Phase resetting and coupling of noisy neural oscillators

A number of experimental groups have recently computed Phase Response Curves (PRCs) for neurons. There is a great deal of noise in the data. We apply methods from stochastic nonlinear dynamics to coupled noisy phase-resetting maps and obtain the invariant density of phase distributions. By exploiting the special structure of PRCs, we obtain some approximations for the invariant distributions. Comparisons to Monte-Carlo simulations are made. We show how phase-dependence of the noise can move the peak of the invariant density away from the peak expected from the analysis of the deterministic system and thus lead to noise-induced bifurcations. B. Ermentrout supported in part by NIMH and NSF. Action Editor: Wulfram Gerstner     

Resetting biological oscillators—A stochastic approach

We present a stochastic approach to phase-resetting of an ensemble of oscillators. In order to describe stimulation-induced dynamical phenomena we develop a stochastic model which consists of an ensemble of phase oscillators interacting via random forces. Every single oscillator is submitted to a phase stimulus. The ensemble's dynamics is determined by a Fokker-Planck equation. The stationary states are calculated explicitly, whereas the transients are analysed numerically. If the stimulus of a given (non-vanishing) intensity is administered at a critical initial cluster phase for a critical duration T _crit the ensemble's synchronized oscillation is annihilated. A transition from type 1 resetting to type 0 resetting occurs when the stimulation duration exceeds T _crit. Stimulation causes a shift of the mean frequency of every single oscillator. This frequency shift is explicitly calculated by deriving the mean first passage time. The model shows that there is a subcritical intensity which is connected with an enhanced vulnerability to stimulation. The desynchronized states, the so-called black holes, are typically associated with a double peak in the ensemble's phase distribution. This is important for analysing experimental data because simple peak-detection algorithms are not able to extract the underlying dynamics.Our results are discussed from the experimentator's point of view so that the insights derived from our model can improve data analysis and design of stimulation experiments.     

Differentiation of human peripheral blood monocytes to macrophages is associated with changes in the cellular respiratory burst activity.

When phagocytic leukocytes, e.g. neutrophils, monocytes and macrophages, interact with soluble or particulate stimuli, the cells respond with an increased production of reactive oxygen metabolites. This production can be measured with the luminol-amplified chemiluminescence (CL) technique. In the present study, the CL reaction induced in monocyte-derived macrophages was investigated and compared to the responses of neutrophils and monocytes. In systems without additives the CL response of macrophages to soluble stimuli (FMLP, PMA and ionomycin) was very low. Addition of a peroxidase (HRP) to the reaction mixtures resulted in a pronounced increase in CL activity. The cellular CL response in macrophages is thus limited by the amount of peroxidase available. The macrophage response differs qualitatively from the responses of neutrophils and monocytes, in that the intracellular phase of the response is missing.