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A multiscale computational model of spatially resolved calcium cycling in cardiac myocytes: from detailed cleft dynamics to the whole cell concentration profiles.

Vierheller J, Neubert W, Falcke M, Gilbert SH, Chamakuri N - Front Physiol (2015)

Bottom Line: Mathematical modeling of excitation-contraction coupling (ECC) in ventricular cardiac myocytes is a multiscale problem, and it is therefore difficult to develop spatially detailed simulation tools.Our concept for a multiscale mathematical model of Ca(2+) -induced Ca(2+) release (CICR) and whole cardiomyocyte electrophysiology incorporates stochastic simulation of individual LC- and RyR-channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca(2+) and Ca(2+)-binding molecules in the bulk of the cell.We developed a novel computational approach to resolve the concentration gradients from dyadic space to cell level by using a quasistatic approximation within the dyad and finite element methods for integrating the partial differential equations.

View Article: PubMed Central - PubMed

Affiliation: Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine Berlin, Germany.

ABSTRACT
Mathematical modeling of excitation-contraction coupling (ECC) in ventricular cardiac myocytes is a multiscale problem, and it is therefore difficult to develop spatially detailed simulation tools. ECC involves gradients on the length scale of 100 nm in dyadic spaces and concentration profiles along the 100 μm of the whole cell, as well as the sub-millisecond time scale of local concentration changes and the change of lumenal Ca(2+) content within tens of seconds. Our concept for a multiscale mathematical model of Ca(2+) -induced Ca(2+) release (CICR) and whole cardiomyocyte electrophysiology incorporates stochastic simulation of individual LC- and RyR-channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca(2+) and Ca(2+)-binding molecules in the bulk of the cell. We developed a novel computational approach to resolve the concentration gradients from dyadic space to cell level by using a quasistatic approximation within the dyad and finite element methods for integrating the partial differential equations. We show whole cell Ca(2+)-concentration profiles using three previously published RyR-channel Markov schemes.

No MeSH data available.


Related in: MedlinePlus

Restitution properties with the (Walker et al., 2014)-RyR model. (A) Membrane potential. (B) Average cytosolic [Ca2+]i]. (C) Average cytosolic  as defined in Equation (20). Solid line: basic cycle length (BCL) = 350 ms; dashed line: BCL = 300 ms; dotted line: BCL = 250 ms. At cycle length 350 ms the DI was 177 ms. At cycle length 300 ms the DI was 132 ms. At cycle length 225 ms the DI was 87 ms. (D) Constant BCL Restitution Curve (Otani and Gilmour, 1997). For clarity, the AP with the shortest DI in (D) is not shown in (A–C). These simulations have been carried out with a single z-disc.
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Figure 10: Restitution properties with the (Walker et al., 2014)-RyR model. (A) Membrane potential. (B) Average cytosolic [Ca2+]i]. (C) Average cytosolic as defined in Equation (20). Solid line: basic cycle length (BCL) = 350 ms; dashed line: BCL = 300 ms; dotted line: BCL = 250 ms. At cycle length 350 ms the DI was 177 ms. At cycle length 300 ms the DI was 132 ms. At cycle length 225 ms the DI was 87 ms. (D) Constant BCL Restitution Curve (Otani and Gilmour, 1997). For clarity, the AP with the shortest DI in (D) is not shown in (A–C). These simulations have been carried out with a single z-disc.

Mentions: We explored the use of three RyR models which all produce realistic action potentials (Figure 9). When using the (Stern et al., 1999) model there were slow kinetics of Ca2+ release and a low RyR maximum open percentage (2.7%). Gain (the ratio of Jrel to JCa) was ~4 during the first 50 ms of the AP and ~3 for the remainder of the AP (AP duration = 265 ms, basic cycle length BCL = 350 ms). With the (Cannell et al., 2013) model many RyRs open and close (spark-like) within 20 ms of the start of the AP, and gain was high in this early phase of the AP (~10) and moderate in the later AP (~6) and there was a corresponding fast rise in the [Ca2+]i with an early peak at ~10 ms, followed by a reduction of [Ca2+]i and a second [Ca2+]i rise and fall through the AP. With the (Walker et al., 2014) model gain was ~6 in the early AP, then ~2 in the remainder of the AP, and there was a relatively high RyR maximum open percentage (32%). The (Cannell et al., 2013; Walker et al., 2014) 2-state RyR-schemes have markedly faster (and more physiological) kinetics of Ca2+ release than the (Stern et al., 1999) 4-state scheme. With the (Walker et al., 2014)-RyR scheme our model displays expected restitution properties with shorter APD and [Ca2+]i transient with shorter BCL (Figure 10).


