Mathematical modelling of calcium homeostasis in yeast cells
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This model runs in OpenCell and COR. This version is able to reproduce figures from the original publication, although some tweeking of variables is required to produce the full range of figures. The model is currently parameterised to reproduce Fig 2a. The units have been checked and they are consistent.
Model Structure
ABSTRACT: In this study, based on currently available experimental observations on protein level, we constructed a mathematical model to describe calcium homeostasis in normally growing yeast cells (Saccharomyces cerevisiae). Simulation results show that tightly controlled low cytosolic calcium ion level can be a natural result under the general mechanism of gene expression feedback control. The calmodulin (a sensor protein) behavior in our model cell agrees well with relevant observations in real cells. Moreover, our model can qualitatively reproduce the experimentally observed response curve of real yeast cell responding to step-like disturbance in extracellular calcium ion concentration. Further investigations show that the feedback control mechanism in our model is as robust as it is in real cells.
The original paper reference is cited below:
Mathematical modeling of calcium homeostasis in yeast cells, Jiangjun Cui and Jaap A. Kaandorp, 2006,
Cell Calcium
, 39, 337-348. PubMed ID: 16445978
A schematic diagram of the model
A simplified diagram of the calcium fluxes described by the mathematical model. Extracellular calcium enters the cell cytosol through an unknown Channel X and also, under certain conditions such as depletion of secretory calcium, through the channel Cch1p-Mid1p. Cytosolic calcium can be pumped into the ER and Golgi through Pmrlp and into the vacuole through Pmc1p and Vcx1p. Under the abnormal condition of extracellular hypertonic shock, the vacuoles can release calcium into cytosol through Yvclp. Cytosolic calmodulin is a calcium-binding protein which in its bound form can activate target proteins such as calcineurin. Activated calcineurin dephosphorylates the transcription factor Crz1p, promoting its translocation into the nucleus where it regulates the transcription of genes such as Pmr1 and Pmc1.
$\frac{d m}{d \mathrm{time}}=\mathrm{kM\_plus}(\mathrm{CaMtotal}-m)x^{3.0}-\mathrm{kM\_minus}m$
$\mathrm{dmdt}=\mathrm{kM\_plus}(\mathrm{CaMtotal}-m)x^{3}-\mathrm{kM\_minus}m$
$\frac{d z}{d \mathrm{time}}=\mathrm{kN\_plus}(\mathrm{CaNtotal}-z)m-\mathrm{kN\_minus}z$
$\mathrm{dzdt}=\mathrm{kN\_plus}(\mathrm{CaNtotal}-z)m-\mathrm{kN\_minus}z$
$\frac{d h}{d \mathrm{time}}=d\mathrm{phi}\frac{1.0}{z}(1.0-h)-f(1.0-\mathrm{phi}\frac{1.0}{z})h$
$\mathrm{phi}=\frac{1.0}{1.0+\frac{\mathrm{L0}((\mathrm{lamda}y)^{(N+1.0)}-1.0)}{(\mathrm{lamda}y-1.0)\frac{y-1.0}{y^{(N+1.0)}-1.0}}}$
$\mathrm{psi}=\frac{1.0+\mathrm{L0}}{\frac{y^{(N+1.0)}-1.0}{y-1.0}+\mathrm{L0}\frac{(\mathrm{lamda}y)^{(N+1.0)}-1.0}{\mathrm{lamda}y-1.0}}$
$\frac{d x}{d \mathrm{time}}=\frac{\mathrm{Vx}\mathrm{Caex}}{\mathrm{Kx}+\mathrm{Caex}}-h\mathrm{psi}\frac{1.0}{z}\frac{\mathrm{V1}x}{\mathrm{K1}+x}+h\mathrm{psi}\frac{1.0}{z}\frac{\mathrm{V2}x}{\mathrm{K2}+x}+\frac{1.0}{1.0+\mathrm{kc}z}\frac{\mathrm{V3}x}{\mathrm{K3}+x}+\mathrm{alpha}x$
$\mathrm{dxdt}=\frac{\mathrm{Vx}\mathrm{Caex}}{\mathrm{Kx}+\mathrm{Caex}}-h\mathrm{psi}\frac{1}{z}\frac{\mathrm{V1}x}{\mathrm{K1}+x}+h\mathrm{psi}\frac{1}{z}\frac{\mathrm{V2}x}{\mathrm{K2}+x}+\frac{1}{1+\mathrm{kc}z}\frac{\mathrm{V3}x}{\mathrm{K3}+x}+\mathrm{alpha}x$
$\mathrm{L0}=10.0^{-\left(\frac{N}{2.0}\right)}y=\frac{1.0}{z}$
gene expression
calcium homeostasis
calcium dynamics
yeast
16445978
The University of Auckland, Auckland Bioengineering Institute
2007-09-07T14:34:45+12:00
4
2007-05-26T00:00:00+00:00
The model has now been fixed such that it runs in PCEnv and COR and can recreate the published results. Units have been checked and are all correct and are consistent.
James
Lawson
Richard
Catherine Lloyd
2006-04-00 00:00
Cui and Kaandorp's 2006 mathematical model of calcium homeostasis in yeast cells.
Catherine
Lloyd
May
c.lloyd@auckland.ac.nz
James
Lawson
Richard
2009-06-08T15:34:20+12:00
Jiangjun
Cui
Mathematical modeling of calcium homeostasis in yeast cells
39
337
348
Some extra equations have been added to define differential expressions as variables to allow them to be graphed. No changes to the guts of the model have been made.
The model has now been fixed such that it runs in PCEnv and COR and can recreate the published results. Units have been checked and are all correct and are consistent.
Jaap
Kaandorp
A
2007-09-01T16:31:11+12:00
Cell Calcium
The University of Auckland
Auckland Bioengineering Institute
Catherine
Lloyd
May
This is the CellML description of Cui and Kaandorp's 2006 mathematical model of calcium homeostasis in yeast cells.
Catherine Lloyd
keyword
Ca-bound calmodulin
m
nuclear fraction of Crz1p
h
updated curation status,
removed reference link from documentation
activated calcineurin
z
cytosolic calcium
x