Influence of oxygen and substrate concentrations on the ideal film thickness and the maximum overall substrate uptake rate in microbial film fermenters

A mathematical model of tumor oxygen and glucose mass transport and metabolism with complex reaction kinetics

Hypoxia imparts radioresistance to tumors, and various approaches have been developed to enhance oxygenation, thereby improving radiosensitivity. This study explores the influence of kinetic and physical factors on substrate metabolism in a tumor model, based on a Krogh cylinder. In tissue, aerobic metabolism is assumed to depend on glucose and oxygen, represented by the product of Michaelis-Menten expressions. For the base case, an inlet pO(2) of 40 mmHg, a hypoxic limit of 5 mmHg, and a tissue/capillary radius ratio of 10 are used. For purely aerobic metabolism, a hypoxic fraction of 0.16 and volume-average pO(2) of 8 mmHg are calculated. Reducing the maximum oxygen rate constant by 9%, decreasing the tissue cylinder radius by 5%, or increasing the capillary radius by 8% abolishes the hypoxic fraction. When a glycolytic term is added, concentration profiles are similar to the base case. Using a distribution of tissue/capillary radius ratios increases the hypoxic fraction and reduces sensitivity to the oxygen consumption rate, compared to the case with a single tissue/capillary radius ratio. This model demonstrates that hypoxia is quite sensitive to metabolic rate and geometric factors. It also predicts quantitatively the effects of inhibited oxygen metabolism and enhanced mass transfer on tumor oxygenation.

Modeling substrate interactions during the biodegradation of mixtures of toluene and phenol by Burkholderia species JS150

The biodegradation kinetics of toluene, phenol, and a mixture of toluene and phenol by Burkholderia species JS150 was measured and modeled. Both of these compounds can serve as the sole source of carbon and energy for this microorganism. The single-substrate biodegradation kinetics was described well using the Monod model, with model constants of mu(max,T) = 0.39 h(-1) and K(S,T) = 0.011 mM for growth on toluene and mu(max,P) = 0.309 h(-1) and K(S,P) = 0.0054 mM for growth on phenol. Degradation of the mixture of toluene and phenol followed simultaneous utilization kinetics with toluene being the preferred substrate. Toluene was found to inhibit the rate of utilization of phenol while the presence of phenol had little effect on the rate of degradation of toluene. Of the kinetic models that were tested, one developed for microbial degradation of multiple substrates was able to describe substrate interactions and to model the mixture utilization by strain JS150. Simple competitive, noncompetitive, or uncompetitive substrate kinetics were not sufficient to describe the observed inhibitory interactions.

A proposed transient model for cometabolism in biofilm systems

A dynamic model was developed to describe the behaviour of primary and secondary substrates in a biofilm reactor. The model incorporates structured kinetics to describe the generation and consumption of reducing power in the catabolic and respiratory subsystems, respectively. Secondary substrate transformation through oxygenolytic or reductive mechanisms can be modelled under either single or dual limitation of the electron donor and electron acceptor substrates. An example simulation of a theoretical biofilm system was performed.

Analysis of double-substrate limited growth

Mathematical models which relate the growth rate of a microorganism to a single limiting substrate concentration have long been established. In recent years, it has become apparent that, under certain conditions, the growth rate of an organism may be simultaneously limited by two or more substrates. Mathematical models of double-substrate limitation fall into two categories: interactive and noninteractive models. A discussion of both types of models is presented in both conceptual and mathematical terms. An analogous case of an enzyme which requires two different substrates to produce a single product is presented. This enzyme analog indicates that both types of double-substrate limitation models appear to be feasible under certain conditions. Based upon stoichiometry and specific growth rate-substrate concentration contour plots, a method for determining the operational conditions which will lead to double-substrate limitation is presented.