Modelling calcium microdomains using homogenisation.
Microdomains of calcium (i.e., areas on the nanometer scale that have qualitatively different calcium concentrations from that in the bulk cytosol) are known to be important in many situations. In cardiac cells, for instance, a calcium microdomain between the L-type channels and the ryanodine receptors, the so-called diadic cleft, is where the majority of the control of calcium release occurs. In other cell types that exhibit calcium oscillations and waves, the importance of microdomains in the vicinity of clusters of inositol trisphosphate receptors, or between the endoplasmic reticulum (ER) and other internal organelles or the plasma membrane, is clear. Given the limits of computational power, it is not currently realistic to model an entire cellular cytoplasm by incorporating detailed structural information about the ER throughout the entire cytoplasm. Hence, most models use a homogenised approach, assuming that both cytoplasm and ER coexist at each point of the domain. Conversely, microdomain models can be constructed, in which detailed structural information can be incorporated, but, until now, methods have not been developed for linking such a microdomain model to a model at the level of the entire cell. Using the homogenisation approach we developed in an earlier paper [Goel, P., Friedman, A., Sneyd, J., 2006. Homogenization of the cell cytoplasm: the calcium bidomain equations. SIAM J. Multiscale Modeling Simulation, in press] we show how a multiscale model of a calcium microdomain can be constructed. In this model a detailed model of the microdomain (in which the ER and the cytoplasm are separate compartments) is coupled to a homogenised model of the entire cell in a rigorous way. Our method is illustrated by a simple model of the diadic cleft of a cardiac half-sarcomere.
Higgins
Erin R
ER
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand.
Goel
Pranay
P
Puglisi
Jose L
JL
Bers
Donald M
DM
Cannell
Mark
M
Sneyd
James
J
D000818:Animals; D002118:Calcium / Q000378:metabolism*; D020746:Calcium Channels, L-Type / Q000378:metabolism; D020013:Calcium Signaling; D003198:Computer Simulation; D003600:Cytosol / Q000378:metabolism*; D004721:Endoplasmic Reticulum / Q000378:metabolism*; D006801:Humans; D008954:Models, Biological; D009200:Myocardial Contraction / Q000502:physiology*; D032383:Myocytes, Cardiac / Q000378:metabolism* / Q000648:ultrastructure; D019837:Ryanodine Receptor Calcium Release Channel / Q000378:metabolism; D012518:Sarcomeres / Q000378:metabolism; D053498:Sarcoplasmic Reticulum Calcium-Transporting ATPases / Q000378:metabolism
D020746:Calcium Channels, L-Type; D019837:Ryanodine Receptor Calcium Release Channel; D053498:Sarcoplasmic Reticulum Calcium-Transporting ATPases; D002118:Calcium