Optimal control and Bayes inference applied to complex microbial communities

Jhoana P. Romero-Leiton; Kernel Prieto; Daniela Reyes-Gonzalez; Ayari Fuentes-Hernandez; Jhoana P. Romero-Leiton; Kernel Prieto; Daniela Reyes-Gonzalez; Ayari Fuentes-Hernandez

doi:10.3934/mbe.2022323

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 7: 6860-6882. doi: 10.3934/mbe.2022323

Previous Article Next Article

Research article Special Issues

Optimal control and Bayes inference applied to complex microbial communities

1.
Engineering Faculty, Cesmag University, Pasto, Colombia
2.
Design and Visual Arts Department, Georgian College, Barrie, Canada
3.
Center for Genomic Sciences, National Autonomous University of Mexico, Cuernavaca, Mexico

Academic Editor: Cristiana J. Silva

Received: 09 January 2022 Revised: 21 March 2022 Accepted: 30 March 2022 Published: 07 May 2022

Interactions between species are essential in ecosystems, but sometimes competition dominates over mutualism. The transition between mutualism-competition can have several implications and consequences, and it has hardly been studied in experimental settings. This work studies the mutualism between cross-feeding bacteria in strains that supply an essential amino acid for their mutualistic partner when both strains are exposed to antimicrobials. When the strains are free of antimicrobials, we found that, depending on the amount of amino acids freely available in the environment, the strains can exhibit extinction, mutualism, or competition. The availability of resources modulates the behavior of both species. When the strains are exposed to antimicrobials, the population dynamics depend on the proportion of bacteria resistant to the antimicrobial, finding that the extinction of both strains is eminent for low levels of the resource. In contrast, competition between both strains continues for high levels of the resource. An optimal control problem was then formulated to reduce the proportion of resistant bacteria, which showed that under cooperation, both strains (sensitive and resistant) are immediately controlled, while under competition, only the density of one of the strains is decreased. In contrast, its mutualist partner with control is increased. Finally, using our experimental data, we did parameters estimation in order to fit our mathematical model to the experimental data.
- antimicrobials,
- sensitive bacteria,
- resistant bacteria,
- amino acids,
- cross-feeding bacteria,
- mutualism,
- competition,
- experimental data,
- parameter estimation
Citation: Jhoana P. Romero-Leiton, Kernel Prieto, Daniela Reyes-Gonzalez, Ayari Fuentes-Hernandez. Optimal control and Bayes inference applied to complex microbial communities[J]. Mathematical Biosciences and Engineering, 2022, 19(7): 6860-6882. doi: 10.3934/mbe.2022323

Related Papers:

Abstract

Interactions between species are essential in ecosystems, but sometimes competition dominates over mutualism. The transition between mutualism-competition can have several implications and consequences, and it has hardly been studied in experimental settings. This work studies the mutualism between cross-feeding bacteria in strains that supply an essential amino acid for their mutualistic partner when both strains are exposed to antimicrobials. When the strains are free of antimicrobials, we found that, depending on the amount of amino acids freely available in the environment, the strains can exhibit extinction, mutualism, or competition. The availability of resources modulates the behavior of both species. When the strains are exposed to antimicrobials, the population dynamics depend on the proportion of bacteria resistant to the antimicrobial, finding that the extinction of both strains is eminent for low levels of the resource. In contrast, competition between both strains continues for high levels of the resource. An optimal control problem was then formulated to reduce the proportion of resistant bacteria, which showed that under cooperation, both strains (sensitive and resistant) are immediately controlled, while under competition, only the density of one of the strains is decreased. In contrast, its mutualist partner with control is increased. Finally, using our experimental data, we did parameters estimation in order to fit our mathematical model to the experimental data.

