Untangling the hairball: fitness based asymptotic reduction of biological networks

Abstract: Complex mathematical models of interaction networks are routinely used for prediction in systems biology. However, it is difficult to reconcile network complexities with a formal understanding of their behavior. Here, we propose a simple procedure (called $\bar \varphi$) to reduce biological models to functional submodules, using statistical mechanics of complex systems combined with a fitness-based approach inspired by $\textit{in silico}$ evolution. $\bar \varphi$ works by putting parameters or combination of parameters to some asymptotic limit, while keeping (or slightly improving) the model performance, and requires parameter symmetry breaking for more complex models. We illustrate $\bar \varphi$ on biochemical adaptation and on different models of immune recognition by T cells. An intractable model of immune recognition with close to a hundred individual transition rates is reduced to a simple two-parameter model. $\bar \varphi$ extracts three different mechanisms for early immune recognition, and automatically discovers similar functional modules in different models of the same process, allowing for model classification and comparison. Our procedure can be applied to biological networks based on rate equations using a fitness function that quantifies phenotypic performance.