Maximum likelihood estimation of pseudo-stoichiometry in macroscopic biological reaction schemes

Abstract

Identification of pseudo-stoichiometric (or yield) coefficients is of primary importance for building a bioprocess model. In most of the applications, the estimation of these coefficients has to be performed without any knowledge of the kinetics and on the basis of a few experiments for which noisy discrete measurements of component concentrations are available. This paper proposes maximum likelihood estimators which are able to deal with measurement errors on all the signals, at each sampling time (including the initial one) and with intrinsic sign constraints on the parameters. This kind of realistic hypotheses exclude the use of the usual (weighted) least-squares estimators. The maximum likelihood estimators are proved to be unbiased (provided a first-order approximation) and their estimation error covariance matrix can be computed (at the same level of first-order approximation). The solutions are proposed in a very general framework, dealing with cell cultures (of bacteria, yeasts or animal cells) performed in stirred tank (continuous, semi-batch or batch) reactors, and without any a priori knowledge on the kinetics. The use of the estimators and their statistical properties are illustrated in a simulation case study (fed-batch bacterial cultures) and in a real case one (batch animal cell cultures).