The first step involves transfer of an amidine group from arginine to glycine by the enzyme glycine transaminidase. The resulting guanidinoacetic acid is methylated via guanidinoacetate methyltransferase with the methyl group coming from S-adenosylmethionine to form creatine.
Dietary creatine is transported from the gastrointestinal tract to the appropriate storage tissues as well. The degradation of creatine is of particular clinical interest.
The only end product of creatine degradation is creatinine, which diffuses into the bloodstream from the muscle. Upon entry into the renal parenchyma, creatinine is filtered in the glomerulus and excreted in the urine. Therefore, the clinician must be weary when interpreting the basic metabolic panel from an individual with large amounts of muscle mass, or in patients supplementing their diets with creatine.
Such patients will exhibit elevated creatinine levels in the blood, and therefore, their blood creatinine levels may not be accurate indicators of renal function. The methods of dietary creatinine delivery i. Risks of Creatine Supplementation:. As noted earlier, elevations of plasma creatinine found in patients who supplement their diets with creatine are not indicative of renal function.
Therefore, it is not appropriate to rely on creatinine levels in such patients for diagnosis of renal failure. On a positive note, some studies have failed to report changes in serum markers of hepatorenal function following chronic creatinine supplementation 3,4.
More information regarding the risks of creatine supplementation will follow in subsequent publications. Greenhaff, PL. The nutritional biochemistry of creatine. Nutritional Biochemistry The fate of creatine when administered to man. Influence of chronic creatine supplementation on hepatorenal function. Almada, A.. Mitchell, T. Impact of chronic creatine supplementation on serum enzyme concentrations.
Resistance Training. Cardiovascular Fitness. Men's Fitness. Women's Fitness. Mental Health. Questions or Concerns. University of Michigan. University of Michigan Health System. University of Michigan Medical School. Creatine basics: Creatine, or methyl guanidine-acetic acid, is an endogenously formed made within the organism during natural metabolic processes molecule that is stored largely in skeletal muscle, in both free and phosphorylated forms.
Creatine biochemistry: The majority of in vivo creatine synthesis takes place in the liver. To investigate whether processes inside the mitochondria delay the response further, we tested a model of the mitochondrial matrix including metabolite transport across the inner mitochondrial membrane with instananeous step changes in ADP or P i and also with ADP and P i simultaneously outside the inner mitochondrial membrane.
This corresponds to the model applied in Text S2 with all processes outside the inner mitochondrial membrane removed and the ADP and P i concentrations outside the inner mitochondrial membrane set as forcing function.
The response time, calculated as for t mito , was 0. For a simultaneous change in ADP and P i the mitochondrial response was essentially complete within half a second, with a response time of 0. It was shown with radioactively labeled phosphate groups that if the concentration of ATP in the environment of the mitochondria is larger than 0. This is incompatible with a model where a major part of PCr is synthesized from ATP directly transferred to creatine kinase via a very small compartment with limited exchange with its environment.
By in silico analysis, we inferred distinct roles for the mitochondrial and myofibrillar creatine kinase enzymes. MM-CK is mainly responsible for damping large swings in metabolite concentrations and large oscillations in the rate of oxidative phosphorylation which would otherwise be caused by the large peaks of ATP hydrolysis during the cardiac cycle.
Mi-CK restricts high concentrations of inorganic phosphate, which is surprising considering that inorganic phosphate is not handled directly by CK. The effect of the CK isoforms on the buffering of ADP oscillations and the prevention of high concentrations of inorganic phosphate may play a role in the prevention of formation of reactive oxygen species ROS.
ROS production highly depends on the mitochondrial membrane potential, which is increased at low ADP levels [38] , [39]. The electric membrane potential in mitochondria can also be altered by inorganic phosphate, leading to enhanced ROS release [40].
A protective role of Mi-CK against oxygen radical formation by preventing high inorganic phosphate concentrations is also predicted by our model. A function of Mi-CK to prevent oxygen radical formation has been found experimentally in isolated brain mitochondria [38].
The energy buffering role of the CK system has been linked to the prevention of oxidative stress in neurons [41] , [42]. Creatine supplements to nutrition have also been shown to have a neuroprotective effect in models of Huntington's disease [43] , [44]. The effects of creatine as a nutritional supplement in health and disease have recently been reviewed by Wallimann et al.
