Preliminary Results Towards Decoding Planktonic Life via Symbolic Regression

Oceans, covering over $70\%$ of Earth's surface, play a crucial role in regulating the global climate by absorbing excess heat and \ce{CO2} emissions. Marine microbiomes are key drivers of biogeochemical cycles, supporting food webs and the biological carbon pump that sequesters carbon into the deep ocean. However, the interactions among taxonomy, gene expression, metabolic pathways, and environmental factors, especially in the context of climate change, remain poorly understood.Explainable Artificial Intelligence including approaches like Symbolic Regression (SR), offers promising methods to model and understand these complex interactions. SR searches for the best-fitting symbolic mathematical expressions to capture these relationships, addressing the vast search space using techniques such as Genetic Programming.We utilized the Ocean Microbial Reference Gene Catalog, which includes 47 million genes annotated in 9024 molecular functions according to KEGG database, to generate $36,214$ interpretable models. These models enabled us to derive equations that predict: i) omics-derived features using environmental factors, and vice versa, ii) relationships within taxonomic compositions, and iii) taxonomic composition based on functional traits such as molecular functions and metabolic pathways.Our results showed that environmental factors could predict $22.6\%$ and $29.4\%$ of molecular functions and metabolic pathways from metagenomes, respectively, while $4.9\%$ and $3.5\%$ of these entities from metatranscriptomes could be predicted with $R^2$ values exceeding $0.5$. Notably, some of the most accurate predictions involved molecular functions associated with carbon sequestration, including Photosynthesis, Photosynthesis Antenna protein, Carbon fixation in photosynthetic organism, Carbon fixation pathways in prokaryotes, and other carbon fixation pathways such as 3-Hydroxypropionate bi-cycle, Dicarboxylate hydroxybutyrate cycle, Hydroxypropionate hydroxybutylate cycle, Reductive citrate cycle (Arnon--Buchanan cycle) and Reductive pentose phosphate cycle (Calvin cycle).In terms of intra-relationships, depending of the taxonomic levels, it was possible to predict from $22.9\%$ to $100\%$ of all the abundances involved ($R^2 \geq 0.5$). For metabolic pathways derived from metagenomes, other pathways from the same source were the most effective predictors, followed by taxonomic class abundances ($95.1\%$ and $61.8\%$ of all pathways predicted with $R^2 \geq 0.5$, respectively). When targeting metabolic pathways from metatranscriptomes, only predictors from the same source achieved high performance ($79.9\%$ of all pathways predicted with $R^2 \geq 0.5$), whereas other predictors yielded lower results ($7.7\%$ pathways being predicted).By generating a dataset of equations that predict key omics-derived features, particularly those involved in the biological carbon pump, our work provides a foundation for data-driven hypotheses on molecular mechanisms and taxonomic relationships. These equations can be used to simulate how environmental changes, such as temperature variations, might impact the function and composition of global microbiome communities.