Saturating growth rate against phosphorus concentration explained by macromolecular allocation

Abstract

The Monod equation has been used to represent the relationship between growth rate and the environmental nutrient concentration under the limitation of this respective nutrient. This model often serves as a means to connect microorganisms to their environment, specifically in ecosystem and global models. Here, we use a simple model of a marine microorganism cell to illustrate the model's ability to capture the same relationship as Monod, while highlighting the additional physiological details our model provides. In this study, we focus on the relationship between growth rate and phosphorus concentration and find that RNA allocation largely contributes to the commonly observed trend. This work emphasizes the potential role our model could play in connecting microorganisms to the surrounding environment while using realistic physiological representations.

Keywords: DNA; Monod kinetics; RNA; carbohydrate; growth; lipid; macromolecular allocation; nutrient; nutrient storage; phytoplankton; protein.

Fig 1

The Cell Flux Model of Phytoplankton (CFM-Phyto) under P limitation. The model allocates carbon (maroon) and phosphorus (olive) to four intracellular macromolecular pools: biosynthesis (teal), photosynthesis (pink), essential (purple), and storage (yellow). Each macromolecule requires varying levels of C and P (24), indicated by the bar below the macromolecule. When C is limited, there is no allocation of C to storage. The essential pool represents macromolecules needed for basic cell survival and structure and is assumed to remain constant with growth rate.

Fig 2

Measured (maroon points) and predicted growth rates with increasing PO₄ ³⁻ using the Cell Flux Model of Phytoplankton (CFM-Phyto; black line) and the Monod formulation (dotted teal line) for various organisms (A) Microcystis (18), (B) Chorella sp. (20), (C) Nitzschia palea (20), (D) Oocystis pusilla (20), (E) Scenedesmus quadricauda (20), (F) Sphaerocystis schroeteri (20), (G) Synechocystis sp. PCC6803 (19), and (H) Pelagomonas capsulatus (17).

Fig 3

An example of simulated growth rate and macromolecular allocation produced by the cell flux model of phytoplankton (CFM-Phyto). (A) Growth rate. (B) Macromolecular allocation based on P (per cellular C). (C) C-based macromolecular allocation. The overall patterns of the relationships are conserved across the simulations.

Fig 4

Species-specific predictions of macromolecular allocation of P to three cellular pools: RNA (green), photosynthetic molecules (orange), and other (blue). Other molecules include DNA and remaining P. (A) Microcystis (18), (B) Chorella sp. (20), (C) Nitzschia palea (20), (D) Oocystis pusilla (20), (E) Scenedesmus quadricauda (20), (F) Sphaerocystis schroeteri (20), (G) Synechocystis sp. PCC6803 (19), and (H) Pelagomonas capsulatus (17).

Fig 5

The Cell Flux Model of Phytoplankton (CFM-Phyto) predicts growth rate (μ) with increasing phosphate concentration (PO₄ ³⁻) for various environmental conditions including light intensity. (A) Darker colors represent higher light intensity or temperature. CFM-Phyto also predicts macromolecular allocation of phosphorus under nitrogen limitation (B).

Fig 6

Comparison of growth with increasing nutrient concentrations (A) of PO₄ ³⁻ (solid, teal line) and NO₃ ⁻ (dashed, maroon line) for the respective nutrient limitation (i.e., P and N limitation) normalized to the cellular ratios of phosphorus using a typical nutrient ratio (30) (i.e., dividing N by 15). (B) Comparisons of intracellular P:C (teal) (Mol P mol C⁻¹) and N:C (maroon) (Mol N mol C⁻¹) for increasing growth rate.