Mucus clears from the trachea in a helix: a new twist to understanding airway diseases.

Background: Mucociliary clearance (MCC) is critical to lung health and is impaired in many diseases. The path of MCC may have an important impact on clearance but has never been rigorously studied. The objective of this study is to assess the three-dimensional path of human tracheal MCC in disease and health.

Effects of quasi-steady-state reduction on biophysical models with oscillations.

Many biophysical models have the property that some variables in the model evolve much faster than others. A common step in the analysis of such systems is to simplify the model by assuming that the fastest variables equilibrate instantaneously, an approach that is known as quasi-steady state reduction (QSSR). QSSR is intuitively satisfying but is not always mathematically justified, with problems known to arise, for instance, in some cases in which the full model has oscillatory solutions; in this case, the simplified version of the model may have significantly different dynamics to the full model.

The Role of Cell Volume in the Dynamics of Seizure, Spreading Depression, and Anoxic Depolarization.

Cell volume changes are ubiquitous in normal and pathological activity of the brain. Nevertheless, we know little of how cell volume affects neuronal dynamics. We here performed the first detailed study of the effects of cell volume on neuronal dynamics.

Neural Excitability and Singular Bifurcations.

We discuss the notion of excitability in 2D slow/fast neural models from a geometric singular perturbation theory point of view. We focus on the inherent singular nature of slow/fast neural models and define excitability via singular bifurcations. In particular, we show that type I excitability is associated with a novel singular Bogdanov-Takens/SNIC bifurcation while type II excitability is associated with a singular Andronov-Hopf bifurcation.

Excitable neurons, firing threshold manifolds and canards.

We investigate firing threshold manifolds in a mathematical model of an excitable neuron. The model analyzed investigates the phenomenon of post-inhibitory rebound spiking due to propofol anesthesia and is adapted from McCarthy et al. (SIAM J.

A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells.

The electrical activity of endocrine pituitary cells is mediated by a plethora of ionic currents and establishing the role of a single channel type is difficult. Experimental observations have shown however that fast-activating voltage- and calcium-dependent potassium (BK) current tends to promote bursting in pituitary cells. This burst promoting effect requires fast activation of the BK current, otherwise it is inhibitory to bursting.

The dynamics underlying pseudo-plateau bursting in a pituitary cell model.

Pituitary cells of the anterior pituitary gland secrete hormones in response to patterns of electrical activity. Several types of pituitary cells produce short bursts of electrical activity which are more effective than single spikes in evoking hormone release. These bursts, called pseudo-plateau bursts, are unlike bursts studied mathematically in neurons (plateau bursting) and the standard fast-slow analysis used for plateau bursting is of limited use.

Understanding anomalous delays in a model of intracellular calcium dynamics.

In many cell types, oscillations in the concentration of free intracellular calcium ions are used to control a variety of cellular functions. It has been suggested [J. Sneyd et al.

Changes in the criticality of Hopf bifurcations due to certain model reduction techniques in systems with multiple timescales.

A major obstacle in the analysis of many physiological models is the issue of model simplification. Various methods have been used for simplifying such models, with one common technique being to eliminate certain 'fast' variables using a quasi-steady-state assumption. In this article, we show when such a physiological model reduction technique in a slow-fast system is mathematically justified.

Mixed mode oscillations as a mechanism for pseudo-plateau bursting.

We combine bifurcation analysis with the theory of canard-induced mixed mode oscillations to investigate the dynamics of a novel form of bursting. This bursting oscillation, which arises from a model of the electrical activity of a pituitary cell, is characterized by small impulses or spikes riding on top of an elevated voltage plateau. Oscillations with these characteristics have been called "pseudo-plateau bursting".

The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales.

In recent work [J. Rubin and M. Wechselberger, Biol.

Giant squid-hidden canard: the 3D geometry of the Hodgkin-Huxley model.

This work is motivated by the observation of remarkably slow firing in the uncoupled Hodgkin-Huxley model, depending on parameters tau( h ), tau( n ) that scale the rates of change of the gating variables. After reducing the model to an appropriate nondimensionalized form featuring one fast and two slow variables, we use geometric singular perturbation theory to analyze the model's dynamics under systematic variation of the parameters tau( h ), tau( n ), and applied current I. As expected, we find that for fixed (tau( h ), tau( n )), the model undergoes a transition from excitable, with a stable resting equilibrium state, to oscillatory, featuring classical relaxation oscillations, as I increases.

Ionic channels and conductance-based models for hypothalamic neuronal thermosensitivity.

Thermoregulatory responses are partially controlled by the preoptic area and anterior hypothalamus (PO/AH), which contains a mixed population of temperature-sensitive and insensitive neurons. Immunohistochemical procedures identified the extent of various ionic channels in rat PO/AH neurons. These included pacemaker current channels [i.