We have explored the impact of different topological and charge properties of the hydrophilic blocks on the equilibrium micellar properties and compared them to predictions from self-consistent field theory and scaling theory. We have found that, at higher degrees of branching in the corona and for short polymer chains, excluded volume interactions strongly influence the micellar aggregation as well as their effective charge.

Hybrid Molecules Consisting of Lysine Dendrons with Several Hydrophobic Tails: A SCF Study of Self-Assembling

In this article, we used the numerical self-consistent field method of Scheutjens-Fleer to study the micellization of hybrid molecules consisting of one polylysine dendron with charged end groups and several linear hydrophobic tails attached to its root. The main attention was paid to spherical micelles and the determination of the range of parameters at which they can appear. A relationship has been established between the size and internal structure of the resulting spherical micelles and the length and number of hydrophobic tails, as well as the number of dendron generations. It is shown that the splitting of the same number of hydrophobic monomers from one long tail into several short tails leads to a decrease in the aggregation number and, accordingly, the number of terminal charges in micelles. At the same time, it was shown that the surface area per dendron does not depend on the number of hydrophobic monomers or tails in the hybrid molecule. The relationship between the structure of hybrid molecules and the electrostatic properties of the resulting micelles has also been studied. It is found that the charge distribution in the corona depends on the number of dendron generations G in the hybrid molecule. For a small number of generations (up to G=3), a standard double electric layer is observed. For a larger number of generations (G=4), the charges of dendrons in the corona are divided into two populations: in the first population, the charges are in the spherical layer near the boundary between the micelle core and shell, and in the second population, the charges are near the periphery of the spherical shell. As a result, a part of the counterions is localized in the wide region between them. These results are of potential interest for the use of spherical dendromicelles as nanocontainers for drug delivery.

Dendritic-Linear Copolymer and Dendron Lipid Nanoparticles for Drug and Gene Delivery

Polymers constitute a diverse class of macromolecules that have demonstrated their unique advantages to be utilized for drug or gene delivery applications. In particular, polymers with a highly ordered, hyperbranched structure─"dendrons"─offer significant benefits to the design of such nanomedicines. The incorporation of dendrons into block copolymer micelles can endow various unique properties that are not typically observed from linear polymer counterparts. Specifically, the dendritic structure induces the conical shape of unimers that form micelles, thereby improving the thermodynamic stability and achieving a low critical micelle concentration (CMC). Furthermore, through a high density of highly ordered functional groups, dendrons can enhance gene complexation, drug loading, and stimuli-responsive behavior. In addition, outward-branching dendrons can support a high density of nonfouling polymers, such as poly(ethylene glycol), for serum stability and variable densities of multifunctional groups for multivalent cellular targeting and interactions. In this paper, we review the design considerations for dendron-lipid nanoparticles and dendron micelles formed from amphiphilic block copolymers intended for gene transfection and cancer drug delivery applications. These technologies are early in preclinical development and, as with other nanomedicines, face many obstacles on the way to clinical adoption. Nevertheless, the utility of dendron micelles for drug delivery remains relatively underexplored, and we believe there are significant and dramatic advancements to be made in tumor targeting with these platforms.

Theory of Linear-Dendritic Block Copolymer Micelles

A self-consistent field theory is applied to study structural properties of micelles formed upon spontaneous assembly of diblock copolymers comprising soluble dendron block covalently linked to insoluble linear block in selective solvent. The structure of spherical micelles is analyzed as a function of degrees of polymerization of the blocks and number of generations and branching functionality of the dendron block. We demonstrate that for a given molecular mass of blocks both the hydrodynamic dimensions of the micelles and the aggregation number decrease as a function of the degree of branching of the dendron block. However, the number of potentially functionalizable terminal segments of dendrons in the corona exposed to the solution increases compared to the number of terminal groups in the corona of linear diblock copolymer micelle. This result may have important implications for construction of linear-dendritic block copolymer micelles with smart functionalities for targeted drug and gene delivery.