The sloppy modeling approach enables to make useful predictions of CK system behavior despite limited experimental input data and limited knowledge of kinetic parameters. The concept of sloppy modeling can also be used to find optimal experimental designs to further test the model [46]. We also demonstrated that combining a computational model analysis with experimental data on the level of cellular organelles and isolated enzymes and with the response of the heart as a whole provides a powerful combination that gives valuable insights in the functional roles of CK, such as regulation of oxidative phosphorylation, energy transport, inorganic phosphate levels and buffering of peaks of ATP hydrolysis at the millisecond time scale.
For our analysis, we employed a previously published computational model [18]. It is available in various formats and can be found in the BioModels database [47] as well as in the CellML model repository [48].
These equations were extensively described previously [18]. Model dynamics depend on 22 kinetic parameters retrieved from the literature which are listed in Table 1. In general the kinetic constants retrieved from the literature have relatively modest standard errors. This large variation is possibly due to mitochondrial isolation or cell membrane permeabilization procedures. The mitochondrial outer membrane permeability-surface product parameter PS mom,AdN influences the response time for dynamic adaptation of oxidative phosphorylation strongly.
Therefore the dynamic measurements of venous oxygen outflow in the heart as a whole in response to an increase of heart rate allow estimating the mitochondrial membrane permeability at the organellar level.
The whole heart measurements were corrected for oxygen transport delay to reflect events at the level of the mitochondria see below. The mitochondrial response time t mito is defined as the generalized time constant of the time-course of oxygen consumption defined to be equivalent to the first central statistical moment of the impulse response function in case the system is linear , previously described in [18] , [50] - [52].
From a model simulation, t mito is calculated as follows: 3. In order to investigate the damping capabilities of the modeled system, ATP hydrolysis is simulated as a pulsatile function representing the alternating nature of energy demand in systole and diastole as described in [18].
Figure 8 shows the dynamic response of mitochondrial ATP production in response to a step in heart rate and ATP hydrolysis. At time 0 s, average ATP hydrolysis rate was increased from Please note the difference in scale of the y-axis between panels A and B. Almost all models in systems biology contain parameters that cannot be determined precisely.
It is common practice to estimate missing parameter values by a parameter fit to experimental data. After the fit, one can make model predictions and analyze the underlying biological processes. This, however, is dangerous because a range of parameter combinations may agree with the available data equally well, potentially leading to deviating model predictions of new experimental situations. Sloppy parameter sensitivity spectra have been identified for numerous biological models by the analysis of the eigenvectors and eigenvalues of a sensitivity matrix calculated from the chi-square cost function [22].
Sloppy models exhibit a characteristic pattern with the logarithms of eigenvalues approximately uniformly distributed over a large range. Since our model shows sloppy parameter sensitivities and is based on data subject to experimental variation, drawing predictions from an ensemble of parameter sets is preferable to merely relying on one parameter set fit to experimental data. According to the sloppy modeling paradigm [21] , [22] , the probability of a set of model parameters to be included in the ensemble is proportional to its likelihood to describe given experiment data multiplied by the likelihood of prior experimental information about the parameter values themselves.
The sampling process is thus based on Bayesian inference of a posterior distribution of parameter sets , where is the likelihood of the data given a parameter set, is the prior probability of the parameter set based on experimental prior knowledge on single parameter values and the posterior is the probability of a parameter set to describe the given experimental data. The Sloppy cell software environment, used for the analysis, was adapted to process all operators which were in the SBML file describing the model.
The modified version is provided in Dataset S1. Measured values of molecular model parameters and their provenance, extracted from the scientific literature, are listed in Table 1. For nine of the 22 parameters reliable standard measurement errors could be found. In addition to the direct measurements on molecular parameters, we employ t mito values from a study by Harrison et al. Isolated hearts were perfused with Tyrode's solution containing among others glucose and pyruvate to provide substrates for energy metabolism.
