Parameter Estimation and Identifiability in Kinetic Flux Profiling Models of Metabolism

TL;DR

This paper develops mathematical and statistical methods to estimate and analyze metabolic fluxes from isotope tracing data, focusing on parameter identifiability and experimental design to improve flux estimation accuracy.

Contribution

It generalizes pathway-to-model conversion, investigates flux identifiability at steady state, and provides Bayesian estimation methods with practical guidelines for KFP experiments.

Findings

Identified conditions for flux parameter identifiability.

Provided criteria for valid parameter estimation with fast-slow dynamics.

Demonstrated Bayesian estimation accuracy on simulated data.

Abstract

Metabolic fluxes are the rates of life-sustaining chemical reactions within a cell and metabolites are the components. Determining the changes in these fluxes is crucial to understanding diseases with metabolic causes and consequences. Kinetic flux profiling (KFP) is a method for estimating flux that utilizes data from isotope tracing experiments. In these experiments, the isotope-labeled nutrient is metabolized through a pathway and integrated into the downstream metabolite pools. Measurements of proportion labeled for each metabolite in the pathway are taken at multiple time points and used to fit an ordinary differential equations model with fluxes as parameters. We begin by generalizing the process of converting diagrams of metabolic pathways into mathematical models composed of differential equations and algebraic constraints. The scaled differential equations for proportions of unlabeled metabolite contain parameters related to the metabolic fluxes in the pathway. We investigate flux parameter identifiability given data collected only at the steady state of the differential equation. Next, we give criteria for valid parameter estimations in the case of a large separation of timescales with fast-slow analysis. Bayesian parameter estimation on simulated data from KFP experiments containing both irreversible and reversible reactions illustrates the accuracy and reliability of flux estimations. These analyses provide constraints that serve as guidelines for the design of KFP experiments to estimate metabolic fluxes.