A mathematical model of the Warburg Effect: Effects of cell size, shape and substrate availability on growth and metabolism in bacteria

Anshuman Swain; William F Fagan; Anshuman Swain; William F Fagan

doi:10.3934/mbe.2019009

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 1: 168-186. doi: 10.3934/mbe.2019009

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A mathematical model of the Warburg Effect: Effects of cell size, shape and substrate availability on growth and metabolism in bacteria

Anshuman Swain ^,,
William F Fagan

Department of Biology, University of Maryland, College Park, MD 20742, USA

Received: 14 March 2018 Accepted: 05 October 2018 Published: 11 December 2018

The Warburg effect refers to a curious behavior observed in many organisms and cell types including cancer cells, yeast and bacteria, wherein both the efficient aerobic pathway and the inefficient fermentation pathway are utilized for respiration, despite the presence of ample oxygen. Also termed as overflow metabolism in bacteria, this phenomena has remained an enigmatic and poorly understood phenomenon despite years of experimental work. Here, we focus on bacterial cells and build a model of three trade offs involved in the utilization of aerobic and anaerobic respiration pathways (rate versus yield, surface area versus volume, and fast versus slow biomass production) to explain the observed behavior in cellular systems. The model so constructed also predicts changes in the relative usage of both pathways in terms of size and shape constraints of the cell, and identifies how substrate availability influences growth rate. Additionally, we use the model to explain certain complex phenomena in modern- and paleo-ecosystems, via the concept of overflow metabolism.
- linear optimization,
- Warburg effect,
- substrate allocation,
- bacteria,
- overflow metabolism
Citation: Anshuman Swain, William F Fagan. A mathematical model of the Warburg Effect: Effects of cell size, shape and substrate availability on growth and metabolism in bacteria[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 168-186. doi: 10.3934/mbe.2019009

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Abstract

The Warburg effect refers to a curious behavior observed in many organisms and cell types including cancer cells, yeast and bacteria, wherein both the efficient aerobic pathway and the inefficient fermentation pathway are utilized for respiration, despite the presence of ample oxygen. Also termed as overflow metabolism in bacteria, this phenomena has remained an enigmatic and poorly understood phenomenon despite years of experimental work. Here, we focus on bacterial cells and build a model of three trade offs involved in the utilization of aerobic and anaerobic respiration pathways (rate versus yield, surface area versus volume, and fast versus slow biomass production) to explain the observed behavior in cellular systems. The model so constructed also predicts changes in the relative usage of both pathways in terms of size and shape constraints of the cell, and identifies how substrate availability influences growth rate. Additionally, we use the model to explain certain complex phenomena in modern- and paleo-ecosystems, via the concept of overflow metabolism.

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