Iterative chemostat: A modelling framework linking biosynthesis to nutrient cycling on ecological and evolutionary time scales

Irakli Loladze ^,

Bryan College of Health Sciences, Bryan Medical Center, Lincoln NE 68506

Received: 23 August 2018 Accepted: 15 November 2018 Published: 30 January 2019

Abstract
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In the classical chemostat, the output of the system has no effect on its input. This contrasts with many ecological systems, where the output at the end of a growing season affects nutrient inputs for subsequent seasons. Here, an iterative-continuous modelling framework is introduced that retains the structure of classical ecological models within each iteration but accounts for nutrient feedbacks between iterations. As an example, the framework is applied to the classical chemostat model, where nutrient outputs affect the supply ratio at each iteration. Furthermore, the biotic parameters in the model, including organismal demands for nitrogen (N) and phosphorus (P), are linked to core biogenic processes—protein and rRNA synthesis. This biosynthesis is further deconstructed into 11 biological constants and rates, most of which are deeply shared among all organisms. By linking the fundamental macromolecular machinery to the cycling of nutrients on the ecosystem scale, the framework enables to rigorously formulate qualitative and quantitative questions about the evolution of nutrient ratios and the existence of stoichiometric attractors, such as the puzzling persistence of the Redfield N:P ratio of 16 in the ocean. While the framework presented here is theoretical, it readily permits setting up empirical experiments for testing its predictions.
- chemostat,
- Redfield ratio,
- nitrogen,
- plankton,
- nutrient cycling,
- mathematical model,
- nucleotide,
- amino acid,
- ribosome,
- RNA polymerase
Citation: Irakli Loladze. Iterative chemostat: A modelling framework linking biosynthesis to nutrient cycling on ecological and evolutionary time scales[J]. Mathematical Biosciences and Engineering, 2019, 16(2): 990-1004. doi: 10.3934/mbe.2019046

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Abstract

In the classical chemostat, the output of the system has no effect on its input. This contrasts with many ecological systems, where the output at the end of a growing season affects nutrient inputs for subsequent seasons. Here, an iterative-continuous modelling framework is introduced that retains the structure of classical ecological models within each iteration but accounts for nutrient feedbacks between iterations. As an example, the framework is applied to the classical chemostat model, where nutrient outputs affect the supply ratio at each iteration. Furthermore, the biotic parameters in the model, including organismal demands for nitrogen (N) and phosphorus (P), are linked to core biogenic processes—protein and rRNA synthesis. This biosynthesis is further deconstructed into 11 biological constants and rates, most of which are deeply shared among all organisms. By linking the fundamental macromolecular machinery to the cycling of nutrients on the ecosystem scale, the framework enables to rigorously formulate qualitative and quantitative questions about the evolution of nutrient ratios and the existence of stoichiometric attractors, such as the puzzling persistence of the Redfield N:P ratio of 16 in the ocean. While the framework presented here is theoretical, it readily permits setting up empirical experiments for testing its predictions.

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