Shorten, Wall, 2000

Model Status

This model runs in OpenCell and COR and the units are consistent throughout. It it an accurate reproduction of the paper equations but does not reproduce the published results for unknown reasons, possibly because initial conditions for state variables were guessed.

Model Structure

ABSTRACT: We investigate bursting behaviour generated in an electrophysiological model of pituitary corticotrophs. The active and silent phases of this mode of bursting are generated by moving between two stable oscillatory solutions. The bursting is indirectly driven by slow modulation of the endoplasmic reticulum Ca2+ concentration. The model exhibits different modes of bursting, and we investigate mode transitions and similar modes of bursting in other Hodgkin-Huxley models. Bifurcation analysis and the use of null-surfaces facilitate a geometric interpretation of the model bursting modes and action potential generation, respectively.

The original paper reference is cited below:

A Hodgkin-Huxley Model Exhibiting Bursting Oscillations, Paul R. Shorten and David J.N. Wall, 2000, Bulletin of Mathematical Biology, 62, 695-715. PubMed ID: 10938629

Schematic diagram of a pituitary corticotroph cell showing the transmembrane ionic currents and the intracellular Ca²⁺ dynamics captured by the mathematical model. Arrows indicate ionic channels and pumps. I_Ca-L represents an L-type Ca²⁺ current responsible for most of the Ca²⁺ influx during an action potential. I_Ca-T is a T-type voltage-sensitive Ca²⁺ current. A voltage-sensitive K⁺ current, I_K-DR , is mainly responsible for action potential repolarisation. A Ca²⁺-activated K⁺ current, I_K-Ca , is essential for bursting behaviour. The remaining leak current, I_leak , represents all other ionic fluxes across the plasma membrane which are not specifically described by the model. J_eff and J_up are the ER and plasma membrane Ca²⁺-ATPase pumps, and J_rel represents the ER Ca²⁺ leakage term. Within the ER and the cytosol, significant portions of Ca²⁺ are bound to buffers, denoted by B_er and B_c respectively.