The Gibbs Free Energy Threshold for the Invasion of a Microbial Population Under Kinetic Constraints

Abstract

Possible chemotrophic metabolism at a site of interest is controlled not only by the catabolic energy expressed as the Gibbs energy of reaction (Δ_rG) but also by the kinetic constraints due to the availability of electron acceptors and donors. We introduced graphical and stochastic approaches for determining the Δ_rG threshold required to support a microbial population with a specific catabolic strategy under kinetic constraints. Invasibility as an indicator of the present reproductive ability of a microbial population was evaluated by simultaneously calculating Δ_rG for the catabolic reaction and the microbial catalytic rate. For example, the neutrophilic iron-oxidizing bacteria's invasibility was calculated by randomly choosing the Fe²⁺ and O₂ concentrations between 10⁻⁸ and 10⁻² mol L⁻¹, and pH between 4 and 8, to determine the Δ_rG threshold for invasion. Parameters were estimated from batch experiments of neutrophilic iron-oxidizing bacteria reported in previous studies. Under the given conditions, the stochastic approach predicted that the neutrophilic iron-oxidizing bacteria can always invade a system in which the Δ_rG for Fe oxidation is below −90 kJ mol Fe⁻¹, can occasionally invade if Δ_rG is between −45 and −90 kJ mol Fe⁻¹, and can never invade if Δ_rG is above −45 kJ mol Fe⁻¹. The Δ_rG threshold for invasion is sifted by the growth yield coefficient, the loss rate of cells, the maximum cell-specific Fe oxidation rate constant, and the temperature. The Δ_rG threshold for invasion may be unable to rigorously predict the stable dominance of microbial metabolism, but can provide a rough indication for the possible microbial metabolism under current conditions.

Keywords:

• energetics of microbial metabolism
• reaction kinetics
• Δ_rG threshold
• neutrophilic iron-oxidizing bacteria

Acknowledgments

We are especially thankful to two anonymous reviewers for their constructive comments. We are grateful to Dr. Philippe Van Cappellen, Dr. William Ghiorse, and Dr. Yuri Gorby for stimulating discussions.

Additional information

Funding

This work was supported by a Grant-in-Aid for Young Scientists (B), 23770024.