Biomedical subjects

L P Endresen

Publications and source records attributed to L P Endresen.

4 recordsLinked to original sources

PubMed2000

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. The model predicts the experimentally observed intracellular ionic concentration of potassium, calcium and sodium. Likewise, the shapes of the simulated action potential and five membrane currents are in good agreement with experiment. We do not see any drift in the values of the concentrations in a long time simulation, and we obtain the same asymptotic values when starting from the full equilibrium situation with equal intracellular and extracellular ionic concentrations.

Action Potentials↗

PubMed2000

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.

Animals↗

PubMed1999

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.

Animals↗

PubMed1997

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. The dynamics of two coupled cells, with and without the presence of periodic acetylcholine pulses, shows examples of bifurcations and strange attractors, mathematical phenomena characterizing chaotic motion. It remains to be clarified whether such dynamics is actually observed, for example in the small irregular variations of the normal heart rate.

Acetylcholine↗