De Vries, Sherman, 2000

Model Status

This model has been validated and is known to run in OpenCell. The paper by Devries and Sherman describes several different parameter sets including single cell and two cell sets, and also describes a deterministic and a stochastic model. This file uses the equations and parameters given for the single cell deterministic model.

ValidateCellML confirms this model as valid CellML but detects unit inconsistencies. We have attempted to balance this model's units by replacing tau's units to picoF, but this breaks the model.

Model Structure

When exposed to a threshold concentration of glucose, pancreatic beta-cells 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.

Normal bursting patterns are only observed when the beta-cells act synchronously, as they do in vivo, in electrically coupled organs called the islets of Langerhans. Isolated beta-cells display atypical bursting or continuous spike activity. In their 2000 paper, Gerda De Vries and Arthur Sherman study bursting as an emergent property of the population, with especial focus on interactions between the subclass of spiking cells. The equations describing the ionic currents are based on a biophysical model of bursting pancreatic beta-cells according to the formula developed by Hodgkin and Huxley (The Hodgkin-Huxley Squid Axon Model, 1952). The biophysical model was simplified to produce a minimal, but representative, model of bursting. This minimal model describes three ionic currents: a fast voltage-activated calcium current, I_Ca; a delayed rectifier potassium current, I_K; and a very slow inhibitory potassium current, I_s. De Vries and Sherman modify this minimal model by including an additional ATP sensitive potassium current, I_K(ATP) (see the figure below). The calcium and delayed rectifier potassium currents are responsible for generating action potentials. The slow potassium current is responsible for switching between the active and the silent phases of the bursting pattern. Finally, I_K(ATP) is a backgroud current which is responsible for setting the plateau fraction, the ratio of the active phase duration to the burst period. For the deterministic version of the model that is presented here, p, representing the average fraction of open K(ATP) channels, is constant at 0.5.

The complete original paper reference is cited below:

Channel Sharing in Pancreatic Beta-Cells Revisited: Enhancement of Emergent Bursting by Noise, Gerda De Vries and Arthur Sherman, 2000, The Journal Of Theoretical Biology , 207, 513-530. (A PDF version of the article is available to subscibers on the Science Direct website.) PubMed ID: 11093836

A schematic representation of the four transmembrane currents captured by the De Vries and Sherman 2000 pancreatic beta-cell model.