Comparing the Effects of Interactive and Noninteractive Complementary Nutrients on Growth in a Chemostat

Abstract

We compare the effects of interactive and noninteractive complementary nutrients on the growth of an organism in the chemostat. We also compare these two situations to the case when the nutrients are substitutable. In previous studies, complementary nutrients have been assumed to be noninteractive. However, more recent research indicates that some complementary nutrient relationships are interactive. We show that interactive complementary and substitutable nutrients can lead to higher population densities than do noninteractive complementary nutrients. We numerically illustrate that if the washout rate is high, an organism can persist at higher densities when the complementary nutrients are interactive than when they are noninteractive, which can result in the extinction of the organism. Finally, we present an example by making a small adjustment to the model that leads to a single nutrient model with an intermediate metabolite of the original substrate as the nutrient for the organism.

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J. Braselton, M. Abell and L. Braselton, "Comparing the Effects of Interactive and Noninteractive Complementary Nutrients on Growth in a Chemostat," Open Journal of Applied Sciences, Vol. 3 No. 5, 2013, pp. 323-331. doi: 10.4236/ojapps.2013.35042.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] S. R. Hansen and S. P. Hubbell, “Single Nutrient Microbial Competition: Agreement between Experimental and Theoretical Forecast Outcomes,” Science, Vol. 20, No. 4438, 1980, pp. 1491-1493. http://dx.doi.org/10.1126/science.6767274
[2] H. L. Smith and P. Waltman, “The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge Studies in Mathematical Biology,” Cambridge University Press, Cambridge, 1995. http://dx.doi.org/10.1017/CBO9780511530043
[3] C. P. L. Grady, Jr., G. T. Daigger and H. C. Lim, “Biological Wastewater Treatment,” Second Edition, revised and expanded, Marcel Dekker, New York, 1999.
[4] U. Lendenmann and T. Egli, “Kinetic Models for the Growth of Escherichia Coli with Mixtures of Sugars Under Carbon-Limited Conditions,” Biotechnology and Bioengineering, Vol. 59, No. 1, 1998, pp. 99-107. http://dx.doi.org/10.1002/(SICI)1097-0290(19980705)59:1<99::AID-BIT13>3.0.CO;2-Y
[5] P. G. Stroot, P. E. Saikaly and D. B. Oerther, “Dynamic Growth Rates of Microbial Populations in Activated Sludge Systems,” Journal of Environmental Engineering, Vol. 131, No. 12, 2005, pp. 1698-1705. http://dx.doi.org/10.1061/(ASCE)0733-9372(2005)131:12(1698)
[6] W. Bae and B. E. Rittmann, “Effects of Electron Acceptor and Electron Donor on Biodegradation of CC14 by Biofilms,” Environmental Engineering: Proceedings of the 1990 Specialty Conference, American Society of Civil Engineers, New York, 1990, pp. 390-395.
[7] J. L. Sherwood, J. N. Petersen, R. S. Skeen and N. B. Valentine, “Effects of Nitrate and Acetate Availability on Chloroform Production during Carbon Tetrachloride Destruction,” Biotechnology and Bioengineering, Vol. 51, No. 5, 1996, pp. 551-557. http://dx.doi.org/10.1002/(SICI)1097-0290(19960905)51:5<551::AID-BIT7>3.0.CO;2-B
[8] D. V. Vayenas and S. Pavlou, “Coexistence of Three Microbial Populations Competing for Three COMPLEMENTARY Nutrients in a Chemostat,” Mathematical Biosciences, Vol. 161, No. 1-2, 1999, pp. 1-13. http://dx.doi.org/10.1016/S0025-5564(99)00040-1
[9] L.-M. Whang, C.-J. Hsiao and S.-S. Cheng, “A Dual-Substrate Steady-State Model for Biological Hydrogen Production in an Anaerobic Hydrogen Fermentation Process,” Biotechnology and Bioengineering, Vol. 95, No. 3, 2006, pp. 492-500. http://dx.doi.org/10.1002/bit.21041
[10] P. M. Bapat, S. Bhartiya, K. V. Venkatesh and P. Wangikar, “Structured Kinetic Model to Represent the Utilization of Multiple Substrates in Complex Media During Rifamycin B Fermentation,” Biotechnology and Bioengineering, Vol. 93, No. 4, 2006, pp. 779-790. http://dx.doi.org/10.1002/bit.20767
[11] P. Champagne, P. J. Van Geel and W. J. Parker, “A Proposed Transient Model for Cometabolism in Ciofilm Systems,” Biotechnology and Bioengineering, Vol. 60, No. 5, 1998, pp. 541-550. http://dx.doi.org/10.1002/(SICI)1097-0290(19981205)60:5<541::AID-BIT4>3.0.CO;2-Q
[12] W. Bae and B. E. Rittmann, “A Structured Model of Dual-Limitation Kinetics,” Biotechnology and Bioengineering, Vol. 49, No. 6, 1996, pp. 683-689. http://dx.doi.org/10.1002/(SICI)1097-0290(19960320)49:6<683::AID-BIT10>3.3.CO;2-E
[13] M. M. Ballyk and G. S. K. Wolkowicz, “Exploitive Competition in the Chemostat for Two Perfectly Substitutable Resources,” Mathematical Biosciences, Vol. 118, No. 2, 1993, pp. 127-180. http://dx.doi.org/10.1016/0025-5564(93)90050-K
[14] G. J. Butler and G. S. K. Wolkowicz, “Exploitive Competition in a Chemostat for Two Complementary, and Possible Inhibitory, Resources,” Mathematical Biosciences, Vol. 83, No. 1, 1987, pp. 1-48. http://dx.doi.org/10.1016/0025-5564(87)90002-2
[15] S-B. Hsu, K-S. Cheng and S. P. Hubbell, “Exploitive Competition for Two Complementary Nutrients in Continuous Cultures,” SIAM Journal on Applied Mathematics, Vol. 41, No. 3, 1981, pp. 422-444. http://dx.doi.org/10.1137/0141036
[16] S.-B. Hsu and Y.-H. Tzeng, “Plasmid-Bearing, Plasmid-Free Organisms Competing for Two Complementary Nutrients in a Chemostat,” Mathematical Biosciences, Vol. 179, No. 2, 2002, pp. 183-206. http://dx.doi.org/10.1016/S0025-5564(02)00105-0
[17] H. R. Thieme, “Convergence Results and a Poincaré- Bendixson Trichotomy for Asymptotically Autonomous Differential Equations,” Journal of Mathematical Biology, Vol. 30, No. 7, 1992, pp. 755-763. http://dx.doi.org/10.1007/BF00173267
[18] J. L. Garcia-Sanchez, B. Kamp, K. A. Onysko, H. Budman and C. W. Robinson, “Double Inhibition Model for Degradation of Phenol by Pseudomonas Putida Q5,” Biotechnology and Bioengineering, Vol. 60, No. 5, 1998, pp. 560-567. http://dx.doi.org/10.1002/(SICI)1097-0290(19981205)60:5<560::AID-BIT6>3.0.CO;2-L

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