Complex Calcium Oscillations and the Role of Mitochondria and Cytosolic Proteins
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in both OpenCell and COR to recreate the published results. The units have been checked and are consistent.
Model Structure
ABSTRACT: Intracellular calcium oscillations, which are oscillatory changes of cytosolic calcium concentration in response to agonist stimulation, are experimentally well observed in various living cells. Simple calcium oscillations represent the most common pattern and many mathematical models have been published to describe this type of oscillation. On the other hand, relatively few theoretical studies have been proposed to give an explanation of complex intracellular calcium oscillations, such as bursting and chaos. In this paper, we develop a new possible mechanism for complex calcium oscillations based on the interplay between three calcium stores in the cell: the endoplasmic reticulum (ER), mitochondria and cytosolic proteins. The majority ( approximately 80%) of calcium released from the ER is first very quickly sequestered by mitochondria. Afterwards, a much slower release of calcium from the mitochondria serves as the calcium supply for the intermediate calcium exchanges between the ER and the cytosolic proteins causing bursting calcium oscillations. Depending on the permeability of the ER channels and on the kinetic properties of calcium binding to the cytosolic proteins, different patterns of complex calcium oscillations appear. With our model, we are able to explain simple calcium oscillations, bursting and chaos. Chaos is also observed for calcium oscillations in the bursting mode.
The original paper reference is cited below:
Complex calcium oscillations and the role of mitochondria and cytosolic proteins, Marko Marhl, Thomas Haberichter, Milan Brumen and Reinhart Heinrich, 2000, Biosystems, 57, 75-86. PubMed ID: 11004387
cell schematic for the model
Schematic diagram of the model sysytem.
$\mathrm{Ca\_Pr}=\mathrm{Ca\_tot}-\mathrm{Ca\_cyt}+\frac{\mathrm{rho\_ER}}{\mathrm{beta\_ER}}\mathrm{Ca\_ER}+\frac{\mathrm{rho\_m}}{\mathrm{beta\_m}}\mathrm{Ca\_m}$
$\mathrm{Pr}=\mathrm{Pr\_tot}-\mathrm{Ca\_Pr}$
$\frac{d \mathrm{Ca\_cyt}}{d \mathrm{time}}=\mathrm{J\_ch}+\mathrm{J\_leak}+\mathrm{J\_out}+\mathrm{k\_minus}\mathrm{Ca\_Pr}-\mathrm{J\_pump}+\mathrm{J\_in}+\mathrm{k\_plus}\mathrm{Ca\_cyt}\mathrm{Pr}$
$\frac{d \mathrm{Ca\_ER}}{d \mathrm{time}}=\frac{\mathrm{beta\_ER}}{\mathrm{rho\_ER}}(\mathrm{J\_pump}-\mathrm{J\_ch}+\mathrm{J\_leak})$
$\frac{d \mathrm{Ca\_m}}{d \mathrm{time}}=\frac{\mathrm{beta\_m}}{\mathrm{rho\_m}}(\mathrm{J\_in}-\mathrm{J\_out})$
$\mathrm{J\_pump}=\mathrm{k\_pump}\mathrm{Ca\_cyt}$
$\mathrm{J\_ch}=\mathrm{k\_ch}\frac{\mathrm{Ca\_cyt}^{2.0}}{\mathrm{K1}^{2.0}+\mathrm{Ca\_cyt}^{2.0}}(\mathrm{Ca\_ER}-\mathrm{Ca\_cyt})$
$\mathrm{J\_leak}=\mathrm{k\_leak}(\mathrm{Ca\_ER}-\mathrm{Ca\_cyt})$
$\mathrm{J\_in}=\mathrm{k\_in}\frac{\mathrm{Ca\_cyt}^{8.0}}{\mathrm{K2}^{8.0}+\mathrm{Ca\_cyt}^{8.0}}$
$\mathrm{J\_out}=(\mathrm{k\_out}\frac{\mathrm{Ca\_cyt}^{2.0}}{\mathrm{K3}^{2.0}+\mathrm{Ca\_cyt}^{2.0}}+\mathrm{k\_m})\mathrm{Ca\_m}$
calcium dynamics
electrophysiology
mitochondria
oscillator
The University of Auckland, Auckland Bioengineering Institute
Catherine
Lloyd
May
keyword
Added more metadata.
Reinhart
Heinrich
Marko
Marhl
Added publication date information.
Catherine
Lloyd
May
2000-07
Catherine Lloyd
A mathematical model of Ca2+ oscillations and the role of mitochondria
and cytosolic proteins.
Autumn
Cuellar
A
Milan
Brumen
2003-04-09
BioSystems
Thomas
Haberichter
Complex calcium oscillations and the role of mitochondria and cytosolic proteins
57
75
86
2002-04-04
2002-07-18
c.lloyd@auckland.ac.nz
The University of Auckland
Auckland Bioengineering Institute
This is the CellML description of Marhl et al's 2000 model of Ca2+
oscillations and the role of mitochondria and cytosolic proteins.
With their model they are able to explain simple Ca2+ oscillations,
bursting and chaos.
11004387