Explicit oxygen concentration expression for estimating extant biodegradation kinetics from respirometric experiments.

We present a simple method for estimating extant biodegradation kinetic parameters from oxygen uptake data obtained during respirometric experiments. Specifically, a novel closed-form solution based on the Lambert W function is presented for the differential equation describing substrate biodegradation based on the Monod equation. Unlike the existing implicit solution, this novel solution is explicit with respect to the substrate concentration and, when coupled with the oxygen uptake equation, results in a simple algebraic expression for dissolved oxygen concentration in respirometric experiments. This new solution provided highly accurate estimates of dissolved oxygen concentrations with accuracy on the order of 10(-15) for calculations performed using double precision arithmetic. The applicability of this approach for estimating extant biodegradation kinetic parameters was verified using synthetic dissolved oxygen concentration data that incorporated normally distributed noise to mimic experimental data. A combination of the W function description of oxygen concentration and a nonlinear optimization routine resulted in estimates of the Monod kinetic parameters, mu(m) and K(s), that were close to the actual values, indicating the suitability of this approach for extant kinetic parameter estimation. This approach was subsequently tested on experimental oxygen concentration data obtained during ethylene-glycol biodegradation in respirometric experiments. The availability of simple algorithms for evaluating the W function makes the new solution easier to compute than current methods that rely on numerical solution of differential or nonlinear equations. The simplicity and accuracy associated with use of the W function to describe oxygen concentration data should make it an attractive approach for estimating extant Monod biodegradation kinetic parameters from respirometric experiments.

Nonlinear estimation of microbial and enzyme kinetic parameters from progress curve data.

A computer program (BIOKINFIT) was developed to estimate microbial and enzyme kinetic parameters from progress curve data by nonlinear regression. BIOKINFIT overcomes the limitations associated with parameter estimation in nonlinear equations that are implicit in the dependent variable by numerically approximating the substrate concentration in the integrated kinetic expressions. The simplex method was used to minimize the error between experimentally observed and theoretically predicted substrate depletion data. The robustness of this approach was initially verified using synthetic substrate depletion data that were characterized by either simple or relative errors of known magnitude. Subsequently, previously published data from three different experiments including the pyruvate kinase reaction, 2-chlorophenol biodegradation, and glucose uptake by Penicillium chrysogenum were used to verify the utility of the present approach for kinetic parameter estimation. In all cases, experimental substrate depletion data were accurately described by the theoretical curves and kinetic parameter estimates obtained in this study using the simplex method were in close agreement with those reported previously. BIOKINFIT, available free of charge on request, offers a convenient and robust method of analyzing progress curve data in implicit kinetic expressions.

Influence of microbial concentration on the rheology of non-Newtonian fermentation broths.

The objective of this study was to quantify the effect of fungal biomass concentration on the rheology of non-Newtonian fermentation systems. Batch fermentations of Penicillium chrysogenum were carried out with glucose as the sole carbon source. The flow behavior of the system was characterized at various fermentation times and was adequately described by the power-law model. The apparent viscosity of the fermentation broth was significantly affected by biomass concentrations in the fermenter. Fermentation broths containing 17.71 g/l biomass as dry weight were characterized by an apparent viscosity of 0.25 Pa s at a shear rate of 50 s-1. Microbial concentration also affected the power-law flow-behavior index and the consistency index. The value of the consistency index ranged from 0.002 Pa sn at a biomass concentration of 0.1 g/l to 6.14 Pa sn at a biomass concentration of 17.71 g/l. The flow-behavior index decreased from an initial value of 1 to a final value of 0.17. Simple empirical correlations have been proposed to quantify the dependence of the power-law parameters on fungal biomass concentration. Experimental data obtained in this study were accurately described by these correlations. The general applicability of these relationships was tested, using previously published rheological data on Aspergillus awamori and Aspergillus niger fermentation broths, and good agreement was seen between experimental data and the predictions from the empirical correlations.

Parameter estimation using a direct solution of the integrated Michaelis-Menten equation.

A novel method of estimating enzyme kinetic parameters is presented using the Lambert omega function coupled with nonlinear regression. Explicit expressions for the substrate and product concentrations in the integrated Michaelis-Menten equation were obtained using the omega function which simplified kinetic parameter estimation as root-solving and numerical integration of the Michaelis-Menten equation were avoided. The omega function was highly accurate in describing the substrate and product concentrations in the integrated Michaelis-Menten equation with an accuracy of the order of 10(-16) when double precision arithmetic was used. Progress curve data from five different experimental systems were used to demonstrate the suitability of the omega function for kinetic parameter estimation. In all cases, the kinetic parameters obtained using the omega function were almost identical to those obtained using the conventional root-solving technique. The availability of highly efficient algorithms makes the computation of omega simpler than root-solving or numerical integration. The accuracy and simplicity of the omega function approach make it an attractive alternative for parameter estimation in enzyme kinetics.