Mathematical modeling to validate on-line CO2 measurements as a metric for cellulolytic biofilm activity in continuous-flow bioreactors

• A mathematical model for Clostridium thermocellum biofilms on cellulose sheets is formulated.
• The biofilm growth model accounts for CO2 production, as measurement for microbial activity.
• Excellent quantitative agreement between online CO2 measurement data and model is found.
• The utility of CO2 online measurements to assess microbial growth activity is demonstrated.

A mathematical model for the growth of thin Clostridium thermocellum biofilms on cellulose sheets with penetration from the surface into the interior fiber matrix is formulated, and used to assess the potential of CO2 on-line measurements for activity of cellulolytic biofilms. The biofilm growth model is linked to a product formation model. It includes the processes of carbon substrate consumption, biofilm growth, biofilm upkeep, and carbon dioxide production. The mathematical description leads to a system of ordinary differential equations that is simple enough to lend itself to qualitative analysis, yet complex enough to capture the essential features of the system. Numerical fitting of the model against experimental data showed excellent quantitative agreement. The model substantiates the utility of on-line CO2 measurements as indicator of cellulose substrate colonization and consumption, which may be useful for reporting bioreactor performance.