Mathematical modeling of lipase and protease production by Penicillium restrictum in a batch fermenter

This work presents a mathematical model that describes time course variations of extracellular lipase and protease activities for the batch fermentation of the fungus Penicillium restrictum, a new and promising strain isolated from soil and wastes of a Brazilian babassu coconut oil industry. The fermentation process was modeled by an unstructured model, which considered the following dependent variables: cells, fat acid, dissolved oxygen concentrations, lipase and protease activities, and cell lysate concentration. The last variable represents the amount of cells that has been lysed by the shear stress and natural cell death. Proteases released to the medium, as consequence of this process, enhance lipase inactivation. The model is able to predict the effects of some operation variables such as air flow rate and agitation speed. The mathematical model was validated against batch-fermentation data obtained under several operating conditions. Because substrate concentration has antagonistic effects on lipase activity, a typical optimization scheme should be developed in order to minimize these deleterious effects while maximizing lipase activity.