A mechanistic mathematical model for photo fermentative hydrogen and polyhydroxybutyrate production

Grazia Policastro; Vincenzo Luongo; Luigi Frunzo; Nick Cogan; Massimiliano Fabbricino; Grazia Policastro; Vincenzo Luongo; Luigi Frunzo; Nick Cogan; Massimiliano Fabbricino

doi:10.3934/mbe.2023321

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 4: 7407-7428. doi: 10.3934/mbe.2023321

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Research article

A mechanistic mathematical model for photo fermentative hydrogen and polyhydroxybutyrate production

1.
Department of Civil, Architectural and Environmental Engineering, University of Naples Federico II, via Claudio 21, 80125 Naples, Italy
2.
Telematic University Pegaso, Piazza Trieste e Trento 48, 80132 Naples, Italy
3.
Department of Mathematics and Applications "Renato Caccioppoli", University of Naples Federico II, via Cintia, Monte S. Angelo, I-80126 Naples, Italy
4.
Department of Mathematics, Florida State University, 208 Love Building, 1017 Academic Way, Tallahassee, FL 32304, USA

Academic Editor: Geng Dong

Received: 06 November 2022 Revised: 07 December 2022 Accepted: 11 December 2022 Published: 15 February 2023

An original mathematical model describing the photo fermentation process is proposed. The model represents the first attempt to describe the photo fermentative hydrogen production and polyhydroxybutyrate accumulation, simultaneously. The mathematical model is derived from mass balance principles and consists of a system of ordinary differential equations describing the biomass growth, the nitrogen and the substrate degradation, the hydrogen and other catabolites production, and the polyhydroxybutyrate accumulation in photo fermentation systems. Moreover, the model takes into account important inhibiting phenomena, such as the self-shading and the substrate inhibition, which can occur during the evolution of the process. The calibration was performed using a real experimental data set and it was supported by the results of a sensitivity analysis study. The results showed that the most sensitive parameters for both hydrogen and PHB production were the hydrogen yield on substrate, the catabolites yield on substrate, and the biomass yield. Successively, a different experimental data set was used to validate the model. Performance indicators showed that the model could efficiently be used to simulate the photo fermentative hydrogen and polyhydroxybutyrate production by Rhodopseudomonas palustris. For instance, the index of agreement of 0.95 was observed for the validated hydrogen production trend. Moreover, the model well predicted the maximum PHB accumulation in bacterial cells. Indeed, the predicted and observed accumulated PHB were 4.5 and 4.8%, respectively. Further numerical simulations demonstrated the model consistency in describing process inhibiting phenomena. Numerical simulations showed that the acetate and nitrogen inhibition phenomena take place when concentrations are higher than 12.44 g L^-1 and lower than 4.76 mg L^-1, respectively. Finally, the potential long term hydrogen production from accumulated polyhydroxybutyrate in bacterial cells was studied via a fast-slow analysis technique.
- photo fermentation,
- ordinary differential equations,
- sensitivity analysis,
- calibration and validation,
- fast-slow analysis
Citation: Grazia Policastro, Vincenzo Luongo, Luigi Frunzo, Nick Cogan, Massimiliano Fabbricino. A mechanistic mathematical model for photo fermentative hydrogen and polyhydroxybutyrate production[J]. Mathematical Biosciences and Engineering, 2023, 20(4): 7407-7428. doi: 10.3934/mbe.2023321

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Abstract

An original mathematical model describing the photo fermentation process is proposed. The model represents the first attempt to describe the photo fermentative hydrogen production and polyhydroxybutyrate accumulation, simultaneously. The mathematical model is derived from mass balance principles and consists of a system of ordinary differential equations describing the biomass growth, the nitrogen and the substrate degradation, the hydrogen and other catabolites production, and the polyhydroxybutyrate accumulation in photo fermentation systems. Moreover, the model takes into account important inhibiting phenomena, such as the self-shading and the substrate inhibition, which can occur during the evolution of the process. The calibration was performed using a real experimental data set and it was supported by the results of a sensitivity analysis study. The results showed that the most sensitive parameters for both hydrogen and PHB production were the hydrogen yield on substrate, the catabolites yield on substrate, and the biomass yield. Successively, a different experimental data set was used to validate the model. Performance indicators showed that the model could efficiently be used to simulate the photo fermentative hydrogen and polyhydroxybutyrate production by Rhodopseudomonas palustris. For instance, the index of agreement of 0.95 was observed for the validated hydrogen production trend. Moreover, the model well predicted the maximum PHB accumulation in bacterial cells. Indeed, the predicted and observed accumulated PHB were 4.5 and 4.8%, respectively. Further numerical simulations demonstrated the model consistency in describing process inhibiting phenomena. Numerical simulations showed that the acetate and nitrogen inhibition phenomena take place when concentrations are higher than 12.44 g L^-1 and lower than 4.76 mg L^-1, respectively. Finally, the potential long term hydrogen production from accumulated polyhydroxybutyrate in bacterial cells was studied via a fast-slow analysis technique.

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