A schematic representation of the principles of the tracer dilution model is depicted in Fig. 3A. To determine R_a tracee (e.g., glucose), a tracer of the same compound (e.g., [6,6-²H₂]glucose tracer) is constantly infused into the blood at a predefined rate (F), typically after administration of a priming dose of the same glucose tracer (called a primed constant infusion). The practical purpose of administering a priming dose is to reduce the time needed to reach to the point at which tracer enrichment is constant, referred to as plateau enrichment (E_p), while not affecting the magnitude of enrichment at isotopic equilibrium (i.e., E_p). When a tracer is constantly infused into the blood at a given F, tracer enrichment will rise and eventually reach E_p, the magnitude of which is inversely related to the turnover rate of the tracee of interest for a given F. At physiological steady states where the pool size is constant, R_a tracee is equal to R_d tracee. At E_p, R_a tracer (i.e., F) is also equal to R_d tracer. The relation between R_a tracer (i.e., F) and R_a tracee dictates the tracer-to-tracee ratio at E_p. Thus, the following relations can be established: F:R_a glucose=[tracer]:[tracee]. After rearrangement of the equation, we can see that R_a glucose is the product of F and 1/MPE, which is then equal to F/E_p. From this relation, it is clear that the magnitude of dilution of the tracer by the tracee in the compartment at E_p directly reflects R_a tracee. In other words, the faster the tracee turnover, the lower the E_p for a given F. The tracer dilution model can be applicable to assessments of in vivo kinetics of various metabolites including amino acids [26,44-46], palmitate [6,47,48], glycerol [49-51], pyruvate [52], lactate [53-55] as well as glucose [8,11,56,57] in steady states and non-steady states.

Alterations in rates of polymer synthesis such as protein [26,58], DNA [59,60], RNA [59,61], triacylglycerol [62,63], and glucose (e.g., GNG) [64,65], from their respective precursors have clinical implications [66,67]. In this regard, the tracer incorporation model has been widely used to obtain the polymer synthesis rate and is predicated on the rate of tracer precursor incorporation to product for a given time period, yielding the fractional synthesis rate (FSR), which refers to the percent of the pool size that has been newly synthesized from the precursor for the most recent defined time period (%/time) [68]. Fig. 3B represents the schematic principles of the tracer incorporation model to determine polymer FSR. To assess FSR, various precursor tracers can be infused. After achieving isotopic equilibrium of a precursor enrichment (i.e., E_p), labeled and unlabeled precursors will be incorporated into a product (made of two identical monomers, like the synthesis of glucose from two 3-carbon precursors) in proportion to their relative abundance (i.e., precursor enrichment). Thus, the magnitude of product enrichment will be determined by (1) the precursor enrichment at E_p and (2) the rate of product synthesis [69]. FSR is calculated as the change in product enrichment divided by precursor enrichment (assumed to be constant) multiplied by 100 (for the expression as %/time) for a given time period. As its definition implies, FSR is a relative term, denoting the % of the product pool size that has been newly synthesized in the most recent time period. Thus, to obtain the absolute synthesis rate, the FSR term must be multiplied by the pool size (or the production rate of the polymer product when it is released into other compartments, like glucose). The importance of obtaining absolute rates becomes clear when comparing FSRs between two distinct pool sizes (one being half of the other). In this case, an identical muscle protein FSR obtained from two heterogenous groups translates to 2-fold differences in the absolute muscle protein synthesis rate. If one can assume the pool size is similar between groups or constant over the experimental time period, then the simple comparison of FSRs is valid [70,71]. The incorporation model can be applicable to the assessments of the kinetic calculations of various compounds, including the FSR of individual proteins [72,73] and subgroups of proteins (mitochondrial, sarcoplasmic, and mixed muscle protein) [74-79], the substrate oxidation rate [6,80-82], the DNA synthesis rate (thus cell division) [59,60], the nitric oxide synthesis rate from its precursor arginine [83-86], and GNG [30,87], the latter of which will be discussed in the following section in detail.

To determine EGP or HGP, one or more blood samples are collected for obtaining background enrichment before tracer administration. Then, after administration of a priming glucose tracer dose (a bolus injection of a glucose tracer), the same glucose tracer is constantly infused IV at a predefined F. When E_p is reached, blood samples are collected a couple of times for determination of tracer enrichment. Then, the steady state kinetics of the tracee (i.e., R_a glucose) can be calculated as F divided by E_p. For instance, if [6,6-²H₂]glucose (M+2) is infused constantly at 0.80 μmol/kg/min following a priming dose of 80 μmol/kg, and if the value of E_p glucose is 0.04 (MPE=4%) after subtracting the background enrichment, then R_a glucose, calculated as 0.80 μmol/kg/min divided by 0.04, would be 20 μmol/kg/min. Because the plasma glucose pool is constant, R_d glucose must be 20 μmol/kg/min as well. As discussed above, R_a glucose represents EGP, largely reflecting HGP. As HGP is the sum of rates of both hepatic GB and GNG, by knowing GNG, GB can be inferred.

