Parabolic Bursting in Neurons
Catherine
Lloyd
Bioengineering Institute, University of Auckland
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
diagram of the model
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.
neuron
bifurcation
calcium dynamics
electrophysiology
resonance
Neuron
2003-04-09
R
Plant
E
This is the CellML description of Plant's 1981 mathematical model of
bursting nerve cells.
Catherine Lloyd
Autumn
Cuellar
A
The University of Auckland
The Bioengineering Institute
Catherine
Lloyd
May
7252375
Plant's 1981 mathematical model of bursting nerve cells.
Neuron
Bifurcation and resonance in a model for bursting nerve cells
11
15
32
keyword
Journal of Mathematical Biology
The University of Auckland, Bioengineering Institute
c.lloyd@auckland.ac.nz
2003-01-23
1981-01
Added publication date information.