A black box mathematical model to calculate auto- and heterotrophic biomass yields based on Gibbs energy dissipation

On the basis of the estimated Gibbs energy dissipation per C-mol biomass produced and a convenient black box description of microbial growth, a general equation for the calculation of the yield of biomass on electron donor has been obtained. This black box model defines four formal electron donating reactions for biomass, carbon source, electron donor, and electron acceptor. The proposed description leads to a simple equation which gives the biomass yield on electron donor for chemotrophic growth systems under carbon and energy limitation for which biomass is the only anabolic product. The variables involved are the degrees of reduction and the Gibbs energy characteristics of the four compounds, and the required Gibbs energy dissipation per C-mol produced of biomass. It appears that biomass yields on electron donor for auto- and heterotrophic growth under aerobic, denitrifying, and fermentative conditions can be estimated with 10-15% error in a range of Y(DX)-values of 0.01-0.80 C-mol/(C)-mol electron donor. Also, simple regularities in the Gibbs energy and enthalpy of organic substrates are found. Furthermore, simple relations are derived to calculate the thermodynamic maximal biomass yield, conditions required for growth to occur, heat production, biomass yield on electron acceptor, and anaerobic product yield. Finally a new definition of thermodynamic efficiency is derived.