Modeling bacteria pairwise interactions in human microbiota by Sparse Identification of Nonlinear Dynamics (SINDy).

The gut microbiota is a community of high complexity; its composition changes due to ecological interactions, these are studied to understand the relationship with the human health. External stimuli like the administration of probiotics, prebiotics, or drugs are known to modify these interactions. The high complexity of microbiota composition can be studied by considering pairwise interactions. Pairwise interactions in bacterial communities consider each species' directionality and impact on one another, e.g., commensalism (unidirectional positive interaction) or competition (bidirectional negative interaction). These interactions can either be interspecies or intraspecies. The Lotka-Volterra (LV) model has been implemented to characterize these bacteria interactions, considering the ecological relationship among the different species presented. One of the main challenges is determining the specific interaction parameters in LV structure from experimental data. This study implemented a novel approach based on the sparse identification of nonlinear dynamic method (SINDy). One of the assumptions in SINDy method implies the knowledge of the data derivative structure. To fulfill this requirement, a differential neural network algorithm was implemented. We assessed the performance of this approach considering both a simulated and experimental interspecies scenario. A two-species bacterial LV model was simulated in the initial validation stage, and the resulting kinetic growth data was recorded. This data was utilized for training a differential neural network algorithm, which was used to derive a time-derivative structure for the dataset. After this step, SINDy method was implemented to calculate the interaction parameters. Three conditions were evaluated in intraspecies competition, obtaining an average identification parametric error of less than 2%. For experimental data, parametric analysis results are sensitive to detect the influence of a drug presence over the intraspecies interaction with a reduction of 50% in its typical values.Clinical Relevance- In this study, we devised a strategy to determine how two species of the human gastrointestinal microbiota interact and the impact of drug administration on these interactions.