In order to provide a sufficient amount of reducing equivalents to fuel aerobic respiration despite the inhibition of glycolysis, the buffer also contained pyruvate. Adenosine was added to the Tyrode buffer to ensure that oxygen supply is non-limiting when oxygen consumption is recorded.
The whole heart measurements were corrected for the O 2 transport time in the coronary vessels based on a model of oxygen transport by convection in blood vessels and diffusion through tissue. The t mito therefore reflects the response time at the level of the mitochondria cf. The mean response time was also corrected for a small deviation from an ideal step in beat-to-beat ATP hydrolysis measured as an initial overshoot in rate-pressure product [50]. For each condition, steps in heart rate were imposed from to , and beats per minute, respectively, using electrical pacing.
Note that glycolysis is always inactive when the dynamic response is measured, which corresponds to the absence of glycolysis in the computational model.
This approach made it possible to isolate the contribution of the CK system from the contribution of glycolysis, which removes substantial complexity from the model analysis. A step in ATP hydrolysis from From these values, we linearly interpolated hydrolysis rates of To simulate CK inhibition by IA the model parameters for the maximum velocities of both enzyme reactions were set to 2.
Note that the enzyme activities, the mitochondrial capacities and the whole organ dynamic response times were all measured in the same experimental model by the same laboratory. Model parameters are fitted to experimental data using a modified Levenberg-Marquardt least-squares procedure in logarithmic parameter space, which is part of the SloppyCell modeling environment.
For our model and data we calculate the cost for a given parameter set as follows: 4 with y c being the model prediction of t mito Eq. The first term of the cost function takes into account the experimental data on the whole heart level, whereas the second term represents prior experimental information about parameter values found in the literature or measured in conjunction with the modeled experiments.
Note how the prior is used to enter experimentally measured information on parameters measured at the molecular level in the second term of Eq. The deviations of the predicted response times from their measured values are penalized relative to their measured standard errors and the deviation of the molecular parameters from measured values are penalized relative to their reported standard errors.
Values for molecular parameters reported in the literature are usually given as mean and standard error. However, in the sloppy modeling framework, it is preferable to choose a normal distribution in log space [20] , [22] , [54]. A Gaussian distribution of logarithmic parameters has been proposed to be biologically plausible [55]. This forms a convenient way to deal with dimensionless positive quantities as parameter values [56].
If the standard error is small relative to the mean of the parameter, the shapes of the prior distributions become approximately normal see Figure 3.
Since standard errors for only nine of all 22 system parameters could be found, we chose the default value for the remaining parameters to be at the maximum of all values for parameters with known error. This maximum was the error of the parameter for the binary dissociation constant for creatine from Mi-CK K ib,Mi , and see Table 1.
In order to investigate the effect of altered default prior standard deviation on posterior parameter distributions and ensemble predictions, we performed several additional ensemble simulations with lower and higher default values.
Results of these simulations can be found in Text S1. The parameter describing MOM conductance for adenine nucleotides, PS mom,AdN , could not be reliably determined by experiments on the organellar level and was therefore not constrained by a prior.
A first estimate of parameter values was determined by a least-squares fit to the data, using the cost function of equation 4. This initial best parameter estimate resulting from the optimization is used as the starting point for a walk through the parameter space using the Metropolis-Hastings algorithm.
Starting the random walk from the optimized set of parameters made the algorithm converge more quickly to the posterior distribution. We use the algorithm's implementation in SloppyCell to sample parameter sets with probability density proportional to. All scripts to reproduce the presented calculations can be found in Dataset S2. The correlation time of a parameter is defined as the time constant of its autocorrelation function. For our model, taking steps in the random walk is sufficient to obtain more than independent parameter sets.
The independent parameter sets in the ensemble provide the final estimate of the parameters, not only characterized by a mean but also by a standard deviation which reflects the spread of the estimation. For computational performance reasons, we calculated model simulations for parameter estimation and ensemble sampling with an ATP hydrolysis rate averaged over the cardiac cycle rather than the pulsatile pattern shown in Figure 8.
This reduced the time needed for calculations tremendously, making it feasible to do the ensemble calculations in several hours.
