Cellular uptake through endocytosis is crucial for drug delivery and nanomedicine. However, the conditions under which passive endocytosis (i.e., not ATP driven) takes place are not well understood. We report MD simulations of the passive uptake of ligand-coated nanoparticles with varying size, shape, coverage, and membrane-binding strength. We find that the efficiency of passive endocytosis is higher for spherocylindrical particles than for spheres and that endocytosis is suppressed for particles with sharp edges.

A key challenge in nano-science is to design ligand-coated nanoparticles that can bind selectively to surfaces that display the cognate receptors above a threshold (surface) concentration. Nanoparticles that bind monovalently to a target surface do not discriminate sharply between surfaces with high and low receptor coverage. In contrast, "multivalent" nano-particles that can bind to a larger number of ligands simultaneously, display regimes of "super selectivity" where the fraction of bound particles varies sharply with the receptor concentration. We present numerical simulations that show that multivalent nano-particles can be designed such that they approach the "on-off" binding behavior ideal for receptor-concentration selective targeting. We propose a simple analytical model that accounts for the super selective behavior of multivalent nano-particles. The model shows that the super selectivity is due to the fact that the number of distinct ligand-receptor binding arrangements increases in a highly nonlinear way with receptor coverage. Somewhat counterintuitively, our study shows that selectivity can be improved by making the individual ligand-receptor bonds weaker. We propose a simple rule of thumb to predict the conditions under which super selectivity can be achieved. We validate our model predictions against the Monte Carlo simulations.ne of the key challenges in nano-medicine is to acquire the ability to design supramolecular constructs that can target surfaces that display a motif or receptor above a threshold concentration while leaving surfaces with lower coverage of such receptors unaffected (1-4). Experiments indicate that such selective behavior can be obtained using multivalency (5-8). During multivalent interactions a type of particle (henceforth referred to as the "guest") uses multiple ligands to bind simultaneously to several of the receptors displayed by another type of particle or surface (the "host") (9, 10). Mammen et al. (9) recognized the importance of this type of system more than ten years ago. Since then, the concept of multivalency has found numerous applications in cell biology (7, 11), supramolecular chemistry (10), nano-medicine (4, 6), immunology (12, 13), and cancer treatment (2,3,5,14), to name but a few examples. The work of Davis et al. There is a substantial body of theoretical work that aims to explain the pronounced enhancement in binding strength that certain multivalent systems can present in comparison with their monovalent counterparts (15-17). In particular, Kitov and Bundle (18) have pointed out that the strength of multivalent binding can be enhanced if there are many possible permutations in the binding pattern of receptors and ligands. The role of steric repulsion and conformational entropy in multivalent systems have been studied using molecular theories (19) and Monte Carlo (MC) simulations (20, 21). However, a unified picture that explains why high selectivity is observed in some experimental realizations of multivalent systems but not in others is still lacki...

Multivalency has an important but poorly understood role in molecular self-organization. We present the noncovalent synthesis of a multicomponent supramolecular polymer in which chemically distinct monomers spontaneously coassemble into a dynamic, functional structure. We show that a multivalent recruiter is able to bind selectively to one subset of monomers (receptors) and trigger their clustering along the self-assembled polymer, behavior that mimics raft formation in cell membranes. This phenomenon is reversible and affords spatiotemporal control over the monomer distribution inside the supramolecular polymer by superselective binding of single-strand DNA to positively charged receptors. Our findings reveal the pivotal role of multivalency in enabling structural order and nonlinear recognition in watersoluble supramolecular polymers, and it offers a design principle for functional, structurally defined supramolecular architectures.self-assembly | simulations | energy transfer O ne of the most fascinating features of living matter is the precise control over biological activity in space and time.The cell membrane provides a remarkable example of such highfidelity spatiotemporal control in a complex biological setting, wherein thousands of different components, namely lipids and proteins, self-assemble into a 2D fluid mosaic (1). To perform the functions that the cell requires, lipids and proteins are heterogeneously distributed and specific biomolecules are segregated in active nanometer-sized domains often referred to as rafts (2). This distribution is highly dynamic, such that these platforms can be rapidly assembled and disassembled (3). The principles that underlie control over the molecular composition of the cellular microenvironment in space and time are the subject of great scientific debate as they are of crucial importance for cell functioning, signaling, growth, and division (4).One of the main goals of supramolecular chemistry is the noncovalent synthesis of functional molecular architectures through weak and reversible interactions (5). In this framework, a key challenge is the design of molecular building blocks that are able to self-organize hierarchically and in a cooperative fashion (6), thus mimicking the dynamic and structural complexity of living systems as well as their functionality. Various modular multicomponent systems have been successfully developed (7), but the spatiotemporal control of the localization of distinct components within synthetic supramolecular assemblies has yet to be realized. Mastering the spatial distribution of assembled molecules in a noncovalent synthesis is as crucial for their functionality as regio-selectivity impacts the molecular properties of organic molecules synthesized in a classical covalent manner. An interesting supramolecular polymer, where multiple components coassemble cooperatively in water, is based on 1,3,5-benzenetricarboxamide derivatives (BTAs) (8).Of particular relevance for the present work, is the fact that reversible interactions between ...

Particle-based molecular simulations of pure diblock copolymer (DBC) systems were performed in continuum space via dissipative particle dynamics and Monte Carlo methods for a bead-spring chain model. This model consisted of chains of soft repulsive particles often used with dissipative particle dynamics. The gyroid phase was successfully simulated in DBC melts at selected conditions provided that the simulation box size was commensurate with the gyroid lattice spacing. Simulations were concentrated at conditions where the gyroid phase is expected to be stable which allowed us to outline approximate phase boundaries. When more than one phase was observed by varying simulation box size, thermodynamic stability was discerned by comparing the Helmholtz free energy of the competing phases. For this purpose, chemical potentials were efficiently simulated via an expanded ensemble that gradually inserts/deletes a target chain to/from the system. These simulations employed a novel combination of Bennett's [J. Comput. Phys. 22, 245 (1976)] acceptance-ratio method to estimate free-energy differences and a recently proposed method to get biasing weights that maximize the number of times that the target chain is regrown. The analysis of the gyroid nodes revealed clear evidence of packing frustration in the form of an (entropically) unfavorably overstretching of chains, a phenomenon that has been suggested to provide the structural basis for the limited region of stability of the gyroid phase in the DBC phase diagram. Finally, the G phase and nodal chain stretching were also found in simulations with a completely different DBC particle-based model.

Lattice Monte Carlo (MC) simulations in the NVT ensemble together with a coarse-grained model of the block copolymer chains are used to explore the phase diagram of pure and bidisperse diblock copolymer melts as a function of temperature and block volume fraction. In the pure systems, we found that the gyroid phase is stable in only a narrow region of the phase diagram. Through the analysis of the structure of the channels and nodes formed by the minority component in the gyroid phase, we found evidence of “packing frustration” of the chains inside each such node, manifested as a central low-density region. The use of chain-length bidispersity was then investigated as a way to reduce such packing frustration in the gyroid phase. We found that the longer chains in such systems tend to segregate preferentially inside the gyroid nodes. For a system with components with a 2:1 ratio of chain lengths, we observed an increased range of temperatures where the gyroid phase is stable.