A stochastic model for topographically influenced cell migration.

Migrating cells traverse a range of topographic configurations presented by the native extracellular environment to conduct their physiologic functions. It is well documented cells can modulate their behaviour in response to different topographic features, finding promising applications in biomaterial and bioimplant design. It is useful, in these areas of research, to be able to predict which topographic arrangements could be used to promote certain patterns of migration prior to laboratory experimentation. Despite a profusion of study and interest shown in these fields by experimentalists, the related modelling literature is as yet relatively sparse and tend to focus more on either cell-matrix interaction or morphological responses of cells. We propose a mathematical model for individual cell migration based on an Ornstein-Uhlenbeck process, and set out to see if the model can be used to predict migration patterns on 2-d isotropic and anisotropic topographies, whose characteristics can be broadly described as either uniform flat, uniform linear with variable ridge density or non-uniform disordered with variable feature density. Results suggest the model is capable of producing realistic patterns of migration for flat and linear topographic patterns, with calibrated output closely approximating NIH3T3 fibroblast migration behaviour derived from an experimental dataset, in which migration linearity increased with ridge density and average speed was highest at intermediate ridge densities. Exploratory results for non-uniform disordered topographies suggest cell migration patterns may adopt disorderedness present in the topography and that 'distortion' introduced to linear topographic patterns may not impede linear guidance of migration, given its magnitude is bounded within certain limits. We conclude that an Ornstein-Uhlenbeck based model for topographically influenced migration may be useful to predict patterns of migration behaviour for certain isotropic (flat) and anisotropic (linear) topographies in the NIH3T3 fibroblast cell line, but additional investigation is required to predict with confidence migration patterns for non-uniform disordered topographic arrangements.

Exact Equations for SIR Epidemics on Tree Graphs.

We consider Markovian susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson and where network links may be directed or undirected. We prove that a particular pair-based moment closure representation generates the expected infectious time series for networks with no cycles in the underlying graph. Moreover, this "deterministic" representation of the expected behaviour of a complex heterogeneous and finite Markovian system is straightforward to evaluate numerically.

Technoeconomic and environmental assessment of industrial organotin compounds.

Current uses of organotins include heat stabilizers for polyvinyl chloride (PVC), catalysts for polyurethane foam and silicone rubber, biocides, and animal health products. Domestic production consumption in 1982 is about 28 million pounds, and overall growth is estimated at 7 percent per year. Physical properties of organotins, including solubility in water, octanol-water partition coefficients, and Freundlich adsorption isotherm constants, are not well characterized. Analytical methods for tin in environmental and biological matrices involve concentration, separation, and identification by chromatography, spectrometry, and spectroscopy. Environmental fate and effects of organotins are not well understood. Degradation reactions may yield a complex set of products, including inorganic tin oxide. The effects of exposure of workers and release of organotins to the environment at point sources have been documented. Nonpoint sources of environmental exposure include discard and sanitary landfill disposal of plastics and direct release of biocides to aquatic or marine environments. Other dissipative uses of organotins which pose potential human risk include PVC food wrapping and bottles and rigid potable water pipe. The long term health effects of low level exposure to organotins are not known. Toxic metal cycling in the environment, including biomethylation of inorganic tin by naturally occurring bacteria, is of rising concern.

The transient-state kinetics of L-glutamate dehydrogenase. pH-dependence of the burst rate parameters.

The pH dependence of the initial transient velocity of NADPH production during the burst phase of the oxidative deamination of L-glutamate by L-glutamate dehydrogenase (L-glutamate : NAD(P)+ oxidoreductase (deaminating), EC 1.4.1.3) and NADP+ has been measured by stopped-flow spectrophotometry. These studies provide evidence that the entire pH dependence below pH 8.26 arises from reaction steps contributing to V of the burst with an apparent pKa of 8.1 +/- 0.1. The data are consistent with a model in which the formation of the first enzyme-coenzyme-substrate ternary complex on the reaction path equilibrates rapidly and in which the pH-dependent steps are mechanistically close to and may include the catalytic hydrogen transfer itself. At pH 8.87, there is evidence that L-glutamate binds less tightly to the enzyme and to the enzyme-NADP+ complex than at lower pH values.

Location of deuterium oxide solvent isotope effects in the glutamate dehydrogenase reaction.

Stopped flow studies of D2O kinetic solvent isotope effects on the reaction catalyzed by L-glutamate dehydrogenase reveal, in addition to several effects apparently attributable simply to pKa shifts, a 2-fold pH-independent effect on the velocity of the steady state oxidative deamination of L-glutamate by enzyme and NADP. Comparable pH-independent D2O kinetic solvent isotope effects are seen both in a transient phase of the reaction in which alpha-ketoglutarate is displaced by L-glutamate from an enzyme-NADPH-alpha-ketoglutarate (product) complex and in an analogous model reaction in which alpha-ketoglutarate is displaced by D-glutamate. These results suggest that alpha-ketoglutarate dissociation from an enzyme-NADPH-alpha-ketoglutarate complex is rate-limiting in the steady state.