Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers.

Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population models predict that a species with a lower dispersal rate always drives a competing species to extinction in the presence of spatial variation of resources. However, the introduction of intrinsic demographic stochasticity can reverse this conclusion. We present a simple model in which competition between the exploitation of resources and stochastic fluctuations leads to victory by either the faster or slower of two species depending on the environmental parameters. A simplified limiting case of the model, analyzed by closing the moment and correlation hierarchy, quantitatively predicts which species will win in the complete model under given parameters of spatial variation and average carrying capacity.

Origin of broad polydispersion in functionalized dendrimers and its effects on cancer-cell binding affinity.

Nanoparticles with multiple ligands have been proposed for use in nanomedicine. The multiple targeting ligands on each nanoparticle can bind to several locations on a cell surface facilitating both drug targeting and uptake. Experiments show that the distribution of conjugated ligands is unexpectedly broad, and the desorption rate appears to depend exponentially upon the mean number of attached ligands. These two findings are explained with a model in which ligands conjugate to the nanoparticle with a positive cooperativity of ≈4 kT , and that nanoparticles bound to a surface by multiple bonds are permanently affixed. This drives new analysis of the data, which confirms that there is only one time constant for desorption, that of a nanoparticle bound to the surface by a single bond.

The implications of stochastic synthesis for the conjugation of functional groups to nanoparticles.

Stochastic synthesis of a ligand coupled to a nanoparticle results in a distribution of populations with different numbers of ligands per nanoparticle. This distribution was resolved and quantified using HPLC and is in excellent agreement with the ligand/nanoparticle average measured by 1H NMR, gel permeation chromatography (GPC), and potentiometric titration, and yet significantly more disperse than commonly held perceptions of monodispersity. Two statistical models were employed to confirm that the observed heterogeneity is consistent with theoretical expectations.