Metabolic labelling pulse–chase experiments are important means to study molecular turnover rates. However, the inherent problem associated with the method is precursor re-utilization, which can cause a significant overestimation of the actual rates of molecular degradation. In published studies on mitochondrial degradation, this problem has led to widely differing results. Practically, the extra information required to correct these errors is not easy to obtain. Using an example of a mitochondrial protein degradation study with NaH14CO3 as the precursor label, we explain the limitations of the method and our approaches to mathematical correction. A dynamic model, including error, used the full power of the data and resulted in sensitive and specific distributed parameter estimates, helping to reduce numbers of experimental animals. This example has important implications not only for similar pulse–chase experiments, but also in a more general context where comparable types of data are generated.
- mathematical model
We are interested in mitochondrial turnover because replacing damaged mitochondria is an important potential quality control mechanism. Mitochondrial dysfunction and mitochondrial DNA damage accumulation have been implicated in the aging process as well as in pathological conditions [1,2]. Aging may slow down mitochondrial turnover, while stimulation of autophagy, the major degradation pathway in mitochondria, may enhance it. In fact, the latter has been proposed as a beneficial mechanism in DR (dietary restriction), an experimental manipulation that extends lifespan and delays the onset of age-related pathologies in a variety of organisms [3,4].
Across the existing literature on mitochondrial turnover, there is a wide range of estimated rates (half-lives ranging from a few days to more than a month) that are partly due to tissue-specific differences, but appear to be largely caused by methodological variation. In the present article, we discuss commonly used methods for measuring mitochondrial half-lives and the potential sources of these inconsistencies. Using our data set as an example, we describe the nature of methodology-related errors, their correction using a mathematical model and the difference it made to the results. This approach enabled us to use the full power of the data generated and is important for all similar experiments in which the numbers of experimental animals used are a concern.
The label re-utilization problem
The half-life of mitochondria is somewhat enigmatic and loosely defined. Mitochondria consist of at least a thousand different proteins, most of which are assembled within mitochondria from imported preproteins synthesized in the cytosol. Moreover, mitochondria exist not as separate units, but as a dynamic syncytium, defined by frequent fusion and fission events. Every part of this syncytium (‘one mitochondrion’) will thus contain proteins synthesized at different times, and this composition will change dynamically. Moreover, some of these proteins have very short half-lives (minutes to hours) (e.g. ). However, whole mitochondria are primarily degraded by macroautophagy . In other words, within the confines of a turnover study, ‘mitochondria’ are defined as the parts of the syncytium that are degraded as a unit.
Protein turnover rate can be determined by measuring either synthesis or degradation rates, as these two are balanced and are equal at steady state (for review, see [7,8]). However, measuring the rate of degradation of mitochondrial proteins is the most direct way to study the mitochondrial turnover rate in vivo. Typically, radioisotope pulse–chase methods with a selection of pre-labelled precursors are employed (but see ): labelled amino acid is injected into the animals, incorporated into proteins (‘pulse’ labelling) and the kinetics of disappearance of the label from isolated mitochondria is ‘chased’ over a number of days. If protein degradation gives rise to irreversible loss of label, the degradation curve follows a simple first-order decay model, from which the rate constant of decay kd and half-lives can be calculated.
Here, it is critically important to consider the fate of the precursor (pre-labelled amino acid) during the chase period. When labelled proteins are degraded, the labelled amino acid is released as a broken down product, and some of this can be re-incorporated into newly synthesized proteins, i.e. re-labelling new proteins. This is called the ‘re-utilization problem’, an inherent problem for most pulse–chase methods using metabolic labelling. The degradation curve becomes flattened with increasing observation time and fits poorly to a simple first-order decay model, and the apparent rate of degradation appears to be slower than the actual rate: thus the longer the chase period, the longer the estimated half-lives become.
In previous mitochondrial pulse–chase experiments, various amino acid precursors have been used, such as [35S]methionine, [3H]leucine, [14C]leucine and [14C]arginine, with different chase periods (Table 1, the studies on liver mitochondria). (N.B. Apart from amino acid precursors, [3H]δALA (aminolaevulinic acid) and [14C]δALA have been used to label haem proteins [9–11], and [32P]phosphorous [12,13] and [14C]acetate to label phospholipid in mitochondria .) Table 1 shows clearly that, in general, studies that used shorter chase periods resulted in shorter estimated half-lives for any given label. Thus many of the discrepancies in the literature are likely to be explained by the re-utilization problem and poor fitting of the data to the model. To correct the re-utilization problem, ideally, the precursor (concentration of the labelled amino acid, or more precisely, aminoacyl-tRNA) should be measured in parallel with the product (labelled protein) during the whole chase period (e.g. see ). However, the techniques involved are labourious and complicated, especially when samples are radioactive (and volatile in the case of 14C), and require considerable amounts of tissues (possibly requiring more animals).