Complexation of Polyelectrolyte Micelles with Oppositely Charged Linear Chains

The formation of interpolyelectrolyte complexes (IPECs) from linear AB diblock copolymer precursor micelles and oppositely charged linear homopolymers is studied by means of molecular dynamics simulations. All beads of the linear polyelectrolyte (C) are charged with elementary quenched charge +1e, whereas in the diblock copolymer only the solvophilic (A) type beads have quenched charge -1e. For the same Bjerrum length, the ratio of positive to negative charges, Z_+/-, of the mixture and the relative length of charged moieties r determine the size of IPECs. We found a nonmonotonic variation of the size of the IPECs with Z_+/-. For small Z_+/- values, the IPECs retain the size of the precursor micelle, whereas at larger Z_+/- values the IPECs decrease in size due to the contraction of the corona and then increase as the aggregation number of the micelle increases. The minimum size of the IPECs is obtained at lower Z_+/- values when the length of the hydrophilic block of the linear diblock copolymer decreases. The aforementioned findings are in agreement with experimental results. At a smaller Bjerrum length, we obtain the same trends but at even smaller Z_+/- values. The linear homopolymer charged units are distributed throughout the corona.

Synthesis, self-assembly, and immunological activity of α-galactose-functionalized dendron-lipid amphiphiles

Nanoassemblies presenting multivalent displays of biologically active carbohydrates are of significant interest for a wide array of biomedical applications ranging from drug delivery to immunotherapy. In this study, glycodendron-lipid hybrids were developed as a new and tunable class of dendritic amphiphiles. A modular synthesis was used to prepare dendron-lipid hybrids comprising distearylglycerol and 0 through 4th generation polyester dendrons with peripheral protected amines. Following deprotection of the amines, an isothiocyanate derivative of C-linked α-galactose (α-Gal) was conjugated to the dendron peripheries, affording amphiphiles with 1 to 16 α-Gal moieties. Self-assembly in water through a solvent exchange process resulted in vesicles for the 0 through 2^nd generation systems and micelles for the 3^rd and 4^th generation systems. The critical aggregation concentrations decreased with increasing dendron generation, suggesting that the effects of increasing molar mass dominated over the effects of increasing the hydrophilic weight fraction. The binding of the assemblies to Griffonia simplicifolia Lectin I (GSL 1), a protein with specificity for α-Gal was studied by quantifying the binding of fluorescently labeled assemblies to GSL 1-coated beads. It was found that binding was enhanced for amphiphiles containing higher generation dendrons. Despite their substantial structural differences with the natural ligands for the CD1d receptor, the glycodendron-lipid hybrids were capable of stimulating invariant natural killer T (iNKT) cells, a class of innate-like T cells that recognize lipid and glycolipid antigens presented by CD1d and that are implicated in a wide range of diseases and conditions including but not limited to infectious diseases, diabetes and cancer.

Entropic effects, shape, and size of mixed micelles formed by copolymers with complex architectures

The entropic effects in the comicellization behavior of amphiphilic AB copolymers differing in the chain size of solvophilic A parts were studied by means of molecular dynamics simulations. In particular, mixtures of miktoarm star copolymers differing in the molecular weight of solvophilic arms were investigated. We found that the critical micelle concentration values show a positive deviation from the analytical predictions of the molecular theory of comicellization for chemically identical copolymers. This can be attributed to the effective interactions between copolymers originated from the arm size asymmetry. The effective interactions induce a very small decrease in the aggregation number of preferential micelles triggering the nonrandom mixing between the solvophilic moieties in the corona. Additionally, in order to specify how the chain architecture affects the size distribution and the shape of mixed micelles we studied star-shaped, H-shaped, and homo-linked-rings-linear mixtures. In the first case the individual constituents form micelles with preferential and wide aggregation numbers and in the latter case the individual constituents form wormlike and spherical micelles.

Linear-dendritic copolymer composed of polyethylene glycol and all-trans-retinoic acid as drug delivery platform for paclitaxel against breast cancer

A new linear-dendritic copolymer composed of poly(ethylene glycol) (PEG) and all-trans-retinoic acid (ATRA) was synthesized as the anticancer drug delivery platform (PEG-G3-RA8). It can self-assemble into core-shell micelles with a low critical micelle concentration (CMC) at 3.48 mg/L. Paclitaxel (PTX) was encapsulated into PEG-G3-RA8 to form PEG-G3-RA8/PTX micelles for breast cancer treatment. The optimized formulation had high drug loading efficacy (20% w/w of drug copolymer ratio), nanosized diameter (27.6 nm), and narrow distribution (PDI = 0.103). Compared with Taxol, PEG-G3-RA8/PTX remained highly stable in the serum-containing cell medium and exhibited 4-fold higher cellular uptake. Besides, near-infrared fluorescence (NIR) optical imaging results indicated that fluorescent probe loaded micelle had a preferential accumulation in breast tumors. Pharmacokinetics and biodistribution studies (10 mg/kg) showed the area under the plasma concentration-time curve (AUC0-∞) and mean residence time (MRT0-∞) for PEG-G3-RA8/PTX and Taxol were 12.006 ± 0.605 mg/L h, 2.264 ± 0.041 h and 15.966 ± 1.614 mg/L h, 1.726 ± 0.097 h, respectively. The tumor accumulation of PEG-G3-RA8/PTX group was 1.89-fold higher than that of Taxol group 24 h postinjection. With the advantages like efficient cellular uptake and preferential tumor accumulation, PEG-G3-RA8/PTX showed superior therapeutic efficacy on MCF-7 tumor bearing mice compared to Taxol.

