Abstract
We present a framework to model microbial transformations in chemostats and retentostats under transient or quasi-steady state conditions. The model accounts for transformation-induced isotope fractionation and mass-transfer across the cell membrane. It also verifies that the isotope fractionation ϵ can be evaluated as the difference of substrate-specific isotope ratios between inflow and outflow. We explicitly considered that the dropwise feeding of substrate into the reactor at very low dilution rates leads to transient behavior of concentrations and transformation rates and use this information to validate conditions under which a quasi-steady state treatment is justified. We demonstrate the practicality of the code by modeling a chemostat experiment of atrazine degradation at low dilution/growth rates by the strain Arthrobacter aurescens TC1. Our results shed light on the interplay of processes that control biodegradation and isotope fractionation of contaminants at low (μg/L) concentration levels. With the help of the model, an estimate of the mass-transfer coefficient of atrazine through the cell membrane was achieved (0.0025 s(-1)).