A Mathematical Model of the Generation of Action Potentials in Corticotrophs
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This model is not currently functional.
Model Structure
Corticotropin-releaseing hormone (CRH) is an important regulator of adrenocorticotropin (ACTH) secretion from the pituitary corticotroph cells. CRH induces the secretion of ACTH through the actication of the cAMP second messenger system, which results in the activation of protein kinase A (PKA). Secretion of ACTH alo requires an influx of Ca2+, which occurs mainly through voltage-sensitive Ca2+ channels. Corticotrophs generate both spontaneous and CRG-induced action potentials. L-type voltage-sensitive Ca2+ channels are the main channel type that underlie Ca2+-induced action potential generation. It is likely that following activation by CRH, PKA phosphorylates the L-type channel and promotes Ca2+ action potential generation with subsequent Ca2+ influx. The rise in the intracellular concentration of Ca2+ ([Ca2+]i), then leads to the activation of exocytotic pathways, resulting in the secretion of ACTH.
Although the PKA-induced action potential activity is known to play an important role in this secretory pathway, the mechanism by which PKA activates the L-type Ca2+ channel is currently unknown. In the publication described here, LeBeau et al. investigate PKA regulation of the L-type Ca2+ channel. They develop a Hodgkin-Huxley-type mathematical model of action potential generation in corticotrophs (see below). The model includes descriptions of four plasma membrane ionic channels, which allows the analysis of the roles of each channel type in corticotroph electrical responses.
The complete original paper reference is cited below:
Generation of Action Potentials in a Mathematical Model of Corticotrophs, Andrew P. LeBeau, A. Bruce Robson, Alan E. McKinnon, Richard A. Donald, and James Sneyd, 1997,
Biophysical Journal
, 73, 1263-1275. PubMed ID: 9284294
cell diagram
Schematic diagram of the model of a corticotroph. The arrows represent ionic currents and fluxes across the plama membrane and across the membrane of the endoplasmic reticulum.
Using model simulations, the authors found that an increase in the L-type Ca2+ current was sufficient to generate action potentials from a previously resting state. The favoured mechanism which was thought to underlie this increase in the L-type Ca2+ current was a shift in the voltage-dependence of the current towards more negative potentials. The model also showed that the T-type Ca2+ current plays a role in establishing the excitability of the plasma membrane, but it doesn't plauy a major role in action potential generation.
The model has been described here in CellML (the raw CellML description of the LeBeau et al. 1997 model can be downloaded in various formats as described in ).
$\frac{d V}{d \mathrm{time}}=\frac{-(\mathrm{i\_CaL}+\mathrm{i\_CaT}+\mathrm{i\_K\_DR}+\mathrm{i\_K\_Ca}+\mathrm{i\_Leak})}{\mathrm{Cm}}$
$\mathrm{E\_Ca}=V\frac{\mathrm{Cai}-\mathrm{Cae}e^{-\left(\frac{2.0FV}{RT}\right)}}{1.0-e^{-\left(\frac{2.0FV}{RT}\right)}}\mathrm{E\_K}=V\frac{\mathrm{Ki}-\mathrm{Ke}e^{-\left(\frac{FV}{RT}\right)}}{1.0-e^{-\left(\frac{FV}{RT}\right)}}$
$\mathrm{i\_CaL}=\mathrm{g\_CaL}m^{2.0}\mathrm{E\_Ca}$
$\mathrm{m\_infinity}=\frac{1.0}{1.0+e^{-\left(\frac{V--12.0}{12.0}\right)}}\mathrm{tau\_m}=\frac{\mathrm{tau\_m\_}}{e^{\frac{V--60.0}{22.0}}+2.0e^{-(2.0\frac{V--60.0}{22.0})}}\frac{d m}{d \mathrm{time}}=\frac{\mathrm{m\_infinity}-m}{\mathrm{tau\_m}}$
$\mathrm{i\_CaT}=\mathrm{g\_CaT}m^{2.0}h\mathrm{E\_Ca}$
$\mathrm{m\_infinity}=\frac{1.0}{1.0+e^{-\left(\frac{V--30.0}{10.5}\right)}}\mathrm{tau\_m}=\frac{\mathrm{tau\_m\_}}{e^{\frac{V--60.0}{22.0}}+2.0e^{-(2.0\frac{V--60.0}{22.0})}}\frac{d m}{d \mathrm{time}}=\frac{\mathrm{m\_infinity}-m}{\mathrm{tau\_m}}$
$\mathrm{h\_infinity}=\frac{1.0}{1.0+e^{\frac{V--57.0}{5.0}}}\frac{d h}{d \mathrm{time}}=\frac{\mathrm{h\_infinity}-h}{\mathrm{tau\_h}}$
$\mathrm{i\_K\_DR}=\mathrm{g\_K\_DR}n\mathrm{E\_K}$
$\mathrm{n\_infinity}=\frac{1.0}{1.0+e^{-\left(\frac{V--20.0}{4.5}\right)}}\frac{d n}{d \mathrm{time}}=\frac{\mathrm{n\_infinity}-n}{\mathrm{tau\_n}}$
$\mathrm{i\_K\_Ca}=\mathrm{g\_K\_Ca}\frac{\mathrm{Cai}^{4.0}}{\mathrm{Cai}^{4.0}+\mathrm{KC}^{4.0}}\mathrm{E\_K}$
$\mathrm{i\_Leak}=\mathrm{g\_L}(V-\mathrm{E\_L})$
$\frac{d \mathrm{Cai}}{d \mathrm{time}}=\mathrm{j\_exch}+f\mathrm{beta}(\mathrm{j\_in}-\mathrm{j\_eff})$
$\mathrm{j\_exch}=\frac{\mathrm{Ca\_eq}-\mathrm{Cai}}{\mathrm{tau}}\mathrm{j\_in}=-\mathrm{alpha}(\mathrm{i\_CaL}+\mathrm{i\_CaT})\mathrm{j\_eff}=\mathrm{vp}\frac{\mathrm{Cai}^{2.0}}{\mathrm{Cai}^{2.0}+\mathrm{Kp}^{2.0}}$
pituitary gland
electrophysiology
neuron
corticotroph
The University of Auckland, Bioengineering Institute
Catherine
Lloyd
May
9284294
James
Sneyd
The University of Auckland
The Bioengineering Institute
Alan
McKinnon
E
Richard
Donald
A
c.lloyd@auckland.ac.nz
This is the CellML description of LeBeau et al.'s 1997 mathematical model of the generation of action potentials in corticotrophs.
Biophysical Journal
Generation of Action Potentials in a Mathematical Model of Corticotrophs
73
1263
1275
2004-03-20
keyword
1997-09
A
Robson
Bruce
LeBeau et al.'s 1997 mathematical model of the generation of action potentials in corticotrophs.
corticotroph
Andrew
LeBeau
P
Catherine Lloyd