Hepatic GNG is calculated as the product of the fractional contribution of GNG to HGP (F_GNG) and HGP (=R_a glucose in the fasted state). F_GNG is determined in relation to the precursor (3-carbon sugar) product (i.e., glucose) rule based on the tracer incorporation model as described above. As described in the FSR calculation above, F_GNG is calculated based on the relationship between the enrichment of the product and that of the precursor. While it is straightforward to identify the enrichment of the product, as new glucose appears into the circulation where plasma glucose can be sampled, determination of the “true” precursor enrichment has been a debatable issue over decades [15,96] due to a number of issues that hinder the quantification of “true” precursor enrichment [96,97]. For example, with a primed constant infusion of a precursor tracer (e.g., tracers of glycerol, pyruvate, alanine, or lactate) [51,52,55,98], it is typical to obtain precursor tracer enrichment from plasma (particularly in the case of humans) [52,99] or directly from liver tissue (typically in animal models) [100,101]. Problems arise at multiple levels including (1) dilution of tracer en route to glucose in a number of points of metabolic steps and/or (2) gradation of enrichment across liver tissue, which over- or under-estimates “true” GNG [15,102]. Regarding this issue, several solutions have been developed, which are conceptually sound and currently widely used with some practical limitations mostly arising from analytical issues [103]. Among others [102,104], mass isotopomer distribution analysis (MIDA), developed by Hellerstein and Neese [96,103], and heavy water labeling methods [105] bypass the true precursor enrichment issues. In this review, we will briefly discuss the MIDA approach for the calculation of true precursor enrichment due to space limitations. Fig. 5 shows the principle of calculating the true precursor enrichment using MIDA from the pattern of enrichment of the product (glucose) in the plasma regardless of the magnitude of ongoing GB. The principle of MIDA is relatively simple and is predicated on combinatorial probabilities with a binomial expansion: _nC_k×p^k×(1−p)^n-k where n is the number of subunits in the product, k is the number of labeled subunits, and p is the labeling probability of the precursor pool [96,103]. With an E_p of the precursor of 0.5 during a constant infusion of singly labeled precursor tracer (e.g., [1-¹³C]glycerol), the probabilities of new glucose being both unlabeled (both, black), singly labeled (S), or doubly labeled (D, both red) in case of no GB can be calculated using the equations with the information (for glucose, n=2, k=1 for S or k=2 for D) to be 0.25 (i.e., 25%), 0.50 (i.e., 50%), and 0.25 (i.e., 25%) respectively. However, when GB (providing unlabeled glucose to the product pool) contributes 50% to HGP, the E_p of the product (i.e., glucose) will be diluted by half. While S (2/8 for pool A vs. 4/8 for pool B) and D (1/8 for pool A vs. 2/8 for pool B) may vary depending on the magnitude of GB, the ratio of D to S (D/S) is constant (i.e., 0.5 for both) for a given precursor enrichment. True precursor enrichment can be obtained by solving the equation (i.e., D/S=p²/[2×p×(1−p)]) for p by rearranging the equation, i.e., p=(2×D/S)/(1+2×D/S). Because D/S for both cases is identical, the p values calculated from both cases are identical regardless of occurring GB. Thus, F_GNG is calculated by dividing E_p product enrichment by the same E_p precursor (0.5): F_GNG of 50% in Fig. 5A and 100% in Fig. 5B. Thus, the absolute rate of GNG will be the product of HGP and F_GNG. Thus, 25 μmol/kg/min×0.5 (50%)= 12.5 μmol/kg/min. Thus, hepatic GP will be inferred as HGP minus GNG, which is 12.5 μmol/kg/min. In the following, we will deal with the calculation of non-steady state glucose kinetics using an example of an OGTT condition.

