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We introduce a spatial graph and hypergraph model that smoothly interpolates between a graph with purely pairwise edges and a graph where all connections are in large hyperedges. The key component is a spatial clustering resolution parameter that varies between assigning all the vertices in a spatial region to individual clusters, resulting in the pairwise case, to assigning all the vertices in a spatial region to a single cluster, which results in the large hyperedge case. A key component of this model is that the spatial structure is invariant to the choice of hyperedges. Consequently, this model enables us to study clustering coefficients, graph diffusion, and epidemic spread and how their behavior changes as a function of the higher-order structure in the network with a fixed spatial substrate. We hope that our model will find future uses to distill or explain other behaviors in higher-order networks. 

At moderate adhesion strength, nanoparticles (NPs) adhering to the inner side of a lipid vesicle self-assemble into highly ordered two-dimensional star-like nanoclusters with a number of arms determined by the number of NPs inside the vesicle. 

We demonstrate a spatial hypergraph model that allows us to vary the amount of higher-order structure in the generated hypergraph. Specifically, we can vary from a model that is a pure pairwise graph into a model that is almost a pure hypergraph. We use this spatial hypergraph model to study higher-order effects in epidemic spread. We use a susceptible-infected-recovered-susceptible (SIRS) epidemic model designed to mimic the spread of an airborne pathogen. We study three types of airborne effects that emulate airborne dilution effects. For the scenario of linear dilution, which roughly corresponds to constant ventilation per person as required in many building codes, we see essentially no impact from introducing small hyperedges up to size 15 whereas we do see effects when the hyperedge set is dominated by large hyperedges. Specifically, we track the mean infections after the SIRS epidemic has run for a while so it is in a ?steady state? and find the mean is higher in the large hyperedge regime whereas it is unchanged from pairwise to small hyperedge regime. 

The adhesion of nanoparticles to lipid vesicles causes curvature deformations to the membrane to an extent determined by the competition between the adhesive interaction and the membrane’s elasticity. These deformations can extend over length scales larger than the size of a nanoparticle, leading to an effective membrane-curvature-mediated interaction between nanoparticles. Nanoparticles with uniform surfaces tend to aggregate into unidimensionally close-packed clusters at moderate adhesion strengths and endocytose at high adhesion strengths. Here, we show that the suppression of close-packed clustering and endocytosis can be achieved by the surface modification of the nanoparticles into Janus particles where a moiety of their surface is grafted with polymers under a good solvent condition. The osmotic pressure of the polymer brushes prevents membrane wrapping of the nanoparticles’ moieties that are grafted with polymers, thus suppressing their endocytosis. Furthermore, a repulsion between polymer brushes belonging to two nearby nanoparticles destabilizes the dimerization of the nanoparticles over a wide range of values of the polymers’ molecular weight and grafting density. This surface modification of nanoparticles should allow for reliable, non-close-packed, and tunable self-assemblies of nanoparticles. 

A 2D tandem mass spectrum of a peptide mixture is organized into a graphical structure. A graph partitioning algorithm extracts the fragmentation trees of individual peptides, and ade novosequencing algorithm identifies the peptide sequences. 

Host-associated resident microbiota can protect their host from pathogens—a community-level trait called colonization resistance. The effect of the diversity of the resident community in previous studies has shown contradictory results, with higher diversity either strengthening or weakening colonization resistance. To control the confounding factors that may lead to such contradictions, we use mathematical simulations with a focus on species interactions and their impact on colonization resistance. We use a mediator-explicit model that accounts for metabolite-mediated interactions to performin silicoinvasion experiments. We show that the relationship between colonization resistance and species richness of the resident community is not monotonic because it depends on two underlying trends as the richness of the resident community increases: a decrease in instances of augmentation (invader species added, without driving out resident species) and an increase in instances of displacement (invader species added, driving out some of the resident species). These trends hold consistently under different parameters, regardless of the number of compounds that mediate interactions between species or the proportion of the facilitative versus inhibitory interactions among species. Our results show a positive correlation between resistance and diversity in low-richness communities and a negative correlation in high-richness communities, offering an explanation for the seemingly contradictory trend in the resistance-diversity relationship in previous reports. 

In recent years, there has been a heightened interest in the self-assembly of nanoparticles (NPs) that is mediated by their adsorption onto lipid membranes. The interplay between the adhesive energy of NPs on a lipid membrane and the membrane’s curvature energy causes it to wrap around the NPs. This results in an interesting membrane curvature-mediated interaction, which can lead to the self-assembly of NPs on lipid membranes. Recent studies have demonstrated that Janus spherical NPs, which adhere to lipid vesicles, can self-assemble into well-ordered nanoclusters with various geometries, including a few Platonic solids. The present study explores the additional effect of geometric anisotropy on the self-assembly of Janus NPs on lipid vesicles. Specifically, the current study utilized extensive molecular dynamics simulations to investigate the arrangement of Janus spherocylindrical NPs on lipid vesicles. We found that the additional geometric anisotropy significantly expands the range of NPs’ self-assemblies on lipid vesicles. The specific geometries of the resulting nanoclusters depend on several factors, including the number of Janus spherocylindrical NPs adhering to the vesicle and their aspect ratio. The lipid membrane-mediated self-assembly of NPs, demonstrated by this work, provides an alternative cost-effective route for fabricating highly engineered nanoclusters in three dimensions. Such structures, with the current wide range of material choices, have great potential for advanced applications, including biosensing, bioimaging, drug delivery, nanomechanics, and nanophotonics 

The adhesion modes of an ensemble of spherical Janus nanoparticles on planar membranes are investigated through large-scale molecular dynamics simulations of a coarse-grained implicit-solvent model.