Estimation of time-varying growth, uptake and excretion rates from dynamic metabolomics data

Abstract

Motivation: Technological advances in metabolomics have made it possible to monitor the concentration of extracellular metabolites over time. From these data, it is possible to compute the rates of uptake and excretion of the metabolites by a growing cell population, providing precious information on the functioning of intracellular metabolism. The computation of the rate of these exchange reactions, however, is difficult to achieve in practice for a number of reasons, notably noisy measurements, correlations between the concentration profiles of the different extracellular metabolites, and discontinuties in the profiles due to sudden changes in metabolic regime. Results: We present a method for precisely estimating time-varying uptake and excretion rates from time-series measurements of extracellular metabolite concentrations, specifically addressing all of the above issues. The estimation problem is formulated in a regularized Bayesian framework and solved by a combination of extended Kalman filtering and smoothing. The method is shown to improve upon methods based on spline smoothing of the data. Moreover, when applied to two actual datasets, the method recovers known features of overflow metabolism in Escherichia coli and Lactococcus lactis, and provides evidence for acetate uptake by L. lactis after glucose exhaustion. The results raise interesting perspectives for further work on rate estimation from measurements of intracellular metabolites.