Figure 1.
Scheme of model of the compartmentalized creatine kinase system.
Main elements are ATP hydrolysis by ATPase, ATP synthesis by mitochondria and creatine kinase (CK) isoforms in the mitochondrial intermembrane space (Mi-CK) and cytosol (MM-CK). Oxidative phosphorylation (OxPhos) takes place in the mitochondrial matrix and responds to ADP and inorganic phosphate (Pi) levels in the mitochondrial intermembrane space. The concentrations of phosphocreatine (PCr), creatine (Cr), ADP, ATP and Pi are dependent on the rates of the enzyme reactions and transport. The figure was generated with CellDesigner [57].
Table 1.
Parameters of the CK model.
Figure 2.
Fit by the model of measured response times to heart rate steps.
The response times of oxidative phosphorylation (tmito) were measured in isolated rabbit hearts [9]. Model parameters were estimated using a modified Levenberg-Marquardt algorithm. Red bars represent the tmito values from the experiment, yellow bars represent the tmito values predicted by the model after the fitting procedure. Data is available for six different conditions: three different amplitudes of heart rate jump (from 135 bpm to 160, 190 and 220 bpm heart rate), each one measured with full wildtype CK activity (100%) or with CK activity inhibited to 2% of wildtype value. The error bars reflect the standard error of the measurements and the standard deviation of the tmito values in the ensemble, respectively.
Figure 3.
Distributions of individual parameters in the ensemble generated by the Metropolis-Hastings algorithm.
Plots show histograms of all values in the ensemble for the given parameter. The ensemble consists of 658 parameter sets. Plotted in red is the probability density function of the lognormal distribution with mean and standard deviation of each parameter scaled to the observed frequencies.
Figure 4.
Prediction of energy transport from mitochondria to cytosol by PCr.
(A) Forcing function of pulsatile cytosolic ATP hydrolysis for the last two cardiac cycles of a simulation over 60 s. (B) Prediction of the relative PCr contribution to high-energy phosphate flux across the mitochondrial outer membrane (Rdiff,PCr) at heart rate 220 bpm. The shaded region gives the central 95% confidence interval of the Rdiff,PCr trajectories derived from ensemble simulations of 658 parameter sets. Solid lines depict a single simulation of the best scoring parameter set. Blue color indicates the condition with CK active. Simulations with CK inhibited by 98% by IA are plotted in orange. Note that two cardiac cycles are plotted after a steady state was reached.
Figure 5.
Dependence of PCr diffusion flux on heart rate and mitochondrial membrane permeability to adenine nucleotides.
Prediction of the PCr contribution to high-energy phosphate flux across the mitochondrial outer membrane (Rdiff,PCr), averaged over the cardiac cycle, as a function of (A) heart rate and (B) mitochondrial outer membrane permeability for adenine nucleotides (PSmom,AdN), respectively. Values for (A) Steady state values for Rdiff,PCr as a function of heart rate (B) Steady state values for Rdiff,PCr as a function of PSmom,AdN at fixed heart rate of 220 bpm. We performed simulations for the ensemble of Figure 3, with the heart rate or PSmom,AdN set according to the x-axis. Blue shaded regions depict the 95% confidence interval of the prediction, black solid lines show the prediction for the optimized parameters (see Table 1).
Figure 6.
Fluctuations of metabolite concentrations and fluxes during the cardiac cycle at three levels of CK activity.
Plots show (A–C) Trajectory of the forcing function of ATP hydrolysis and ensemble predictions of (D–F) Rdiff,PCr, (G–I) mitochondrial ATP synthesis rate, (J–L) cytosolic ADP and (M–O) cytosolic Pi concentrations at heart rate 220 bpm. Mi-CK and MM-CK activities were set to 2, 100, and 300% of wildtype levels. Three cardiac cycles are shown at steady state. Solid lines show the simulated trajectory of the optimized parameter set (see Table 1). Shaded regions show the 95% confidence interval for all trajectories of the ensemble of 658 parameter sets. To alter CK activity, the parameters describing maximum enzyme velocity, Vmax,Mif and Vmax,MMf, are changed in parallel to the indicated percentage.
Figure 7.
Ensemble predictions of metabolite concentration and flux oscillations during the cardiac cycle for selective CK isoform inhibition.
In the first row (panels A–D), the pulsatile forcing function for ATP hydrolysis is plotted. Predictions of the time courses of (E–H) relative contribution of PCr to high-energy phosphate transport, Rdiff,PCr, (I–L) ATP synthesis rate, (M–P) cytosolic ADP and (Q–T) Pi concentrations. Heart rate is 220 bpm. In the four columns we compare: no CK inhibition, 98% Mi-CK inhibition, 98% MM-CK, or both CK enzyme reactions inhibited by 98%. Black solid lines show the simulated trajectory of the optimized parameter set (Table 1). Blue shaded regions show the 95% central confidence interval for all trajectories of the ensemble of 658 parameter sets. To alter CK activity, the parameters describing maximum enzyme velocity, Vmax,Mif and Vmax,MMf, are changed to the indicated percentage. Three cardiac cycles are shown after a steady state was reached. Note that the first and the last column also appear in Figure 6 and are shown here for ease of comparison.
Figure 8.
Pulsatile nature of energy production and consumption in the beating heart and the response to a step in heart rate.
Shown are the time courses of (A) ATP hydrolysis and (B) synthesis simulated with the model of Figure 1. At time 0 s, average ATP hydrolysis rate was increased from 486.5 to 627.6 µM*s−1 corresponding to an increase in heart rate from 135 to 220 bpm, as was imposed in the experiments which were simulated in this study. Please note the difference in scale of the y-axis between panels A and B.