Method of choice
Alternatively, certain precursors might limit the re-utilization problem to acceptable limits by fast and efficient turnover of the non-incorporated label. The NaH14CO3 method, originally described in , is thought to satisfy this requirement. When it is injected, 14C-labelled NaHCO3 is converted into arginine (labelled at the guanidine position, [6–14C]arginine) in liver by the urea cycle enzymes following a series of steps. The HCO3 pool is large, freely diffusible and turns over very fast , rapidly diminishing the free NaH14CO3 levels after a single injection. In the liver, the free arginine pool is small and labelled fast; it is either incorporated into proteins or, much more likely, cleaved to ornithine and urea by arginase, which is highly active in liver. The labelled carbon in the arginine becomes a part of urea, which is readily excreted from the tissue. This means that any labelled free arginine (i.e. protein turnover products) is readily decomposed and the labelled part removed from the system. The probability of re-utilization of labelled arginine derived from protein breakdown has been calculated to be as small as approx. 2% [17,18].
Additionally, because the urea cycle is highly active in liver, but essentially inactive elsewhere, NaH14CO3 results in very low labelling efficiency in all other tissues (as compared with the direct injection of [6–14C]arginine). This avoids re-utilization of labelled products derived from protein degradation in other tissues. The impact of this factor becomes immediately evident by comparing published half-lives of liver mitochondria estimated using NaH14CO3 to those labelled by [6–14C]arginine: the former method results in appreciably shorter half-lives than the latter (Table 1). Hence NaH14CO3 in metabolic labelling pulse–chase assays in liver has been hailed as ‘the precursor of choice’ [19,20].
The re-utilization problem remains even with NaH14CO3 labelling in liver
We attempted to measure mitochondrial turnover rates in mouse liver using the NaH14CO3 labelling method to analyse the effect of DR (see ). We fitted the data to a simple exponential decay model to calculate the rate constant of decay kd and half-lives assuming there is no significant re-utilization of the label. However, we observed that the estimated half-lives became longer with the inclusion of later time points in the calculation (Figure 1). We observed that our half-life estimates were very similar to published data using the same chase periods (see Table 1).
As the data did not follow a simple first-order decay, we fitted a double exponential model. This resulted in a satisfactorily stable fit (but see below), resulting in two populations with half-lives of approx. 1–2 and 5–10 days respectively. Several possibilities could explain this phenomenon. (i) The long half-life could reflect mitochondrial autophagocytosis, whereas the short one would then describe turnover of individual mitochondrial proteins. This is improbable because half-lives of individually degraded mitochondrial proteins appear in general to be significantly shorter than 1 day. (ii) There may be distinct populations of mitochondria that are turned over at different rates. Morphologically and potentially functionally distinct mitochondrial populations have been described in aged animals. Although our animals were younger than 6 months, this possibility cannot be ruled out. (iii) However, the simplest explanation of the data is the possibility that the observed complexity of the decay curve is yet another facet of the re-utilization problem, as explained below.
Identifying the origin of the problem
We hypothesized that the slow decay component of the curve was due to the contribution of non-specific (non-arginine) 14C labels. The injected NaH14CO3 may not only label the guanidine group of arginine ([6–14C]arginine), but also other amino acids in both the liver and other tissues to some degree. Once labelled, amino acids other than arginine would not escape the re-utilization problem in any tissues and thus generate an artificially slow component to the degradation curve. Existing literature indicates that this can be the case: after long-term exposure of rats to 14C-labelled carbon (either by CO2 inhalation  or CaCO3 ingestion ), the 14C labels were recovered not only from [6–14C]arginine in liver, but also from various amino acids in different tissues (albeit in smaller quantities).
Consequently, we measured the 14C labels in mitochondria from skeletal muscle and brain (i.e. the tissues without active urea cycle) in parallel, as a source of information on non-specific and re-utilized labels. Quantitatively the 14C labels found in skeletal muscle and brain mitochondria were similar to each other, but much lower than that in liver mitochondria in the first few days after labelling (Figures 2A and 2B). However, the extrapolated ‘slow’ (non-specific) component in liver was quantitatively very similar to the measured 14C counts in skeletal muscle and brain mitochondria (Figure 2B).
The non-specifically labelled amino acids undergo continuous recycling across all tissues in the animals. The similarity between 14C counts and decay rates in muscle, brain and slow component in liver (Figure 2B) suggested that the recycling of non-specific label masked any differences between muscle and brain mitochondria turnover rates.
