A nonlinear mixed effects approach for modeling the cell-to-cell variability of Mig1 dynamics in yeast

The last decade has seen a rapid development of experimental techniques that allow data collection from individual cells. These techniques have enabled the discovery and characterization of variability within a population of genetically identical cells. Nonlinear mixed effects (NLME) modeling is an established framework for studying variability between individuals in a population, frequently used in pharmacokinetics and pharmacodynamics, but its potential for studies of cell-to-cell variability in molecular cell biology is yet to be exploited. Here we take advantage of this novel application of NLME modeling to study cell-to-cell variability in the dynamic behavior of the yeast transcription repressor Mig1. In particular, we investigate a recently discovered phenomenon where Mig1 during a short and transient period exits the nucleus when cells experience a shift from high to intermediate levels of extracellular glucose. A phenomenological model based on ordinary differential equations describing the transient dynamics of nuclear Mig1 is introduced, and according to the NLME methodology the parameters of this model are in turn modeled by a multivariate probability distribution. Using time-lapse microscopy data from nearly 200 cells, we estimate this parameter distribution according to the approach of maximizing the population likelihood. Based on the estimated distribution, parameter values for individual cells are furthermore characterized and the resulting Mig1 dynamics are compared to the single cell times-series data. The proposed NLME framework is also compared to the intuitive but limited standard two-stage (STS) approach. We demonstrate that the latter may overestimate variabilities by up to almost five fold. Finally, Monte Carlo simulations of the inferred population model are used to predict the distribution of key characteristics of the Mig1 transient response. We find that with decreasing levels of post-shift glucose, the transient response of Mig1 tend to be faster, more extended, and displays an increased cell-to-cell variability

Effect of particle size on the photocatalytic activity of nanoparticulate zinc oxide

In this study, a three-stage process consisting of mechanical milling, heat treatment, and washing has been used to manufacture nanoparticulate ZnO powders with a controlled particle size and minimal agglomeration. By varying the temperature of the post-milling heat treatment, it was possible to control the average particle size over the range of 28&ndash;57 nm. The photocatalytic activity of these powders was characterized by measuring the hydroxyl radical concentration as a function of irradiation time using the spin-trapping technique with electron paramagnetic resonance spectroscopy. It was found that there exists an optimum particle size of approximately 33 nm for which the photocatalytic activity is maximized. The existence of this optimal particle size is attributable to an increase in the charge carrier recombination rate, which counteracts the increased activity arising from the higher specific surface area for a sufficiently small particle size.<br /