Polyamidoamine and polyglycerol; their linear, dendritic and linear–dendritic architectures as anticancer drug delivery systems

This review covers the latest advances in the conjugation of chemotherapeutics such as doxorubicin, paclitaxel, methotrexate, fluorouracil and cisplatin to dendritic polymers, including polyamidoamine dendrimers, hyperbranched polyglycerols and their linear analogues, with a focus on their cytotoxicity, biodistribution and biodegradability.

Coarse-grained simulation study on the self-assembly of miktoarm star-like block copolymers in various solvent conditions

The self-assembly processes of miktoarm star-like block copolymers (Ax1)y-C-(Bx2)y, in which y homopolymer chains of type A with chain length x1 as well as y chains of type B with chain length x2 are connected to a center core C, are investigated by using Brownian dynamics simulations. We focus on the selective solvent condition, i.e., the solvent is poor for components B and C, but varies from good to poor for component A. The miktoarm star-like block copolymers with A and B arms of equal length can form spherical micelles when the solvent is good for component A. In the same solvent conditions, the micelles contain fewer miktoarm star-like block copolymers as the arm length increases. When the solvent is poor for component A, the miktoarm star-like block copolymers can self-assemble into cylindrical or disk-like micelles with decreasing solvent quality. For the miktoarm star-like block copolymers with longer B arms but shorter A arms, self-assembly into spherical vesicles is possible in a wide range of solvent conditions.

Brownian dynamics simulation of comicellization of amphiphilic block copolymers with different tail lengths

Brownian dynamics simulations were performed to study the self-assembly of mixed linear amphiphilic block copolymers. The molecules consist of similar hydrophilic heads and hydrophobic tails of different lengths. The model amphiphilic diblock copolymers have been selected to gain insight into the comicellization process in concentrated regimes, and the micelles were not kinetically frozen on the time scale of simulation. The critical micelle concentration (cmc), micelle size distribution, radius of gyration distribution, density profile of comicelles, shape anisotropy, and dynamics of comicellization have been studied as a function of the varying molar fraction of components. The cmc's of systems rich in the molar fraction of each type were found to be close to the cmc of that component. It has also been found that at a certain concentration comicellization affects the cmc in mixed systems. The weight-average aggregate size distribution of mixed copolymers was found to be between the aggregate distributions of short and long copolymers and becomes broader because of mixing. Moreover, values of the most probable aggregate size and radius of gyration of comicelles follow the mixing rule. Results show that small aggregates are mainly made from shorter block copolymers, whereas longer block copolymers form the major portion of large clusters. Furthermore, the cores of the micelles are mainly composed of longer block copolymers, and in all cases, the concentrations of shorter block copolymers are more dominant in the outer part than in the interior regions. In addition, the dynamics of polymeric micelles was studied using tracer and extraction autocorrelation functions and their relaxation times. The tracer correlation time increases with increasing longer copolymer concentration and deviates positively from the mixing rule. We also find that the total extraction correlation time increases exponentially from short to long copolymers, but the presence of long block copolymers linearly increases the short copolymer extraction correlation times. Short block copolymers, however, linearly decrease the long copolymer correlation times.

Facilitated self-assembly of novel dendron-based copolymers

Self-assembly of newly synthesized dendron-based amphiphilic copolymers with controlled hydrophilic-lipophilic balances has been investigated to evaluate their potential as a novel nanocarrier. The hydroxyl-terminated polyester dendron (G3) bearing a focal alkyne moiety was used to mediate the combination of poly(s-caprolactone) (PCL) with multiple polyethylene glycol (PEG) moieties. Four types of PCL-G3-mPEG with different block lengths were prepared and their structures were confirmed by (1)H NMR, FT-IR, and GPC. Critical micelle concentration (CMC) values varied from 6.50 × 10(-8) to 3.52 × 10(-7) M, which were lower than those reported for linear PCL-mPEG. TEM revealed that all PCL-G3-mPEG micelles were spherical with an average diameter of 20 nm. The drug release profile for each PCL-G3-mPEG was investigated by loading indomethacin (IMC), as a model drug, within the micelles. IMC was released in a controlled manner over 72 hours. Synthesized copolymers used in this study were also found to be non-cytotoxic at concentrations up to 100 μM. The low CMC, along with the controlled morphology, release profile and biocompatibility, all demonstrate the potential of the dendron-based micelles as a novel nanocarrier.

