Voltage oscillations in the barnacle giant muscle fiber
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model represents the reduced model (equations 9 and 2) with parameters values taken from the legend of figure 9. The model runs in both OpenCell and COR to replicate figure 9a (applied current = 400). The units have been checked and they are consistent.
Model Structure
ABSTRACT: Barnacle muscle fibers subjected to constant current stimulation produce a variety of types of oscillatory behavior when the internal medium contains the Ca++ chelator EGTA. Oscillations are abolished if Ca++ is removed from the external medium, or if the K+ conductance is blocked. Available voltage-clamp data indicate that the cell's active conductance systems are exceptionally simple. Given the complexity of barnacle fiber voltage behavior, this seems paradoxical. This paper presents an analysis of the possible modes of behavior available to a system of two noninactivating conductance mechanisms, and indicates a good correspondence to the types of behavior exhibited by barnacle fiber. The differential equations of a simple equivalent circuit for the fiber are dealt with by means of some of the mathematical techniques of nonlinear mechanics. General features of the system are (a) a propensity to produce damped or sustained oscillations over a rather broad parameter range, and (b) considerable latitude in the shape of the oscillatory potentials. It is concluded that for cells subject to changeable parameters (either from cell to cell or with time during cellular activity), a system dominated by two noninactivating conductances can exhibit varied oscillatory and bistable behavior.
The original paper reference is cited below:
Voltage oscillations in the barnacle giant muscle fiber, Morris C and Lecar H, 1981, Biophysical Journal, 35, 193-213. PubMed ID: 7260316
Schematic diagrams of the cell model.
$\frac{d V}{d \mathrm{time}}=\frac{\mathrm{i\_app}-\mathrm{i\_L}+\mathrm{i\_Ca}+\mathrm{i\_K}}{C}$
$\mathrm{i\_L}=\mathrm{g\_L}(V-\mathrm{E\_L})$
$\mathrm{i\_Ca}=\mathrm{g\_Ca}\mathrm{m\_infinity}(V-\mathrm{E\_Ca})\mathrm{m\_infinity}=0.5(1+\tanh \left(\frac{V-\mathrm{V1}}{\mathrm{V2}}\right))$
$\mathrm{i\_K}=\mathrm{g\_K}n(V-\mathrm{E\_K})$
$\mathrm{n\_infinity}=0.5(1+\tanh \left(\frac{V-\mathrm{V3}}{\mathrm{V4}}\right))\mathrm{lambda\_n}=\mathrm{lambda\_n\_bar}\cosh \left(\frac{V-\mathrm{V3}}{2\mathrm{V4}}\right)\frac{d n}{d \mathrm{time}}=\mathrm{lambda\_n}(\mathrm{n\_infinity}-n)$
keyword
Voltage oscillations in the barnacle giant muscle fiber
19335213MorrisC
Voltage oscillations in the barnacle giant muscle fiber: reduced model
LecarH1000010250Biophysical JournalAuckland Bioengineering InstituteThe University of AucklandLloydCatherineMayc.lloyd@auckland.ac.nzmuscle fibreelectrophysiology1981-077260316