### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 623-644 |

Number of pages | 22 |

Journal | Journal of Theoretical Biology |

Volume | 247 |

Issue number | 4 |

DOIs | |

State | Published - Aug 21 2007 |

Externally published | Yes |

### Fingerprint

### Keywords

- Calcium microdomains
- Calcium oscillations
- Effective diffusion coefficients
- Excitation-contraction coupling
- Homogenisation

### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)

### Cite this

*Journal of Theoretical Biology*,

*247*(4), 623-644. https://doi.org/10.1016/j.jtbi.2007.03.019

**Modelling calcium microdomains using homogenisation.** / Higgins, Erin R.; Goel, Pranay; Puglisi, Jose L.; Bers, Donald M; Cannell, Mark; Sneyd, James.

Research output: Contribution to journal › Article

*Journal of Theoretical Biology*, vol. 247, no. 4, pp. 623-644. https://doi.org/10.1016/j.jtbi.2007.03.019

}

TY - JOUR

T1 - Modelling calcium microdomains using homogenisation

AU - Higgins, Erin R.

AU - Goel, Pranay

AU - Puglisi, Jose L.

AU - Bers, Donald M

AU - Cannell, Mark

AU - Sneyd, James

PY - 2007/8/21

Y1 - 2007/8/21

N2 - 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.

AB - 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.

KW - Calcium microdomains

KW - Calcium oscillations

KW - Effective diffusion coefficients

KW - Excitation-contraction coupling

KW - Homogenisation

UR - http://www.scopus.com/inward/record.url?scp=34447512612&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34447512612&partnerID=8YFLogxK

U2 - 10.1016/j.jtbi.2007.03.019

DO - 10.1016/j.jtbi.2007.03.019

M3 - Article

VL - 247

SP - 623

EP - 644

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

IS - 4

ER -