Bayesian estimation and uncertainty quantification in models of urea hydrolysis byE. colibiofilms

Abstract

Urea-hydrolysing biofilms are crucial to applications in medicine, engineering, and science. Quantitative information about ureolysis rates in biofilms is required to model these applications. We formulate a novel model of urea consumption in a biofilm that allows different kinetics, for example either first order or Michaelis-Menten. The model is fit it to synthetic data to validate and compare two approaches: Bayesian and nonlinear least squares (NLS), commonly used by biofilm practitioners. The shortcomings of NLS motivate the Bayesian approach where a simple Markov Chain Monte Carlo (MCMC) sampler is applied. The model is then fit to real data of influent and effluent urea concentrations from experiments on biofilms of Escherichia coli. Results from synthetic data aid in interpreting results from real data, where first order and Michaelis-Menten kinetic models are compared. The method shows potential for general applications requiring biofilm kinetic information.

Multiscale Flux-Based Modeling of Biofilm Communities

“…Estimating metabolic kinetic parameters from data is an active area of research at present, including uncertainty quantification, e.g., [6]. These methods are only recently being applied in microbial community models [17,33,56], despite the clear need, possibly due to the complexity of multispecies microbial interactions as well as the sparsity of appropriate data. We do not utilize them below-the methods presented here do not address and are not aimed at parameter estimation-though we do briefly illustrate the possibility of using available data to modify optimization objectives, a somewhat related issue.…”

Bayesian estimation of Pseudomonas aeruginosa viscoelastic properties based on creep responses of wild type, rugose, and mucoid variant biofilms

“…These techniques were later used in other fields, such as ecology [ 29 , 30 ], and engineering applications, for example, dielectric elastomers, solid amorphous polymers, and lithium-ion batteries [ [31] , [32] , [33] ]. However, this is much less widespread in biomathematics applications, where challenges in estimating relevant parameters are unique [ [34] , [35] , [36] ]. For example, one of the most important outcomes in biological DA is to predict and optimize the relevant factors involved in biofilm development so that efficient optimal control targets can be identified by coupling DA with sensitivity analysis [ 36 ].…”

“…However, this is much less widespread in biomathematics applications, where challenges in estimating relevant parameters are unique [ [34] , [35] , [36] ]. For example, one of the most important outcomes in biological DA is to predict and optimize the relevant factors involved in biofilm development so that efficient optimal control targets can be identified by coupling DA with sensitivity analysis [ 36 ].…”

Bayesian calibration of coupled computational mechanics models under uncertainty based on interface deformation

“…Recent advances in automated biofilm cultivation and design of flow cell experiments [15] have already shown that a variety in biofilm shapes is inevitable even for reproducible environmental conditions and therefore a flexible method of comparing biofilm shapes is required for conclusive inverse analysis. Recently, Bayesian estimation and uncertainty quantification (UQ) have been used for models of urea hydrolysis by biofilms [16].…”

“…Fig 16. Schematic setup of a flow cell experiment with biofilms for measurement with optical coherence tomography (OCT)…”