References

[1]	T. A. Hoek, K. Axelrod, T. Biancalani, E. A. Yurtsev, J. Liu, J. Gore, Resource availability modulates the cooperative and competitive nature of a microbial cross-feeding mutualism, PLoS Biol., 14 (2016), e1002540. https://doi.org/10.1371/journal.pbio.1002540 doi: 10.1371/journal.pbio.1002540
[2]	E. Toby Kiers, T. M. Palmer, A. R. Ives, J. F. Bruno, J. L. Bronstein, Mutualisms in a changing world: an evolutionary perspective, Ecol. Lett., 13 (2010), 1459–1474. https://doi.org/10.1111/j.1461-0248.2010.01538.x doi: 10.1111/j.1461-0248.2010.01538.x
[3]	A. R. Figueiredo, R. Kümmerli, Microbial mutualism: Will you still need me, will you still feed me?, Curr. Biol., 30 (2020), R1041–R1043. https://doi.org/10.1016/j.cub.2020.07.002 doi: 10.1016/j.cub.2020.07.002
[4]	K. Zengler, L. S. Zaramela, The social network of microorganisms - how auxotrophies shape complex communities, Nat. Rev. Microbiol., 16 (2018), 383–390. https://doi.org/10.1038/s41579-018-0004-5 doi: 10.1038/s41579-018-0004-5
[5]	W. M. Johnson, H. Alexander, R. L. Bier, D. R. Miller, M. E. Muscarella, K. J. Pitz, et al., Auxotrophic interactions: a stabilizing attribute of aquatic microbial communities?, FEMS Microbiol. Ecol., 96 (2020), fiaa115. https://doi.org/10.1093/femsec/fiaa115 doi: 10.1093/femsec/fiaa115
[6]	X. Jiang, C. Zerfaß, S. Feng, R. Eichmann, M. Asally, P. Schäfer, et al., Impact of spatial organization on a novel auxotrophic interaction among soil microbes, ISME J., 12 (2018), 1443–1456. https://doi.org/10.1038/s41396-018-0095-z doi: 10.1038/s41396-018-0095-z
[7]	X. Zhu, S. Campanaro, L. Treu, R. Seshadri, N. Ivanova, P. G. Kougias, et al., Metabolic dependencies govern microbial syntrophies during methanogenesis in an anaerobic digestion ecosystem, Microbiome, 8 (2020), 22. https://doi.org/10.1186/s40168-019-0780-9 doi: 10.1186/s40168-019-0780-9
[8]	A. E. Douglas, The microbial exometabolome: ecological resource and architect of microbial communities, Philos. Trans. R. Soc. Lond. B Biol. Sci., 375 (2020), 20190250, https://doi.org/10.1098/rstb.2019.0250 doi: 10.1098/rstb.2019.0250
[9]	A. Dal Co, C. Brannon, M. Ackermann, Division of labor in bacteria, Elife, 7 (2018), e38578. https://doi.org/10.7554/eLife.38578 doi: 10.7554/eLife.38578
[10]	G. D'Souza, C. Kost, Experimental evolution of metabolic dependency in bacteria, PLoS Genet., 12 (2016), e1006364. https://doi.org/10.1371/journal.pgen.1006364 doi: 10.1371/journal.pgen.1006364
[11]	M. A. Henson, P. Phalak, Suboptimal community growth mediated through metabolite crossfeeding promotes species diversity in the gut microbiota, PLoS Comput. Biol., 14 (2018), e1006558. https://doi.org/10.1371/journal.pcbi.1006558 doi: 10.1371/journal.pcbi.1006558
[12]	W. H. Fleming, R. W. Rishel, Deterministic and stochastic optimal control, Springer Science and Business Media, 2012.
[13]	S. Lenhart, J. T. Workman, Optimal control applied to biological models, Chapman and Hall/CRC, 2007.
[14]	H. Mena, L. M. Pfurtscheller, J. P. Romero-Leiton, Random perturbations in a mathematical model of bacterial resistance: Analysis and optimal control, Math. Biosci. Eng., 17 (2020), 4477–4499, https://doi.org/10.3934/mbe.2020247 doi: 10.3934/mbe.2020247
