The authors have declared that no competing interests exist.
Conceived and designed the experiments: MV. Performed the experiments: DWS PP. Analyzed the data: DWS MV. Contributed reagents/materials/analysis tools: DWS PP. Wrote the paper: DWS PP AI MV.
To characterize intracellular energy transfer in the heart, two organlevel methods have frequently been employed:
In heart, the movement of energy metabolites between forceproducing myosin, other ATPases, and mitochondria is vital for its function and closely related to heart pathologies. In addition to diffusion, transport of ATP, ADP, Pi, and phosphocreatine occurs along parallel pathways such as the adenylate kinase and creatine kinase shuttles. Two organlevel methods have been developed to study the relative flux through these pathways. However, their results differ. It was recently demonstrated that
In heart, the mechanisms that ensure energy production meets demand over a wide range of workloads, remains unclear. Fundamental to this search is an accurate understanding of the recycling fluxes of ATP, ADP, Pi, and phosphocreatine (PCr) between the mitochondrial inner membrane space and the ATPases on both the myofibrils and sarcoplasmic reticulum. In highly compartmentalized environments, such as heart muscle
There are several complications that have to be considered when interpreting magnetization transfer experiments. As summarized recently
Dynamic
CK fluxes are taken from Vendelin et al.
The incorporation of
The
The aim of this work is to analyze the properties of
An integrated kinetic model was constructed to account for all isotope transformations that occur in the highenergy phosphotransfer network reactions in heart (
Prior to conducting the sensitivity analysis a number of model validation steps were performed. First, we tested if the steady state labeling distribution predicted by the model matches the theoretical distribution provided by Dawis et al.
All labeled species are plotted separately with the number of attached
Additionally, it is important to ensure that the model we constructed is able to provide predictions that adequately match published dynamic
The fluxes used to simulate the labeling state plotted here correspond to flux distribution 1 from
Flux distribution  Percentage of energy export  Bidirectional fluxes  
AdK  ATP  CK  CK  AdK  
shuttle  diffusion  shuttle  shuttle  shuttle  
1 
5  45  50 


