A Mechanistic Investigation of the Algae Growth “Droop” Model

Abstract

In this work a mechanistic explanation of the classical algae growth model built by M. R. Droop in the late sixties is proposed. We first recall the history of the construction of the "predictive" variable yield Droop model as well as the meaning of the introduced cell quota. We then introduce some theoretical hypotheses on the biological phenomena involved in nutrient storage by the algae that lead us to a "conceptual" model. Though more complex than Droop's one, our model remains accessible to a complete mathematical study: its confrontation to the Droop model shows both have the same asymptotic behavior. However, while Droop's cell quota comes from experimental bio-chemical measurements not related to intra-cellular biological phenomena, its analogous in our model directly follows our theoretical hypotheses. This new model should then be looked at as a re-interpretation of Droop's work from a theoretical biologist's point of view.

Demonstration of a two-stage aerobic/anaerobic chemostat for the enhanced production of hydrogen and biomass from unicellular nitrogen-fixing cyanobacterium

“…(8), has been frequently and effectively used to fit kinetic parameters to algal growth and nutrient uptake data [23,42]. For the modelling of nutrient uptake, [C total ] represents the total consumption of a particular nutrient.…”

A fast and systematic procedure to develop dynamic models of bioprocesses: application to microalgae cultures

“…Indeed, rather than directly depending on the external substrate concentrations, their growth rate varies as a function of the concentration of intracellular nutrients. The dynamic model considered in this example was developed by Lemesle and Mailleret (2008) as a mechanistic reformulation of the well-known Droop model that represents the limitation of growth by a single substrate.…”

A Linear Programming Approach for Modeling and Simulation of Growth and Lipid Accumulation of Phaeodactylum tricornutum

“…The internal quota of the limiting element subsequently affects cell growth and lipid accumulation. Despite the high relevance of the model, the interpretation of the variable "cell quota" and its mechanistic implications were questioned by Lemesle [18]. In this context, we present a structured approach to model the physiological response of P. tricornutum to a nutrient limitation by simulation.…”