Assessment of glucose metabolism needs to be performed in the conscious state as anesthesia affects glucose homeostasis [116, 117]. Tracer administration can be achieved by using an oral gavage injection, IP injection, or IV infusion (Fig. 6A) [69,117, 118]. While useful in exploring dynamics of metabolism, both oral methods are not practically feasible for assessing absolute rates of glucose turnover due to the inability to achieve E_p and the requirement of frequent blood sampling, both of which make kinetic calculations more complicated. In contrast, a (primed) constant infusion method via IV catheterization indwelling on the right jugular vein is a frequently used technique that not only enables the determination of absolute rate of glucose turnover but also avoids excess irritation in response to gavage or IP injection [69,119]. However, the surgical procedure of catheterization requires a skillful mouse surgeon, which will be described first.

Briefly, a median incision, approximately 5 mm, is made at a subtle palpating spot that is approximately 5 mm on the right side of the trachea, the isolation of the right jugular vein is conducted, and a silastic catheter is inserted into the vessel. The other end of the catheter is tunneled to the back of the neck for two purposes: (1) preventing mice from pulling out and damaging the catheter and (2) easy assessment of the catheter in the tracer infusion experiments. The surgical procedure can be completed in approximately 20 minutes by an experienced mouse surgeon, and it typically takes approximately 5 to 7 days for the mouse to fully recover from the surgery.

After a 5 to 15-hour fast (depending on the research question), experimental mice undergo a (primed) constant infusion of ¹³C glucose. Before and at isotopic equilibrium during the tracer infusion, blood and expired air samples are collected for the calculations of systemic glucose turnover and substrate oxidation, respectively. At the end of the infusion, experimental mice are anesthetized, and tissues are harvested for determining tissue specific metabolic flux.

Plasma and homogenized tissues are deproteinized. The supernatant containing metabolites is collected, desiccated, and chemically derivatized in order to increase the volatility and stability of metabolites at high temperature on a GC capillary column (Fig. 6B).

Using GC-MS, the metabolites undergo the separation of substances in GC capillary columns and fragmentation of the substrate of interest. Then, tracer abundance of ion peaks will be counted using selective ion monitoring. To analyze substrate oxidation, isotope ratio mass spectrometry (IRMS) with high detection sensitivity is utilized to measure enrichment of ¹³CO₂ from the expired air of the model animals (Fig. 6C).

At the end of the procedures, various flux parameters can be calculated (Fig. 6D). First, systemic glucose flux such as R_a tracee (e.g., glucose, amino acids, fatty acids) can be calculated based on the tracer dilution model using critical information including E_p and F in fasted steady states and E_p, F, and tracee concentrations (reflection of tracee pool size) in the non-steady state. In addition, intracellular metabolite flux can be estimated via an examination of labeling patterns (i.e., patterns of mass isotopomer distribution [MID]) of each metabolite. Finally, by using ¹³C-labeled substrate as a tracer, the rate of substrate oxidation (e.g., rates of oxidation of glucose, palmitate, leucine, etc.) can be assessed with additional analyses of ¹³CO₂ enrichment of expired air and CO₂ production from the mice.

In the process of MFA with the assistance of computer software such as INCA, the labeling patterns of intracellular metabolites (i.e., MID) derived from ¹³C-labeled nutrient(s), cellular uptake of the nutrient(s), and secretion rates of selected product(s), and prior knowledge of the metabolic pathway network are combined for computational estimation of metabolic flux [120,121]. To examine intracellular metabolic flux, an experiment is initially designed (Fig. 7A). In the experimental design, the selection of an optimal tracer(s) is best made in silico (i.e., in computer simulations) [122] and is important to ensure an accurate analysis of metabolic flux, followed by constructing a metabolic pathway network for MFA (e.g., glycolysis pathway, pentose phosphate pathway, etc.) (Fig. 7B). A metabolic pathway network can be constructed using databases such as the Kyoto Encyclopedia of Genes and Genomes (KEGG). The next step is to measure external flux rates (e.g., rates of uptake of glucose and/or glutamine and rates of secretion of lactate and/or pyruvate) based on changes in concentrations of substrate of interest for a defined time period, normalized for the number of cells after treatment of the medium with ¹³C tracer(s) (Fig. 7C). Sequentially, isotopic labeling patterns (i.e., MID) of intermediates from the cells and medium are determined by using GC-MS (Fig. 7D). With the assistant of MFA software such as INCA, factors including constructed metabolic pathway network, measured external flux rates, and MIDs of intermediates are utilized for flux estimation. Then, through rigorous statistical processes, the goodness-of-fit of the constructed model to the observed values is first verified and then the sum-of-squared residuals between the simulated and measured MID results is minimized through repetitions of model reconstruction (e.g., modeling assumptions, additional information from the literature, or novel hypotheses) until being statistically acceptable (Fig. 7E) [123]. The statistically accepted results finally represent the absolute rates of intracellular metabolic flux (Fig. 7F).