A Physiologically Structured Equation to Consider Quota Heterogeneity in the Droop Model

Type Article
Date 2019
Language English
Author(s) Mairet FrancisORCID1, Baron RegisORCID2
Affiliation(s) 1 : IFREMER, Physiol & Biotechnol Algae Lab, Rue Ile Yeu, F-44311 Nantes, France.
2 : IFREMER, Unite Biotechnol & Ressources Marines, Rue Ile Yeu, F-44311 Nantes, France.
Meeting 8th Conference on Foundations of Systems Biology in Engineering (FOBSE), Valencia, SPAIN, OCT 15-18, 2019
Source Ifac Papersonline (2405-8963) (Elsevier), 2019 , Vol. 52 , N. 26 , P. 275-280
DOI 10.1016/j.ifacol.2019.12.270
Keyword(s) Population Balance Model, Variable-yield model, Cell Quota, Phytoplankton, Microalgae
Abstract

The Droop model allows to represent microalgae growth limited by a nutrient, using a cell quota (also referred to as variable-yield) approach. Single-cell measurements have revealed quota heterogeneity in phytoplankton collected from field studies. Such heterogeneity can be due, among other factors, to spatial structure (e.g. in biogeochemical cycles in the ocean, or for photobioreactors connected in series). Nonetheless, quota heterogeneity is generally omitted in modelling studies, using an average quota approach, or included in size-structured or individual-based models. Here, we propose a distributed Droop equation to tackle this problem, considering subpopulation growth -in line with Droop macroscopic view- rather than cell division dynamics. We provide analytical solutions for two case studies. First, we consider a constant substrate concentration without biomass input, which leads to a monomorphic population. The second case, considering a biomass input without substrate, leads to quota heterogeneity. Simulations are then carried out for the two case studies (showing good agreements with the analytical solutions) and for a more general case. Finally, we show that the error induced by the average quota approach increases considerably with microalgae plasticity (i.e. the maximal over minimal quota ratio), which points out the benefit of considering quota heterogeneity in these cases.

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