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Data-driven Bayesian estimation of Monod kinetics

Kévin Colin, Håkan Hjalmarsson, Véronique Chotteau

TL;DR

This work tackles nonlinear identification of Monod-kinetic rates under minimal quantitative prior information by developing a data-driven Bayesian framework. It employs log-Gaussian priors for the kinetic parameters, Empirical Bayes via an EM algorithm to tune hyperparameters, and a novel enforced Metropolis-Hastings within Gibbs sampler to accelerate convergence. The approach is demonstrated on a relatively large Monod model with 12 metabolites, showing competitive accuracy and favorable computation time compared with literature baselines, while addressing identifiability concerns intrinsic to double-component kinetics. The resulting framework enables robust parameter estimation from limited data, with direct implications for model-based optimization of bioreactor feeds and related bioprocess applications.

Abstract

In this paper, we consider the well known problem of non-linear identification of the rates of the reactions involved in cells with Monod functions. In bioprocesses, generating data is very expensive and long and so it is important to incorporate prior knowledge on the Monod kinetic parameters. Bayesian estimation is an elegant estimation technique which deals with parameter estimation with prior knowledge modeled as probability density functions. However, we might not have an accurate knowledge of the kinetic parameters such as interval bounds, especially for newly developed cell lines. Hence, we consider the case when there is no accurate prior information on the kinetic parameters except qualitative knowledge such that their non-negativity. A log-Gaussian prior distribution is considered for the parameters and the mean and variances of these distribution are tuned using the Expectation Maximization algorithm. The algorithm requires to use Metropolis Hastings within Gibbs sampling which can be computationally expensive. We develop a novel variant of the Metropolis-Hastings within Gibbs sampling sampling scheme in order to accelerate and improve on the hyperparameter tuning. We show that it can give better modeling performances on a relatively large-scale simulation example compared to available methods in the literature.

Data-driven Bayesian estimation of Monod kinetics

TL;DR

This work tackles nonlinear identification of Monod-kinetic rates under minimal quantitative prior information by developing a data-driven Bayesian framework. It employs log-Gaussian priors for the kinetic parameters, Empirical Bayes via an EM algorithm to tune hyperparameters, and a novel enforced Metropolis-Hastings within Gibbs sampler to accelerate convergence. The approach is demonstrated on a relatively large Monod model with 12 metabolites, showing competitive accuracy and favorable computation time compared with literature baselines, while addressing identifiability concerns intrinsic to double-component kinetics. The resulting framework enables robust parameter estimation from limited data, with direct implications for model-based optimization of bioreactor feeds and related bioprocess applications.

Abstract

In this paper, we consider the well known problem of non-linear identification of the rates of the reactions involved in cells with Monod functions. In bioprocesses, generating data is very expensive and long and so it is important to incorporate prior knowledge on the Monod kinetic parameters. Bayesian estimation is an elegant estimation technique which deals with parameter estimation with prior knowledge modeled as probability density functions. However, we might not have an accurate knowledge of the kinetic parameters such as interval bounds, especially for newly developed cell lines. Hence, we consider the case when there is no accurate prior information on the kinetic parameters except qualitative knowledge such that their non-negativity. A log-Gaussian prior distribution is considered for the parameters and the mean and variances of these distribution are tuned using the Expectation Maximization algorithm. The algorithm requires to use Metropolis Hastings within Gibbs sampling which can be computationally expensive. We develop a novel variant of the Metropolis-Hastings within Gibbs sampling sampling scheme in order to accelerate and improve on the hyperparameter tuning. We show that it can give better modeling performances on a relatively large-scale simulation example compared to available methods in the literature.
Paper Structure (31 sections, 24 equations, 7 figures, 2 tables)

This paper contains 31 sections, 24 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Notations
  3. Macroscopic kinetic modeling with Monod functions
  4. Monod kinetics
  5. Data and identification
  6. Bayesian estimation - a general presentation
  7. Prior and posterior distributions
  8. Loss function, risk and Bayes estimator
  9. Empirical Bayes and Expectation Maximization algorithm for hyperparameter tuning
  10. Bayesian estimation applied to Monod kinetic modeling
  11. Choice of the prior
  12. Likelihood function
  13. Choice of the loss function and computation procedure of the Bayes estimator
  14. Adaptation of the EM algorithm for the hyperparameter estimation linked to kinetic parameters
  15. Metropolis-Hastings within Gibbs sampling and the proposed variation
  16. ...and 16 more sections

Figures (7)

  • Figure 1: Different activation (top left), inhibition (top right) and double-component (bottom) functions.
  • Figure 2: Chosen order for Gibbs sampling applied to Monod estimation.
  • Figure 3: Scheme of the E-MHWGS sampling
  • Figure 4: Box plots of the fit obtained with C-MHWGS, E-MHWGS, GP-2019 and GP-2022 with the 100 Monte Carlo simulations.
  • Figure 5: Box plots of the computation time obtained with C-MHWGS, E-MHWGS, GP-2019 and GP-2022 with the 100 Monte Carlo simulations.
  • ...and 2 more figures

Theorems & Definitions (3)

  • Remark 1
  • Remark 2
  • Remark 3