Dendron-mediated self-assembly of highly PEGylated block copolymers: a modular nanocarrier platform

PEGylated dendron coils (PDCs) were investigated as a novel potential nanocarrier platform. PDCs self-assembled into micelles at lower CMCs than linear copolymer counterparts by 1-2 orders of magnitude, due to the unique architecture of dendrons. MD simulations also supported thermodynamically favourable self-assembly mediated by dendrons.

Brownian dynamics simulations on the self-assembly behavior of AB hybrid dendritic-star copolymers

The micellization behavior of hybrid dendritic-star copolymers with solvophilic dendritic units is studied by means of Brownian dynamics simulations. The critical micelle concentration and the micelle size and shape are examined for different solvophobic/solvophilic ratios r as a function of the number of the dendritic and linear arms. Hybrid dendritic-star copolymers with one dendritic and up to three solvophobic linear branches form spherical micelles with preferential aggregation number. Those with two dendritic arms and three solvophobic branches form micelles with wide aggregation numbers only for small values of r. For hybrid dendritic-star copolymers with three dendritic arms and two or three solvophobic linear arms, micelles with wide aggregation numbers are also formed but for slightly higher values of r. Our results for the aggregation number are compared with existing results of other architectures obtained at the same temperature, and an inequality for the aggregation number is proposed.

Cholic acid micelles--controlling the size of the aqueous cavity by PEGylation

Data show that cholic acid (CA) micelles are less densely packed and much smaller than micelles formed by typical surfactants, suggesting that CA derivatives can be used to synthesize drug nanocarriers. Presumably, the formation of internal cavities is favored by the facial characteristics of the CA molecule, i.e. the convex molecular structure that is hydrophobic on one side and hydrophilic on the other. Here, we present a thermodynamical approach to quantify the effect of facial characteristics on forces governing the self-assembling process of CA molecules. We show that facial characteristics favor the entrapment of water molecules at interfaces upon CA aggregation, which weakens the attraction between CA hydrophobic moieties. Our computer simulations suggest that these effects contribute significantly to the tendency of CA molecules to form small "hollow-core" micelles. The attachment of polyethylene glycol (PEG) molecular chains to CA increases the repulsive forces in the system, reducing even further the micelle size. We use the present molecular model and experimental critical micelle concentration (cmc) data for CA-PEG systems to predict the change of the micelle size and cavity volume with the increase of the PEG chain length (x). Our computations indicate that the CA-PEG micelles are good candidates for drug delivery. The structural stability of CA-PEG micelles was further assessed by molecular dynamics simulations. We also tested the drug loading efficiency of this system and found an average of 0.5 mg paclitaxel load per 20 mg of CA-PEG polymer. The present study helps to identify critical parameters that control structural properties of the CA based nanocarriers and suggests practical means to optimize the ratio between micelle size and volume of the internal cavity.

Effect of tail architecture on self-assembly of amphiphiles for polymeric micelles

Brownian dynamics simulations were carried out to explore the self-assembly of amphiphilic copolymers composed of a linear hydrophilic head and a hydrophobic tail with different architectures. In order to investigate the effect of architecture of hydrophobic tail on self-assembling behavior, these architectures of linear, branched, starlike, and dendritic tails were selected for comparison, and the branching parameter of the tail was employed to characterize the tail architectures. The critical micelle concentration (cmc), dynamics of aggregation, aggregate distribution, gyration radius distribution, density profiles of micelle, shape anisotropy, and thermal stability were examined for the four typical types of copolymers. The calculated results reveal that the self-assembly of linear tail copolymer has the lowest cmc, and the consequently formed polymeric micelles have narrow dispersion and greater aggregate size, and the micelle is closer to spherical shape. It was found that the cmc is inversely proportional to the branching parameter. Linear tail aggregates in solution to form polymeric micelles with higher physical stability, compared to other architectures of tail. The size of polymeric micelle increases with the increase of the branching parameter of the tail, and it exhibits an exponential relationship with the branching parameter. In addition, the micelles formed from copolymers with a high branching parameter of the tail were found to have higher thermal stability. This work provides useful information on designing self-assembling systems for preparing polymeric micelles applied to drug delivery.