Using mass measurements in tracer studies—a systematic approach to efficient modeling

Abstract

Tracer enrichment data are fitted by multicompartmental models to estimate rate constants and fluxes or transport rates. In apolipoprotein turnover studies, mass measurements are also available, e.g., apolipoprotein B (apoB) levels in VLDL, IDL and LDL, and are often essential to calculate some of the rate constants. The usual method to use mass measurements is to estimate pool masses along with rate constants. A systematic alternative approach is developed to use flux balances around pools to express some rate constants in terms of the other rate constants and the measured masses. The resulting reduction in the number of parameters to be estimated makes the modeling more efficient. In models that would be unidentifiable without mass measurements, the usual approach and the proposed approach yield identical results. In a simple two-pool model, the number of unknown parameters is reduced from four to two. In a published 5-pool model for apoB kinetics with three mass measurements, the number of parameters is reduced from 12 to 9. With m mass measurements, the number of responses to be fitted and the number of parameters to be estimated are each reduced by m, a simplification by 1/4 to 1/3 in a typical pool model. Besides a proportionate reduction in computational effort, there is a further benefit since the dimensionality of the problem is also decreased significantly, which means ease of convergence and a smaller likelihood of suboptimal solutions. While our approach is conceptually straightforward, the dependencies get considerably more complex with increasing model size. To generate dependency definitions automatically, a webaccessible program is available at http://biomath.info/poolfit/constraints.

Complex effects of inhibiting hepatic apolipoprotein B100 synthesis in humans

“…Individual participant apoB kinetics of VLDL, IDL, LDL, and VLDL TG FCR. References (43)(44)(45)(46)(47)(48)(49)…”

A State Space Transformation Can Yield Identifiable Models for Tracer Kinetic Studies with Enrichment Data

“…Even in such structures, it may be of interest to know which parameters are identifiable without the mass data, and which require mass measurements. We have considered this question elsewhere (Ramakrishnan and Ramakrishnan, 2008). Enrichment modeling can help answer the question, as in the examples considered here.…”

Gaussian Process Modeling of Protein Turnover

“…Traditionally, exponential decay curves have been used to fit the experimental data and infer the protein turnover rate constants. 11,18,20,21 Single-compartment (single exponential) and multicompartment (first-order synthesis and multiexponential) 21,22 models have been employed. Time-dependent ordinary differential equations (ODE) have also been used to model the stable isotope incorporation in metabolic labeling.…”

“…Briefly, the metabolic incorporation of stable isotope and LC–MS measurements of time course peptide and protein labeling provide data on protein kinetics. Traditionally, exponential decay curves have been used to fit the experimental data and infer the protein turnover rate constants. ,,, Single-compartment (single exponential) and multicompartment (first-order synthesis and multiexponential) , models have been employed. Time-dependent ordinary differential equations (ODE) have also been used to model the stable isotope incorporation in metabolic labeling. , However, the general applicability of these models to in vivo studies are limited because they may result in negative decay rates (for multicompartment systems) and are not able to explain fluctuations in the experimental data …”

“…Timedependent ordinary differential equations (ODE) have also been used to model the stable isotope incorporation in metabolic labeling. 22,23 However, the general applicability of these models to in vivo studies are limited because they may result in negative decay rates (for multicompartment systems) and are not able to explain fluctuations in the experimental data. 21 Stochastic models were recently applied to high-throughput time-course data in proteome studies.…”