(373d) Stability Analysis and Dynamic Trajectory Clustering in Exploring Parameter Spaces of a Biofuel Production Tripartite Consortia

Engineering of synthetic microbial consortia has emerged as a new and powerful biotechnology platform, because it can capitalize upon natural predispositions by selecting for interspecies relationships or specific community functions. Pairing photosynthetic and diazotrophic organisms with metabolic engineering is a powerful strategy for simultaneously driving bioproduction while reducing the environmental, energetic, and monetary burden of carbon and nitrogen substrates. To this end, tripatite platforms in which the pairing organisms drive production of a third producer species has been proposed to produce biofuels, commodity chemicals, or chemical precursors for bulk polymer production. One such promising system that is analyzed in this work uses Azotobacter vinelandii, Synechococcus elongatus, and E.coli[1,2,3] to convert sunlight, carbon dioxide, and atmospheric nitrogen into isobutanol. As each wet-lab experiment analyzing the microbial systems with different inputs and parameters is costly and time-consuming, building and analyzing a mathematical model representative of the aforementioned system is essential to fully exploring the parameter space to understand how different biological parameters and operating strategies impact the productivity of the tri-culture.

In this work, we develop a comprehensive mathematical model to describe the dynamics of the tri-culture system. When different operating parameters are implemented, the system behaviors can be divided into two operating regions where seeding cells results in continuous growth (unstable dynamics) that we aim to promote, or cells dying (stable dynamics) that we try to avoid. A linear stability analysis of the ordinary differential equations is utilized to identify these regions, which provides insights on the significance of different operational conditions and roughly microbial kinetic parameters in our model. However, there are large number of impactful parameters in our model, such as substrate/product yield coefficients for three bacteria, which display coupled effects on system dynamics, rendering traditional methods of bifurcation analysis ineffective. Thus, we present an approach to identify the categories of microbial growth curves using the k-means clustering method[4] to better investigate the dynamic characteristics of the tripartite system. Through classifying and labeling clusters with related parameter ranges, we propose a mathematical guideline of the relationship between operational/microbial parameters and kinetic trajectories of the tripartite system, which provides insights on how to optimize the experimental conditions.

Using simulations of the mathematical kinetic model of the tri-culture system, we present the stability diagrams with different operational and microbial parameters. Results suggest that a substrate-limited system for all bacteria usually leads to stable dynamics, while having a sufficient amount of at least one substrate shows the unstable behavior. After implementing the clustering algorithm, all trajectories are categorized into different characteristics with corresponding parameter ranges. The stability subspaces from clustering methods generally agree with the stability diagrams, implying the consistence between local linear stability analysis and global dynamic simulations. Using the classifier, parameter ranges can be shrunk when fitting parameters of the tri-culture model with wet-lab data, which is important as it allows for the implementation of tight bounds when formulating optimal decision making models.