2  5  45  50 


3  5  45  50 


4 
5  45  50 


5 
5  45  50  
6  0  50  50 


7  0  0  100 


8  5  0  95 


9  5  95  0 


Relatively high total AdK flux, taken from
Unidirectionality leads to low total AdK flux.
Following model validation, we performed a sensitivity scan of the model parameters. The most sensitive parameters were found to be the ATP synthase rate as well as the net and exchange fluxes through the AdK shuttle.
Keeping the cardiac performance constant and using net fluxes from flux distribution 1 within
Subplot A shows the labeling state predicted using flux distribution 1 within
Referring to
The main application of dynamic
In total, nine flux distributions were studied. These flux distributions were selected to test the labeling sensitivity to the changes of specific fluxes, as explained below. General descriptions of these are provided in
There are several specific questions that are of interest when studying the flux distributions. First, what is the magnitude of the fluxes? In terms of dynamic
Another question of interest is: Do net flux and bidirectional enzyme activity have different influences on the labeling state? Comparing flux distributions 2 and 6, as well as 7 and 8, allows one to test if the labeling state is determined by net AdK flux, or bidirectional AdK enzyme activity. Note that in those pairs of the flux distributions, the net flux of AdK shuttle changes.
Finally, how does the labeling state change when the net transport of energetic phosphoryl groups occurs via the CK shuttle, or direct ATP transport? Insight into this important question could be provided by comparing flux distributions 2, 8, and 9.
Additional combinations of these flux distributions allow for additional comparisons. Transient solutions for these nine flux distributions after a step to 30%
To compare the different influence of bidirectional and net fluxes we introduce two total fluxes, one each for AdK and CK. The total flux through CK is the sum of unidirectional reactions in the mitochondrial intermembrane space (IMS) and cytosol that proceed towards PCr, and the total AdK flux is the sum of unidirectional AdK reactions in the IMS and cytosol that proceed towards ADP. To perform the comparison between fluxes, in our analysis, the total flux is increased by simultaneously increasing the forward and reverse flux in one or both compartmental locations (Method
Excluding
Different flux distributions (see
Because the metabolic system given in
To explore how the two coupled CK fluxes influence the labeling state, a plot (
Different flux distributions (see
Keeping total and net AdK flux constant as well as total CK flux constant, the percentage of energy exported via direct ATP transfer was varied from zero (maximum net flux through the CK shuttle) to its maximum possible value (zero net flux through the CK shuttle). The labeling states of flux distributions 1, 2, 4, and 7 were plotted during this change in
Flux distributions 1, 2, 4, and 7 have constant total and net AdK flux as well as total CK flux over the range of the plot. Flux distributions 3 and 5 have unidirectional CK flux, and thus the total CK flux varies over the range of the plot. The sensitivity displayed by these two flux distributions results from the change in total CK flux and not CK export ratio. Looking at the other four flux distributions, subplot (A) shows that the export of energy via direct ATP export or the CK shuttle has a minor influence on the labeling state. Subplot (B) shows that the change in export ratio provides a small change in labeling state but cannot be considered a sensitive parameter. Line colors indicate the flux distribution, while the symbols indicate the number of
For illustration, two additional flux distributions (3 and 5) with unidirectional CK fluxes are plotted on
To illustrate the properties of the pseudolinear approximation method, used to determine the CK flux in
The total PCr oxygen labeling at 30s after a step change to 30%
The main result of this work is that measuring the dynamic incorporation of
Looking at the sensitivity plots in
Observation (II) does not support the suggestion that the
Observation (III) limits the use of the
With regards to observation (IV), we note that the use of 100%
Taken together, these observations lead to the conclusion that labeling with
The integrated kinetic model presented in this work was constructed to account for the most rapid isotope transformations that occur in the highenergy phosphotransfer reaction network in heart. As a first step in our analysis, a number of tests were conducted to determine if this model is suitable for the analysis of published dynamic
A number of simplifying assumptions were made to construct the model we present in this work. It is explicitly assumed that all metabolic fluxes proceed at a steady metabolic rate. In addition, we do not employ enzyme kinetics in the flux simulations, although this is not seen as a trade off because the resulting model has fewer parameters and many of the enzymatic kinetic parameters are not well characterized. A number of phosphotransfer fluxes were excluded from the model. However, the dynamic
Unfortunately, the original
We produced these modeling results using a step change from
As an alternative approach to the analysis presented in this work, one could compose hypothetical data sets and find the confidence intervals of model parameters. This would give an estimate of the sensitivity of the labeling method. Regardless of the approach used, we expect the conclusions to be the same. The approach used in this work was tailored towards comparison of different flux distributions to see whether the different energy transfer mechanisms proposed in the literature can be distinguished on the basis of
Without going through the published data presented in all dynamic
Importantly, our modeling results resolve all known discrepancies between the results of the dynamic
It has been shown that information regarding the compartmentation of metabolites and the bidirectional nature of metabolic fluxes is contained in the dynamic component of labeling data
For the phosphotransfer network in the heart, sampling at an earlier time, in addition to 30 seconds, would enhance the sensitivity of the method. Adding an additional sampling point at a longer time during the approach to isotopic equilibrium would provide a better means to extract pool size information from the isotopic transient. However, the dynamic
In
While our results show that dynamic
Our results widen the discussion that attempts to reveal the mechanisms that ensure the homeostasis of metabolites during cardiac function (or not)
The metabolic network in
Because the model developed in this work tracks the transient exchange of each oxygen atom in the phosphotransfer network with the surrounding water environment, it is necessary to know how each oxygen atom transfers during the course of each reaction. It is known that exchange of phosphate oxygens with those of water does not occur in glycolysis
The model was constructed by: (I) generating the full set of individual isotopic transformations, (II) combining these transformations into a mass balance around each isotopologue in the system, (III) composing mass isotopologue pool relations while taking into account oxygen atom mappings, and (IV) composing mass isotopologue balances by collecting the isotopologue balances according to the pool relations. The result is a system of 132 ordinary differential equations (ODEs). The intermediate equations for all of these steps are provided in supporting
The 18 metabolic pools are assumed to be constant during the labeling processes. Pool size measurements for total ATP, PCr, and Pi were taken from Vendelin et al. for activation by Ca 1.8 mM
The 20 net flux variables in the model are constrained to metabolic steady state by three independent net flux variables. We chose these to be the net rate of ATP synthase, the net flux of ATP between the IMS and the cytosol, and the net flux of PCr between the IMS and the cytosol. A set of 17 relations between these and all other net flux variables was found using a method we recently developed
The citric acid cycle flux is reported by Des Rosier et al. to be between 0.1 and 4
To solve the system of ODEs we used a variablecoefficient ODE solver with the Backward Differentiation Formula method
Dynamic simulation of the
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Additional time slices for
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Influence of compartmental location of AdK flux on the labeling state at 30 s after a step change to 30%
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Additional time slices for
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Additional time slices for
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Change in labeling state with increasing energy export via AdK at 30 s after a step change to 30%
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Flux distributions used in
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Parameter ranges used to construct
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Derivation of the model equations with all intermediate steps.
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