[15]	T. Baba, T. Ara, M. Hasegawa, Y. Takai, Y. Okumura, M. Baba, et al., Construction of escherichia coli k-12 in-frame, single-gene knockout mutants: the keio collection, Mol. Syst. Biol., 2, https://doi.org/10.1038/msb4100050
[16]	A. San Millan, J. A. Escudero, D. R. Gifford, D. Mazel, R. C. MacLean, Multicopy plasmids potentiate the evolution of antibiotic resistance in bacteria, Nat. Ecol. Evol., 1 (2016), 1–8. https://doi.org/10.1038/s41559-016-0010 doi: 10.1038/s41559-016-0010
[17]	O. Stojanović, J. Leugering, G. Pipa, S. Ghozzi, A. Ullrich, A Bayesian Monte Carlo approach for predicting the spread of infectious diseases, PLoS ONE, 14 (2019), e0225838. https://doi.org/10.1371/journal.pone.0225838 doi: 10.1371/journal.pone.0225838
[18]	T. Luzyanina, G. Bocharov, Markov chain Monte Carlo parameter estimation of the ODE compartmental cell growth model, Math. Biol. Bioinfor., 13 (2018), 376–391.
[19]	G. Brown, A. Porter, J. Oleson, J. Hinman, Approximate Bayesian computation for spatial SEIR(S) epidemic models, Spat. Spatiotemporal Epidemiology, 24 (2018), 2685–2697, https://doi.org/10.1016/j.sste.2017.11.001 doi: 10.1016/j.sste.2017.11.001
[20]	E. Ibarguen-Mondragon, K. Prieto, S. Hidalgo-Bonilla, A model on bacterial resistance considering a generalized law of mass action for plasmid replication, J. Biol. Syst., 29 (2021), 375–412. https://doi.org/10.1142/S0218339021400118 doi: 10.1142/S0218339021400118
[21]	K. Prieto, J. P. Romero–Leiton, Current forecast of HIV/AIDS using Bayesian inference, Nat. Resour. Model., 34 (2021), e12332, https://doi.org/10.1111/nrm.12332 doi: 10.1111/nrm.12332
[22]	B. Carpenter, A. Gelman, D. Hoffman, B. Goodrich, M. Betancourt, M. Brubaker, et. al., Stan: A probabilistic programming language, J. Stat. Softw., 76 (2017), 1–32. https://doi.org/10.18637/jss.v076.i01 doi: 10.18637/jss.v076.i01
[23]	J. Riaño-Moreno, J. P. Romero-Leiton, K. Prieto, Contribution of governance and socioeconomic factors to the P. aeruginosa MDR in Europe, Antibiotics, 11 (2022), 212. https://doi.org/10.3390/antibiotics11020212 doi: 10.3390/antibiotics11020212
[24]	T. Netzker, M. Flak, M. K. Krespach, M. C. Stroe, J. Weber, V. Schroeckh, et. al., Microbial interactions trigger the production of antibiotics, Curr. Opin. Microbiol., 45 (2018), 117–123. https://doi.org/10.1016/j.mib.2018.04.002 doi: 10.1016/j.mib.2018.04.002
[25]	C. Zhang, P. D. Straight, Antibiotic discovery through microbial interactions, Curr. Opin. Microbiol., 51 (2019), 64–71, https://doi.org/10.1016/j.mib.2019.06.006 doi: 10.1016/j.mib.2019.06.006
[26]	T. Van Raay, E. Allen-Vercoe, Microbial interactions and interventions in colorectal cancer, Microbiol. Spectr., 5 (2017). https://doi.org/10.1128/microbiolspec.BAD-0004-2016 doi: 10.1128/microbiolspec.BAD-0004-2016
[27]	W. C. Ratcliff, R. F. Denison, Alternative actions for antibiotics, Science, 332 (2011), 547–548. https://doi.org/10.1126/science.1205970 doi: 10.1126/science.1205970

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)