Constancy and variability of contractile efficiency as a function of calcium and cross-bridge kinetics: simulation
Geoffrey
Nunns
Auckland Bioengineering Institute, The University of Auckland
Model Status
This model is known to run in both OpenCell and COR. It recreates the published results for the simulation, except in the case of FTI_end, FLA_max and ATP, because CellML cannot compute finite integrals or maximums of functions. These values are instead estimated based on graphs, but must be re-estimated for different initial conditions. The parameters for this model are the control values.
Model Structure
Abstract: We simulated myocardial Ca2+ (Ca) and cross-bridge (CB) kinetics to get insight into the experimentally observed constancy and variability of cardiac contractile efficiency in generating total mechanical energy under various inotropic and pathological conditions. The simulation consisted of a Ca transient, Ca association and dissociation rate constants of troponin C, and CB on and off rate constants. We evaluated sarcomere isometric twitch contractions at a constant muscle length. We assumed that each CB cycle hydrolyzes one ATP and that the force-length area (FLA) quantifies the total mechanical energy generated by CB cycles in a twitch contraction. FLA is a linear version of pressure-volume area, which quantifies the total mechanical energy of cardiac twitch contraction and correlates linearly with cardiac oxygen consumption (H. Suga, Physiol. Rev. 70: 247-277, 1990). The simulation shows that the contractile efficiency varies with changes in the Ca transient and Ca and CB kinetics except when they simultaneously speed up or slow down proportionally. These results point to possible mechanisms underlying the constancy and variability of cardiac contractile efficiency.
The original paper reference is cited below:
Constancy and variability of contractile efficiency as a function of calcium and cross-bridge kinetics: simulation, Hiroki Yamaguchi, Miyako Takaki, Hiromi Matsubara, Shingo Yasuhara, and Hiroyuki Suga, 1996, American Journal of Physiology, 270, H1501-1508. PubMed ID: 8967394
model diagram
Schematic diagram showing the calcium kinetics between transient calcium (Ca2+), and troponin C (Tn), and cross bridge kinetics (CB).
$\mathrm{Ca\_t}=\begin{cases}\frac{\mathrm{Ca\_max}(1+\sin \left(\frac{\pi (\frac{t}{\mathrm{D\_Ca}}-0.15)}{0.3}\right))}{2} & \text{if $(t\ge 0)\land (t< 0.3\mathrm{D\_Ca})$}\\ \frac{\mathrm{Ca\_max}(1-\sin \left(\frac{\pi (\frac{t}{\mathrm{D\_Ca}}-0.65)}{0.7}\right))}{2} & \text{if $(t\ge 0.3\mathrm{D\_Ca})\land (t< \mathrm{D\_Ca})$}\\ 0 & \text{otherwise}\end{cases}$
$\frac{d \mathrm{TnCa}}{d t}=\mathrm{k\_1}\mathrm{Ca\_t}(\mathrm{Total\_Tn}-\mathrm{TnCa})-\mathrm{k\_2}\mathrm{TnCa}$
$\frac{d \mathrm{CB\_on}}{d t}=f\mathrm{TnCa}(\mathrm{Total\_CB}-\mathrm{CB\_on})-g\mathrm{CB\_on}$
$\frac{d \mathrm{CumCB\_on}}{d t}=f\mathrm{TnCa}(\mathrm{Total\_CB}-\mathrm{CB\_on})\frac{d \mathrm{CumCB\_off}}{d t}=g\mathrm{CB\_on}$
$F=\mathrm{CB\_on}\mathrm{phi}\frac{d \mathrm{FTI}}{d t}=F\mathrm{FLA}=\mathrm{F\_max}s(L-\mathrm{L\_0})$
$\mathrm{ATP}=\mathrm{CumCB\_on\_end}\mathrm{ATP\_energy}=\mathrm{ATP}\mathrm{epsilon}$
$\mathrm{Efficiency}=\frac{\mathrm{FLA}}{\mathrm{ATP\_energy}}\mathrm{Economy}=\frac{\mathrm{phi}}{\mathrm{epsilon}}\frac{1}{g}$
This model is known to run in both PCEnv and COR. It recreates the published results for the simulation, except in the case of FTI_end, FLA_max and ATP, because CellML cannot compute finite integrals or maximums of functions. These values are instead estimated based on graphs, but must be re-estimated for different initial conditions. The parameters for this model are the control values.
Shingo
Yasuhara
Geoff Nunns
1996-00-00 00:00
Hiroki
Yamaguchi
This model is known to run in both PCEnv and COR. It recreates the published results for the simulation, except in the case of FTI_end, FLA_max and ATP, because CellML cannot compute finite integrals or maximums of functions. These values are instead estimated based on graphs, but must be re-estimated for different initial conditions. The parameters for this model are the control values.
Geoff Nunns
Hiroyuki
Suga
Hiromi
Matsubara
Geoffrey
Nunns
Rogan
Miyako
Takaki
Geoffrey
Nunns
Rogan
This model is known to run in both PCEnv and COR. It recreates the published results for the simulation, except in the case of FTI_end, FLA_max and ATP, because CellML cannot compute finite integrals or maximums of functions. These values are instead estimated based on graphs, but must be re-estimated for different initial conditions. The parameters for this model are the control values.
Geoff Nunns
2008-06-26T00:00:00+00:00
0.5
2008-07-18T14:10:09+12:00
American Journal of Physiology
gnunns1@jhem.jhu.edu
keyword
calcium dynamics
myofilament mechanics
excitation-contraction coupling
Auckland Bioengineering Institute
CellML Team
8967394
Constancy and variability of contractile efficiency as a function of calcium and cross-bridge kinetics: simulation
270
H1501
H1508
Added cmeta ids to variables so that the model works with session files