Bayesian estimation and uncertainty quantification in models of urea hydrolysis by E. coli biofilms

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.