Microbial Interactions as Drivers of a Nitrification Process in a Chemostat

Abstract

This article deals with the inclusion of microbial ecology measurements such as abundances of operational taxonomic units in bioprocess modelling. The first part presents the mathematical analysis of a model that may be framed within the class of Lotka–Volterra models fitted to experimental data in a chemostat setting where a nitrification process was operated for over 500 days. The limitations and the insights of such an approach are discussed. In the second part, the use of an optimal tracking technique (developed within the framework of control theory) for the integration of data from genetic sequencing in chemostat models is presented. The optimal tracking revisits the data used in the aforementioned chemostat setting. The resulting model is an explanatory model, not a predictive one, it is able to reconstruct the different forms of nitrogen in the reactor by using the abundances of the operational taxonomic units, providing some insights into the growth rate of microbes in a complex community.

Construction and application of exact solutions of the diffusive Lotka-Volterra system: a review and new results

“…However, there are other types of interaction between species, cells, chemicals etc. In particular, the nonlinear system (6), in which all the parameters a i and b ij are nonnegative, is a model describing mutualism or cooperation (see, e.g., [6,58]). Obviously, the solutions presented in this work are useful for interactions of such type as well.…”

New Conditional Symmetries and Exact Solutions of the Diffusive Two-Component Lotka–Volterra System

“…In conclusion, we want to highlight an unsolved problem. The nonlinear system (32) with positive parameters a 1 , a 2 and negative b and c is the model describing mutualism or cooperation (see [34,36]). Obviously, the solutions constructed in this work can be used for these types of interaction in a quite similar way as that in Section 4.…”

“…Clearly, the components u and v are bounded and nonnegative, provided that a 1 > a 2 and the asymptotical behavior is the same as in (34). However, solution (36) does not satisfy the boundary condition (35) for any finite values of A and B. It can be done only for A → −∞ and B → +∞.…”