Campus Units

Chemical and Biological Engineering

Document Type


Research Focus Area

Health Care Technology and Biomedical Engineering

Publication Version

Accepted Manuscript

Publication Date


Journal or Book Title

Biotechnology and Bioengineering




An original dynamic model for substrate uptake under transient conditions is established and used to simulate a variety of biological responses to external perturbations. The actual uptake and growth rates, treated as cell properties, are part of the model variables as well as the substrate concentration at the cell‐liquid interface. Several regulatory loops inspired by the structure of the glycolytic chain are considered to establish a set of ordinary differential equations. The uptake rate evolves so as to reach an equilibrium between the cell demand and the environmental supply. This model does not contain any of the usual algebraic closure laws relating the instantaneous uptake, growth rates and the substrate concentration, nor does it enforce the continuity of mass fluxes at the liquid‐cell interface. However, these relationships are found in the steady‐state solution. Previously unexplained experimental observations are well reproduced by this model. Also, the model structure is suitable for further coupling with flux‐based metabolic models and fluid‐flow equations.


This is the peer-reviewed version of the following article: Morchain, Jérôme, Vincent Quedeville, Rodney O. Fox, and Philippe Villedieu. "The closure issue related to liquid‐cell mass transfer and substrate uptake dynamics in biological systems." Biotechnology and Bioengineering (2021), which has been published in final form at DOI: 10.1002/bit.27752. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Posted with permission.

Copyright Owner

Wiley Periodicals, LLC



File Format


Available for download on Sunday, March 13, 2022

Published Version