Cyclic Feedback Systems with Quorum Sensing Coupling.

Synchronization and desynchronization is of great interest in the study of circadian rhythms, metabolic oscillations and time-dependent cell aggregate behaviors. Several recent studies examine synchronization and other dynamics in models of repressilators coupled by a quorum sensing mechanism that uses a diffusive signal. Their numerical simulations have shown the complexity of the collective behavior depends sensitively on which protein upregulates diffusive signal.

A nonautonomous phenomenological model for On and Off responses of cells in sensory system.

Many neurons in mammalian sensory systems exhibit On and Off responses when given appropriate excitatory and inhibitory stimuli. In some instances, such neurons can also exhibit a Mixed response where diminished On and Off responses are both present. In this manuscript, we present a simple single cell model for these ubiquitous stimulus-response patterns.

Traveling wave solutions of a reaction diffusion model for competing pioneer and climax species.

Presented is a reaction-diffusion model for the interaction of pioneer and climax species. For certain parameters the system exhibits bistability and traveling wave solutions. Specifically, we show that when the climax species diffuses at a slow rate there are traveling wave solutions which correspond to extinction waves of either the pioneer or climax species.

Controllability of excitable systems.

Mathematical models of cell electrical activity typically consist of a current balance equation, channel activation (or inactivation) variables and concentrations of regulatory agents. These models can be thought of as nonlinear filters whose input is some applied current I (possibly zero) and output is a membrane potential V. A natural question to ask is if the applied current I can be deduced from the potential V.

Fast subsystem bifurcations in strongly coupled heterogeneous collections of excitable cells.

A continuum model for a heterogeneous collection of excitable cells electrically coupled through gap junctions is introduced and analysed using spatial averaging, asymptotic and numerical techniques. Heterogeneity is modelled by imposing a spatial dependence on parameters which define the single cell model and a diffusion term is used to model the gap junction coupling. For different parameter values, single cell models can exhibit bursting, beating and a myriad of other complex oscillations.

Glucose diffusion in pancreatic islets of Langerhans.

We investigate the time required for glucose to diffuse through an isolated pancreatic islet of Langerhans and reach an equilibrium. This question is relevant in the context of in vitro electrophysiological studies of the response of an islet to step changes in the bath glucose concentration. Islet cells are electrically coupled by gap junctions, so nonuniformities in islet glucose concentration may be reflected in the activity of cells on the islet periphery, where electrical recordings are made.

Correlations of rates of insulin release from islets and plateau fractions for beta-cells.

Pancreatic beta-cells in intact islets of Langerhans perfused with various glucose concentrations exhibit periodic bursting electrical activity (BEA) consisting of active and silent phases. The fraction of the time spent in the active phase is called the plateau fraction and appears to be strongly correlated with the rate of release of insulin from islets as glucose concentration is varied. Here this correlation is quantified and a theoretical development is presented in detail.

The biopharmaceutical properties of solid dosage forms. I. An evaluation of 23 brands of phenylbutazone tablets.

The potency, disintegration and dissolution characteristics of 23 brands of phenylbutazone tablets were determined. Five (21.7%) of the 23 brands failed to comply with the minimum requirements of the compendia or the regulations appended to the Food and Drugs Act.