However, to investigate the damping characteristics of the system, we use a pulsatile forcing function of ATP hydrolysis see Figure 8A [18]. To assess the differences in metabolite levels and fluxes caused by replacing the pulsatile function with a time-averaged continuous function, parameter sets were randomly drawn from all parameter sets tried in the Monte-Carlo random walk, to compare the values of model results between pulsatile and nonpulsatile simulations.
The variables most affected by the pulsatile approximation are R diff,PCr and t mito. The difference between pulsatile vs. The difference between pulsatile and non-pulsatile model results for other variables is below 4. Patched SloppyCell Python library. This additional dataset consists of a patched version of the SloppyCell Python library, version 0.
The package is provided as a zip file. Detailed installation instructions can be found in the zip file. Model files and Python code. This zip file contains the model in SBML format and all Python scripts necessary to reproduce the results in this study. Ensemble predictions with different default prior standard deviations. This supplemental text reports the results of our analysis procedure when smaller or larger default prior standard deviations for parameters with unknown standard error are assumed.
Model analysis with additional microcompartment which couples CK to the adenine nucleotide translocator. In this supplemental text we present the results of the analysis of a computational model which implements substrate channeling between Mi-CK and ANT in a microcompartment, integrated with the data on mitochondrial response times used in this study.
We are very grateful to Ryan Gutenkunst for excellent advice on using the SloppyCell modeling environment and to Bernd Brandt for scientific advice and help with the computer cluster. We also thank Jaap Heringa for suggestions and comments on the manuscript.
Performed the experiments: HH. Author Summary Creatine kinase CK has several functions in cellular energy metabolism. Introduction It is well established that creatine kinase CK catalyzes the reversible transfer of phosphate from ATP to creatine Cr : 1 However, how this biochemical function plays a role in cell functioning has been the subject of intense controversy [1].
Download: PPT. Figure 1. Scheme of model of the compartmentalized creatine kinase system. Results We employed experimental data from three scales: molecular kinetic parameters, organellar capacity parameters and whole organ dynamic response data.
Figure 2. Fit by the model of measured response times to heart rate steps. Parameter estimation Model parameters were estimated simultaneously to fit the t mito values for all conditions using a least-squares optimization procedure.
Monte Carlo sampling of parameter sets Starting from the optimized parameter set see Table 1 , we sampled the parameter space to generate an ensemble of independent parameter sets using the Metropolis-Hastings algorithm. Figure 3. Distributions of individual parameters in the ensemble generated by the Metropolis-Hastings algorithm. Figure 4. Prediction of energy transport from mitochondria to cytosol by PCr.
Figure 5. Dependence of PCr diffusion flux on heart rate and mitochondrial membrane permeability to adenine nucleotides. Prediction of temporal energy buffering The results described above indicate that direct ATP transport is predominant in working heart muscle.
Figure 6. Fluctuations of metabolite concentrations and fluxes during the cardiac cycle at three levels of CK activity. The specific role of the mitochondrial CK isoform Transport of HEP by PCr from mitochondria to cytosol partially takes place via the circuit formed by both CK isoforms, but was predicted to be quantitatively not very important. Figure 7. Ensemble predictions of metabolite concentration and flux oscillations during the cardiac cycle for selective CK isoform inhibition.
Discussion The relative importance of the different roles of the CK system in myocytes is still hotly debated [4]. Methods Computational model For our analysis, we employed a previously published computational model [18].
Figure 8. Pulsatile nature of energy production and consumption in the beating heart and the response to a step in heart rate. Sloppy ensemble modeling Almost all models in systems biology contain parameters that cannot be determined precisely. Experimental data Measured values of molecular model parameters and their provenance, extracted from the scientific literature, are listed in Table 1.
Cost function Model parameters are fitted to experimental data using a modified Levenberg-Marquardt least-squares procedure in logarithmic parameter space, which is part of the SloppyCell modeling environment. Determining prediction uncertainty: Ensemble simulations A first estimate of parameter values was determined by a least-squares fit to the data, using the cost function of equation 4. Supporting Information.
Dataset S1. Dataset S2. Text S1. Text S2. Acknowledgments We are very grateful to Ryan Gutenkunst for excellent advice on using the SloppyCell modeling environment and to Bernd Brandt for scientific advice and help with the computer cluster.
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