Ioanna Malton (Ontario) coauthored a paper entitled “A mechanistic derivation of the Monod bioreaction equation for a limiting nutrient” that was published in the Journal of Mathematical Biology in Volume 84, Article number 62 on June 23, 2022.

Robert W. Enouy was the lead author, and additional coauthors were Kenneth M. Walton, Kanwartej S. Sra, Natasha N. Sihota, Eric J. Daniels, and Andre J. A. Unger.

Ioanna Malton is a Laboratory Technician based in Guelph, Ontario who joined Geosyntec’s SiREM Lab after completing her studies at the University of Waterloo. She works as a Treatability Lab Technician on bioremediation and chemical remediation of contaminated groundwater and soil.

The Journal of Mathematical Biology focuses on mathematical biology – work that uses mathematical approaches to gain biological understanding or explain biological phenomena. Papers provide biological insight as a result of mathematical analysis or identify and open up challenging new types of mathematical problems that derive from biological knowledge (in the form of data, or theory, or simulation results). Mathematical ideas, methods, techniques, and results are provided and show a sufficient potential for usefulness in a biological context.


We present a quasi-steady state mechanistic derivation of the Monod bioreaction equation based upon a conceptual model involving aqueous phase diffusive transport of substrate towards a spherical microbe; transport of the substrate across its surface membrane; and reaction depleting the substrate within the microbe. The resulting Monod coefficients KS and μmax are dependent upon substrate-species pairs and the mass transfer properties of the system. Two substrate transport scenarios are investigated: (1) a constant rate model that is a function of a constant flux across the surface of the microbe; and (2) a linear rate model that is the product of a constant transport velocity and the concentration of substrate in contact with the surface of the microbe. The model is verified and parameterized using benzene, toluene, and phenol depletion and biomass growth data obtained from Reardon et al. (Biotechnol Bioeng: 385–400, 2000). Calibration results indicate a normalized surface to bulk concentration ratio of nearly unity in all simulations for benzene, toluene, and phenol when paired with P. putida F1, implying that the process is not aqueous phase diffusion limited.

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