Title: 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.