A multiscale computational model of spatially resolved calcium cycling in cardiac myocytes: from detailed cleft dynamics to the whole cell concentration profiles.

Vierheller J, Neubert W, Falcke M, Gilbert SH, Chamakuri N - Front Physiol (2015)

Restitution properties with the (Walker et al., 2014)-RyR model. (A) Membrane potential. (B) Average cytosolic [Ca2+]i]. (C) Average cytosolic  as defined in Equation (20). Solid line: basic cycle length (BCL) = 350 ms; dashed line: BCL = 300 ms; dotted line: BCL = 250 ms. At cycle length 350 ms the DI was 177 ms. At cycle length 300 ms the DI was 132 ms. At cycle length 225 ms the DI was 87 ms. (D) Constant BCL Restitution Curve (Otani and Gilmour, 1997). For clarity, the AP with the shortest DI in (D) is not shown in (A–C). These simulations have been carried out with a single z-disc.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4585174&req=5

Figure 10: Restitution properties with the (Walker et al., 2014)-RyR model. (A) Membrane potential. (B) Average cytosolic [Ca2+]i]. (C) Average cytosolic as defined in Equation (20). Solid line: basic cycle length (BCL) = 350 ms; dashed line: BCL = 300 ms; dotted line: BCL = 250 ms. At cycle length 350 ms the DI was 177 ms. At cycle length 300 ms the DI was 132 ms. At cycle length 225 ms the DI was 87 ms. (D) Constant BCL Restitution Curve (Otani and Gilmour, 1997). For clarity, the AP with the shortest DI in (D) is not shown in (A–C). These simulations have been carried out with a single z-disc.
Mentions: We explored the use of three RyR models which all produce realistic action potentials (Figure 9). When using the (Stern et al., 1999) model there were slow kinetics of Ca2+ release and a low RyR maximum open percentage (2.7%). Gain (the ratio of Jrel to JCa) was ~4 during the first 50 ms of the AP and ~3 for the remainder of the AP (AP duration = 265 ms, basic cycle length BCL = 350 ms). With the (Cannell et al., 2013) model many RyRs open and close (spark-like) within 20 ms of the start of the AP, and gain was high in this early phase of the AP (~10) and moderate in the later AP (~6) and there was a corresponding fast rise in the [Ca2+]i with an early peak at ~10 ms, followed by a reduction of [Ca2+]i and a second [Ca2+]i rise and fall through the AP. With the (Walker et al., 2014) model gain was ~6 in the early AP, then ~2 in the remainder of the AP, and there was a relatively high RyR maximum open percentage (32%). The (Cannell et al., 2013; Walker et al., 2014) 2-state RyR-schemes have markedly faster (and more physiological) kinetics of Ca2+ release than the (Stern et al., 1999) 4-state scheme. With the (Walker et al., 2014)-RyR scheme our model displays expected restitution properties with shorter APD and [Ca2+]i transient with shorter BCL (Figure 10).

Bottom Line: Mathematical modeling of excitation-contraction coupling (ECC) in ventricular cardiac myocytes is a multiscale problem, and it is therefore difficult to develop spatially detailed simulation tools.Our concept for a multiscale mathematical model of Ca(2+) -induced Ca(2+) release (CICR) and whole cardiomyocyte electrophysiology incorporates stochastic simulation of individual LC- and RyR-channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca(2+) and Ca(2+)-binding molecules in the bulk of the cell.We developed a novel computational approach to resolve the concentration gradients from dyadic space to cell level by using a quasistatic approximation within the dyad and finite element methods for integrating the partial differential equations.

View Article: PubMed Central - PubMed

Affiliation: Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine Berlin, Germany.

ABSTRACT
Mathematical modeling of excitation-contraction coupling (ECC) in ventricular cardiac myocytes is a multiscale problem, and it is therefore difficult to develop spatially detailed simulation tools. ECC involves gradients on the length scale of 100 nm in dyadic spaces and concentration profiles along the 100 μm of the whole cell, as well as the sub-millisecond time scale of local concentration changes and the change of lumenal Ca(2+) content within tens of seconds. Our concept for a multiscale mathematical model of Ca(2+) -induced Ca(2+) release (CICR) and whole cardiomyocyte electrophysiology incorporates stochastic simulation of individual LC- and RyR-channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca(2+) and Ca(2+)-binding molecules in the bulk of the cell. We developed a novel computational approach to resolve the concentration gradients from dyadic space to cell level by using a quasistatic approximation within the dyad and finite element methods for integrating the partial differential equations. We show whole cell Ca(2+)-concentration profiles using three previously published RyR-channel Markov schemes.

No MeSH data available.


Related in: MedlinePlus