Limit cycle oscillations in pacemaker cells.

In recent decades, several mathematical models describing the pacemaker activity of the rabbit sinoatrial node have been developed. We observe that membrane voltage and membrane charge are treated as independent dynamic variables in some of those models, resulting in an infinite number of limit cycles. Then we display numerical results from a new model where membrane voltage (v) is not a dynamic variable, and observe a limit cycle oscillation that can be reached from many different initial conditions.

A theory for the membrane potential of living cells.

We give an explicit formula for the membrane potential of cells in terms of the intracellular and extracellular ionic concentrations, and derive equations for the ionic currents that flow through channels, exchangers and electrogenic pumps. We demonstrate that the work done by the pumps equals the change in potential energy of the cell, plus the energy lost in downhill ionic fluxes through the channels and exchangers. The theory is illustrated in a simple model of spontaneously active cells in the cardiac pacemaker.

A possible resolution of the gating paradox.

We introduce a Markov model for the gating of membrane channels. The model features a possible solution to the so-called gating current paradox, namely that the bell-shaped curve that describes the voltage dependence of the kinetics is broader than expected from, and shifted relative to, the sigmoidal curve that describes the voltage dependence of the activation. The model also predicts some temperature dependence of this shift, but presence of the latter has not been tested experimentally so far.

Chaos in weakly-coupled pacemaker cells.

A model of the rabbit sinoatrial action potential is introduced, based on a model by Morris & Lecar. One cell is described by two nonlinear first-order ordinary differential equations, with ten constant parameters. The model is much simpler than most other models in use, but can reproduce perfectly experimentally recorded action potentials.

Kinetics of mercaptopurine and thioguanine nucleotides in renal transplant recipients during azathioprine treatment.

The purpose of this study was to examine the pharmacokinetics of mercaptopurine (6-MP) and thioguanine nucleotides (6-TGN) during azathioprine treatment. Plasma profiles and urinary excretion of 6-MP and 6-TGN concentrations in red blood cells (RBCs) were measured repeatedly during the first 3 weeks following transplantation in 10 adults, who had received kidney grafts from living related donors. Mean maximal 6-MP plasma concentration (Cmax) was 340 nmol/L (SD = 290), mean time to Cmax (Tmax) was 2 h (SD = 1.