Therefore the observed complexity of the decay curve probably consisted of two components: (i) a fast component, due to [6–14C]arginine (which would follow a first-order decay function), and (ii) a slow component, due to non-specific 14C labels that is the collective outcome of extensively re-utilized 14C labels from mixed products. It is the fast component that we are interested in, as it is driven by the true mitochondrial protein degradation rate. However, fitting the liver data with a double exponential model resulted in very low confidence levels of the estimates for both the fast and the slow components. Essentially there was insufficient information in this data set alone to infer two independent decay rates. Therefore we searched for a quantitative model that would make more efficient use of the other available data.
Although mathematical models have been used in metabolic labelling studies for decades, recent advances in statistical and mathematical techniques offer new ways to extract information from these experiments. We performed Bayesian inference for a simple two-component decay model. We chose the simplest model, a linear model, to describe the slow component because the complexity of non-specific label metabolism is too large to assume any other model structure a priori. In the absence of further information, we simply used the average of the slow processes observed in other tissues as our best estimate for the slow linear process in liver (see Figure 2B). This technique provided us with information about likely parameter distributions given noisy observations.
Mathematically, the model is expressed as follows: where μji (count·mg−1) is the expected radiolabel count at time t (days) for tissue i and treatment j, μj0 (count·mg−1) are parameters representing the value of the exponential component of the modelled label count in the liver at t=0 immediately after injection of the label, kjd (day−1) are rate parameters describing the exponential decay of the label with time in the liver tissues, and mji (count·mg−1·t−1) and cji (count·mg−1) are the slope and intercept value of the slow linear processes observed in tissue i and treatment j respectively.
By fitting this combined model of all processes (exponential and linear in liver and linear in brain and muscle) to all of the data simultaneously, we maximize the amount of information we gather on the dynamics of 14C labels in all of these tissues. The main advantage of this method over more traditional methods, such as least squares, is that parameter and model estimate distributions could be obtained instead of just a single ‘best’ value, which allows us to test for the significance of differences observed between treatments.
Using this approach, we obtained excellent fits to the data with very narrow confidence intervals (Figure 2A). This enabled us to conclude that half-lives of liver mitochondria in control and DR animals, which we estimated as 1.83 and 1.16 days respectively, were significantly different with an error probability of less than 0.001 (Figure 2C). These data, after correction for non-specific 14C label re-utilization, show that mouse liver mitochondria are turned over significantly faster than suggested by the majority of previous estimates, including our own data using a simple first-order decay model (see Table 1 and Figure 1).
Summary and future
We have found evidence that label re-utilization is a significant problem for the assessment of mitochondrial turnover rates in pulse–chase experiments, even using the best available combination of label and tissue, i.e. NaH14CO3 in liver. Assuming the same re-utilization kinetics for the non-specific non-arginine labels in all tissues allowed us to employ data generated in non-liver tissues from the same mice to precisely estimate and eliminate the contaminating contribution from the slow (re-utilization) component in liver. Estimating model parameters by Bayesian parameter inference made maximal use of the available data. This resulted in high-precision estimates of liver mitochondrial degradation rates from reasonably low numbers of experimental animals. Evidently, similar dynamic simulation models can be applied for data analysis in a wide variety of metabolic labelling pulse–chase experiments. Our experience with the present simple model motivated us to move on to a more comprehensive systemic analysis of label re-utilization and mitochondrial turnover in pulse–chase experiments. Using labels other than NaH14CO3 will increase the impact of the re-utilization problem in liver; however, if this can still be corrected with sufficient precision, it would allow more efficient labelling and thus reliable estimation of mitochondrial turnover in other tissues. After measuring label kinetics not only in mitochondria, but also other compartments, such as in tissue homogenates and free amino acids in various tissues and in blood, it should be possible to construct a holistic model of the entire organism which should allow the estimation of mitochondrial protein degradation rates in multiple tissues in parallel. We feel this is a thrilling possibility, and this is surely the art of systems biology.
Our work leading to this article was supported by the Biotechnology and Biological Sciences Research Council (BBSRC) and Engineering and Physical Sciences Research Council (EPSRC) [grant number BB/C008200/1 to Centre for Integrated Systems Biology of Ageing and Nutrition (CISBAN)].
Systems Approaches to Health and Disease: A Biochemical Society Focused Meeting held at University of York, U.K., 22–24 March 2010, as part of the Systems Biochemistry Linked Focused Meetings. Organized and Edited by David Fell (Oxford Brookes, U.K.), Hans Westerhoff (Manchester, U.K., and Amsterdam, The Netherlands) and Michael White (Liverpool, U.K.).
Abbreviations: ALA, aminolaevulinic acid; DR, dietary restriction
- © The Authors Journal compilation © 2010 Biochemical Society