Plant, 1981

Model Status

This is the original unchecked version of the model imported from the previous CellML model repository, 24-Jan-2006.

Model Structure

When exposed to a threshold concentration of glucose, pancreatic beta-cells from a wide range of species exhibit a complicated pattern of electrical activity. Bursts of action potential spikes (the "active" phase) are observed, separated by a "silent" phase of membrane repolarisation. At even higher glucose concentrations, continuous action potentials are seen. This electrical activity has two important physiological correlates: increased cytosolic Ca²⁺ concentration ([Ca²⁺]_i) and increased rate of insulin secretion during the active phase. It is generally accepted that the rise in [Ca²⁺]_i plays a major role in insulin secretion and that the action potential spikes during a burst are responsible for the rise in [Ca²⁺]_i.

Bursting in pancreatic beta-cells is a well studied phenomenon, and many mathematical models describing the process have been developed, including:

• Magnus and Keizer, 1997

• Chay, 1997

• Magnus and Keizer, 1999

• Gall and Susa, 1999

• Bertram et al., 2000

Another well studied example of busting is found in neurons (for example see the model by Friel, 1995). Analysis of a detailed mathematical model developed by Plant in 1981 reveals that the structure of this bursting oscillator is different from that in the beta-cell model. Where the beta-cell model has bistability, in Plant's model, oscillations arise from the autonomous activity of two slow variables. The bursting period is almost a parabolic function of time, which has lead to the name parabolic bursting.

Plant's model is similar to the beta-cell model in that it has a Ca²⁺-activated K⁺ channel and a voltage-gated K⁺ channel. However, it is distinct by having a voltage gated Na⁺ channel and a slowly activating Ca²⁺ current. The Na⁺, K⁺, and leak currents form the fast subsystem, while the Ca²⁺ current forms the slow subsystem (see the figure below for a description of the model).

The complete original paper reference is cited below:

Bifurcation and resonance in a model for bursting nerve cells, R.E. Plant, 1981, Journal of Mathematical Biology , 11, 15-32. PubMed ID: 7252375

A schematic representation of the transmebrane ionic currents described by the Plant 1981 model of a bursting neuron. The model includes a voltage dependent sodium current, INa; a slowly activating calcium current, ICa; a voltage gated potassium current, IK; a calcium activated potassium current, IK,Ca; and a leak current, IL.