Isotope regression model

Antoniewicz, M.R., Stephanopoulos, G., and Kelleher, J.K., Evaluation of regression models in metabolic physiology Predicting fluxes from isotopic data without knowledge of the pathway, Metabolomics 2,41, 2006. 

This is the model equation for the calibration of isotope amount ratios based on the log-linear temporal isotope amount ratio regression. Note that a and b are perfectly correlated (p = +1) if Rtp < 1 (inRup < 0) and perfectly anti-correlated (p = —1) if Rk/i > 1 (InRfe/ > 0). It is important to stress that this calibration method is fundamentally different from the conventional mass bias correction la vs. Since the regression model does not invoke the principle of time-mass separation, it does not need either the discrimination exponent or the equality of the discrimination functions [17]. 

This expression has been used as the model equation for the regression model in the past. As pointed out by Baxter et aJ.[36], however, this is equivalent to assuming fip =fk/i- The pitfall of this approach is that the resultant value of the regression intercept is not used, rather its value is assumed from Eq. (5.35). To avoid the errors of Eq. (5.39), Baxter et al. proposed a revised regression model that combines two regressions one for the reference material of the analyte and internal standard, and the other that combines the sample and the internal standard [36]. Reliance on the reference material for the measurand, however, is unnecessary, provided that the isotope amount ratio of the internal standard is known [Eq. (5.39)]. However, it is a viable option nevertheless. 

Doucet et described the determination of isotope ratios using LIBS in air at atmospheric pressure for partially resolved uranium-235-uranium-238 and hydrogen-deuterium isotope shift lines. A PLSl regression model could accurately predict the isotopic ratio under conditions where the application of traditional univariate approaches for hydrogen and uranium would not be achievable. 

Instead of artificially transforming the data to a linear model, our group developed an approach in which the relation between isotope ratios and mole ratios is described by means of a polynomial regression (Jonckheere et al., 1982). In this, the basic IDMS equation [Eq. (1)] is seen as a rational function ... 

Jouzel et al. (2000) have compared the simulated relationships between annual mean isotope concentration and annual mean temperature for the ECHAM, GISS, and LMD isotopic models. The linear regressions between these parameters are performed over two temperature ranges, namely, temperatures above and temperatures below 15 °C (0 °C for ECHAM). The upper range encompasses tropical sites for which the isotope content of precipitation is controlled mostly by the amount of precipitation and not by temperature. Isotopic GCMs are successful in simulating this effect. However, predicted slopes between and the amount of precipitation... 

FIG. 5. Isotopic enrichment of urinary folate in an adult female subject during chronic ingestion of a low-folate diet supplemented with d2-folic acid. The value of 0.284 enrichment represents the labeling (i.e., isotopic enrichment) of ingested folate from dietary and supplemental sources. In this figure, the data were fit to the two-pool, one-output model depicted in Fig. 3, which yielded the solid regression line (Gregory el aL, 1994). 

The absolute rise in shown here occurred in only three of the ten studies but in each case there was a marked divergence between the concentration of and tritium. The mean rates of change for each isotope could be determined from regression lines through the experimental points. Summary data are shown on the next slide. The rate for water (-0.72 %/min) is strikingly faster than that for urate (-0.18 %/tnin) or inulin (-0.08 %/inin). They could only occur as a result of diffusion away from the injection site. It is this process of differential diffusion which concentrates total urate in this experimental model and which I would like to implicate in the pathogenesis of podagra. 

To date, interrogation of the efficacy of mass bias correction models has largely resorted to attempts to determine the value of the discrimination exponent. In such experiments, the slope of the log-linear two-isotope ratio regression is used, which, in turn, leads to the discrimination exponent by solving the following expression [43-46] ... 

The permeation kinetic parameters Dy, k, and can be determined by regressing the experimental oxygen fluxes measured at different conditions with the above permeation model. Table 5.1 lists the expressions of permeation parameters for the Lao.jSro4Coo2Feo803 j perovskite membrane. The diffusion coefficients of oxygen vacancies in other perovskite membranes were also studied by the isotopic method, as summarized in Table 5.2. The activation energy for oxygen vacancy diffusion is in the range of 77 21 kj mol" [20]. 

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