### Abstract

Calcium (Ca^{2+})-induced Ca^{2+}-release (CICR) takes place in spatially restricted microdomains known as dyads. The length scale over which CICR occurs is on the order of nanometers and relevant time scales range from micro- to milliseconds. Quantitative understanding of CICR therefore requires development of models that are applicable over a range of spatio-temporal scales. We will present several new approaches for multiscale modeling of CICR. First, we present a model of dyad Ca^{2+} dynamics in which the Fokker-Planck equation (FPE) is solved for the probability P(x, t) that a Ca^{2+} ion is located at dyad position x at time t. Using this model, we demonstrate that (a) Ca^{2+} signaling in the dyad is mediated by approximately tens of Ca^{2+} ions; (b) these signaling events are noisy due to the small number of ions involved; and (c) the geometry of the RyR (ryanodine receptors) protein may function to restrict the diffusion of and to "funnel" Ca^{2+} ions to activation-binding sites on the RyR, thus increasing RyR open probability and excitation-contraction (EC) coupling gain. Simplification of this model to one in which the dyadic space is represented using a single compartment yields the stochastic local-control model of CICR developed previously. We have shown that this model captures fundamental properties of CICR, such as graded release and voltage-dependent gain, may be integrated within a model of the myocyte and may be simulated in reasonable times using a combination of efficient numerical methods and parallel computing, but remains too complex for general use in cell simulations. To address this problem, we show how separation of time scales may be used to formulate a model in which nearby L-type Ca^{2+} channels (LCCs) and RyRs gate as a coupled system that may be described using low-dimensional systems of ordinary differential equations, thus reducing computational complexity while capturing fundamentally important properties of CICR. The simplified model may be solved many orders of magnitude faster than can either of the more detailed models, thus enabling incorporation into tissue-level simulations.

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

Title of host publication | Annals of the New York Academy of Sciences |

Pages | 362-375 |

Number of pages | 14 |

Volume | 1080 |

DOIs | |

State | Published - Oct 2006 |

### Publication series

Name | Annals of the New York Academy of Sciences |
---|---|

Volume | 1080 |

ISSN (Print) | 00778923 |

ISSN (Electronic) | 17496632 |

### Fingerprint

### Keywords

- Calcium-induced
- Calcium-release
- Dyad
- Excitation-contraction coupling
- Modeling

### ASJC Scopus subject areas

- Biochemistry, Genetics and Molecular Biology(all)

### Cite this

*Annals of the New York Academy of Sciences*(Vol. 1080, pp. 362-375). (Annals of the New York Academy of Sciences; Vol. 1080). https://doi.org/10.1196/annals.1380.027

**Multiscale modeling of calcium signaling in the cardiac dyad.** / Winslow, Raimond; Tanskanen, Antti; Chen, Mindao; Greenstein, Joseph L.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Annals of the New York Academy of Sciences.*vol. 1080, Annals of the New York Academy of Sciences, vol. 1080, pp. 362-375. https://doi.org/10.1196/annals.1380.027

}

TY - GEN

T1 - Multiscale modeling of calcium signaling in the cardiac dyad

AU - Winslow, Raimond

AU - Tanskanen, Antti

AU - Chen, Mindao

AU - Greenstein, Joseph L.

PY - 2006/10

Y1 - 2006/10

N2 - Calcium (Ca2+)-induced Ca2+-release (CICR) takes place in spatially restricted microdomains known as dyads. The length scale over which CICR occurs is on the order of nanometers and relevant time scales range from micro- to milliseconds. Quantitative understanding of CICR therefore requires development of models that are applicable over a range of spatio-temporal scales. We will present several new approaches for multiscale modeling of CICR. First, we present a model of dyad Ca2+ dynamics in which the Fokker-Planck equation (FPE) is solved for the probability P(x, t) that a Ca2+ ion is located at dyad position x at time t. Using this model, we demonstrate that (a) Ca2+ signaling in the dyad is mediated by approximately tens of Ca2+ ions; (b) these signaling events are noisy due to the small number of ions involved; and (c) the geometry of the RyR (ryanodine receptors) protein may function to restrict the diffusion of and to "funnel" Ca2+ ions to activation-binding sites on the RyR, thus increasing RyR open probability and excitation-contraction (EC) coupling gain. Simplification of this model to one in which the dyadic space is represented using a single compartment yields the stochastic local-control model of CICR developed previously. We have shown that this model captures fundamental properties of CICR, such as graded release and voltage-dependent gain, may be integrated within a model of the myocyte and may be simulated in reasonable times using a combination of efficient numerical methods and parallel computing, but remains too complex for general use in cell simulations. To address this problem, we show how separation of time scales may be used to formulate a model in which nearby L-type Ca2+ channels (LCCs) and RyRs gate as a coupled system that may be described using low-dimensional systems of ordinary differential equations, thus reducing computational complexity while capturing fundamentally important properties of CICR. The simplified model may be solved many orders of magnitude faster than can either of the more detailed models, thus enabling incorporation into tissue-level simulations.

AB - Calcium (Ca2+)-induced Ca2+-release (CICR) takes place in spatially restricted microdomains known as dyads. The length scale over which CICR occurs is on the order of nanometers and relevant time scales range from micro- to milliseconds. Quantitative understanding of CICR therefore requires development of models that are applicable over a range of spatio-temporal scales. We will present several new approaches for multiscale modeling of CICR. First, we present a model of dyad Ca2+ dynamics in which the Fokker-Planck equation (FPE) is solved for the probability P(x, t) that a Ca2+ ion is located at dyad position x at time t. Using this model, we demonstrate that (a) Ca2+ signaling in the dyad is mediated by approximately tens of Ca2+ ions; (b) these signaling events are noisy due to the small number of ions involved; and (c) the geometry of the RyR (ryanodine receptors) protein may function to restrict the diffusion of and to "funnel" Ca2+ ions to activation-binding sites on the RyR, thus increasing RyR open probability and excitation-contraction (EC) coupling gain. Simplification of this model to one in which the dyadic space is represented using a single compartment yields the stochastic local-control model of CICR developed previously. We have shown that this model captures fundamental properties of CICR, such as graded release and voltage-dependent gain, may be integrated within a model of the myocyte and may be simulated in reasonable times using a combination of efficient numerical methods and parallel computing, but remains too complex for general use in cell simulations. To address this problem, we show how separation of time scales may be used to formulate a model in which nearby L-type Ca2+ channels (LCCs) and RyRs gate as a coupled system that may be described using low-dimensional systems of ordinary differential equations, thus reducing computational complexity while capturing fundamentally important properties of CICR. The simplified model may be solved many orders of magnitude faster than can either of the more detailed models, thus enabling incorporation into tissue-level simulations.

KW - Calcium-induced

KW - Calcium-release

KW - Dyad

KW - Excitation-contraction coupling

KW - Modeling

UR - http://www.scopus.com/inward/record.url?scp=33845667860&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845667860&partnerID=8YFLogxK

U2 - 10.1196/annals.1380.027

DO - 10.1196/annals.1380.027

M3 - Conference contribution

C2 - 17132795

AN - SCOPUS:33845667860

SN - 1573316512

SN - 9781573316514

VL - 1080

T3 - Annals of the New York Academy of Sciences

SP - 362

EP - 375

BT - Annals of the New York Academy of Sciences

ER -