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.
Subject(s)
Bioreactors , Computer Simulation , Models, BiologicalABSTRACT
The cell-age and interdivision-time probability density functions (PDFs) have been extensively investigated since the 1940s due to their fundamental role in cell growth. The pioneering work of Powell established the first relationship between the interdivision-time and cell-age PDFs. In the literature, two definitions for the interdivision-time PDF have been proposed. One stands for the age-at-rupture PDF and is experimentally observable, whereas the other is the probability density that a cell divides at a certain age and is unobservable. From Powell's results pertaining to the unobservable interdivision-time PDF, Painter and Marr derived an inequality that is true but is incorrectly used by experimentalists to analyse single-cell data. Unfortunately, the confusion between these two PDFs persists. To dissipate this confusion, exact relationships between the cell-age and the interdivision-time PDFs are derived in this work from an age-structured model, which can be used by experimentalists to analyse cell growth in batch and continuous culture modes.
