The closure issue related to liquid–cell mass transfer and substrate uptake dynamics in biological systems

Abstract

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 to 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.

A Monte‐Carlo approach for the simulation of microbial population dynamics in an heterogeneous scale‐down bioreactor

“…The comparison can be found in Data S1. However, using uncouples the uptake and growth rates from substrate concentration which is crucial for the description of the cell response to external fluctuations 40 . Note that at steady state, the values of , , and (and , not shown here) form a quadruplet of consistent values, corresponding to a balanced metabolism.…”

Modeling large‐scale bioreactors with diffusion equations. Part II: Characterizing substrate, oxygen, temperature, carbon dioxide, and pH profiles

“…The linearized kinetics alleviate this to some extent by allowing the uptake rate to exceed the conventional maximal uptake rate set by the standard Monod kinetics. The multiple uptake systems existing in the considered microorganisms were all represented here by a single rate expression, which is a conventional choice despite neglecting an inherent biological feature (Morchain et al, 2021). The net uptake rate of the various substrate uptake systems with different affinities in an adapted population is often quite well represented by a single Monod‐ or Michaelis–Menten‐type expression both in E. coli (Quedeville et al, 2018) and S. cerevisiae (Youk & van Oudenaarden, 2009), though.…”