Quantifying <i>Geobacter sulfurreducens</i> growth: A mathematical model based on acetate concentration as an oxidizing substrate

Virgínia Villa-Cruz; Sumaya Jaimes-Reátegui; Juana E. Alba-Cuevas; Lily Xochilt Zelaya-Molina; Rider Jaimes-Reátegui; Alexander N. Pisarchik; Virgínia Villa-Cruz; Sumaya Jaimes-Reátegui; Juana E. Alba-Cuevas; Lily Xochilt Zelaya-Molina; Rider Jaimes-Reátegui; Alexander N. Pisarchik

doi:10.3934/mbe.2024263

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 5: 5972-5995. doi: 10.3934/mbe.2024263

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Quantifying Geobacter sulfurreducens growth: A mathematical model based on acetate concentration as an oxidizing substrate

1.
Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Díaz de León 1144, Colonia Paseos de la Montaña, 47460 Lagos de Moreno, Jalisco, Mexico
2.
Universidad Nacional Hermilio Valdizán, Av. Universitaria, 601-607, Pilco Marca, C.P. 10003, Huánuco, Perú
3.
Centro Nacional de Recursos Genéticos, Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias, Boulevard de la Biodiversidad No. 400, Rancho Las Cruces, CP 47600. Tepatitlán de Morelos, Jalisco, Mexico
4.
Center for Biomedical Technology, Universidad Politécnica de Madrid, Campus de Montegancedo, Pozuelo de Alarcón, 28223 Madrid, Spain

Received: 06 March 2024 Revised: 30 April 2024 Accepted: 07 May 2024 Published: 17 May 2024

We developed a mathematical model to simulate dynamics associated with the proliferation of Geobacter and ultimately optimize cellular operation by analyzing the interaction of its components. The model comprises two segments: an initial part comprising a logistic form and a subsequent segment that incorporates acetate oxidation as a saturation term for the microbial nutrient medium. Given that four parameters can be obtained by minimizing the square root of the mean square error between experimental Geobacter growth and the mathematical model, the model underscores the importance of incorporating nonlinear terms. The determined parameter values closely align with experimental data, providing insights into the mechanisms that govern Geobacter proliferation. Furthermore, the model has been transformed into a scaleless equation with only two parameters to simplify the exploration of qualitative properties. This allowed us to conduct stability analysis of the fixed point and construct a co-dimension two bifurcation diagram.
- Geobacter,
- model,
- microbial growth,
- nonlinear dynamics,
- fixed point,
- bifurcation
Citation: Virgínia Villa-Cruz, Sumaya Jaimes-Reátegui, Juana E. Alba-Cuevas, Lily Xochilt Zelaya-Molina, Rider Jaimes-Reátegui, Alexander N. Pisarchik. Quantifying Geobacter sulfurreducens growth: A mathematical model based on acetate concentration as an oxidizing substrate[J]. Mathematical Biosciences and Engineering, 2024, 21(5): 5972-5995. doi: 10.3934/mbe.2024263

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Abstract

We developed a mathematical model to simulate dynamics associated with the proliferation of Geobacter and ultimately optimize cellular operation by analyzing the interaction of its components. The model comprises two segments: an initial part comprising a logistic form and a subsequent segment that incorporates acetate oxidation as a saturation term for the microbial nutrient medium. Given that four parameters can be obtained by minimizing the square root of the mean square error between experimental Geobacter growth and the mathematical model, the model underscores the importance of incorporating nonlinear terms. The determined parameter values closely align with experimental data, providing insights into the mechanisms that govern Geobacter proliferation. Furthermore, the model has been transformed into a scaleless equation with only two parameters to simplify the exploration of qualitative properties. This allowed us to conduct stability analysis of the fixed point and construct a co-dimension two bifurcation diagram.

References

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