Metal reduction kinetics in Shewanella

Motivation: Metal reduction kinetics have been studied in cultures of dissimilatory metal reducing bacteria which include the Shewanella oneidensis strain MR-1. Estimation of system parameters from time-series data faces obstructions in the implementation depending on the choice of the mathematical model that captures the observed dynamics. The modeling of metal reduction is often based on Michaelis - Menten equations. These models are often developed using initial in vitro reaction rates and seldom match with in vivo reduction profiles. Results: For metal reduction studies, we propose a model that is based on the power law representation that is effectively applied to the kinetics of metal reduction. The method yields reasonable parameter estimates and is illustrated with the analysis of time-series data that describes the dynamics of metal reduction in S.oneidensis strain MR-1. In addition, mixed metal studies involving the reduction of Uranyl (U(VI)) to the relatively insoluble tetravalent form (U(IV)) by S.alga strain (BR-Y) were studied in the presence of environmentally relevant iron hydrous oxides. For mixed metals, parameter estimation and curve fitting are accomplished with a generalized least squares formulation that handles systems of ordinary differential equations and is implemented in Matlab. It consists of an optimization algorithm (Levenberg - Marquardt, LSQCURVEFIT) and a numerical ODE solver. Simulation with the estimated parameters indicates that the model captures the experimental data quite well. The model uses the estimated parameters to predict the reduction rates of metals and mixed metals at varying concentrations.