Untangling the hairball: fitness based asymptotic reduction of biological networks

TL;DR

This paper introduces a novel asymptotic reduction method, $ar $, that simplifies complex biological networks into functional modules while maintaining or improving predictive performance, aiding understanding and comparison of biological models.

Contribution

The paper presents $ar $, a new systematic procedure for reducing biological network models to core functional modules using asymptotic parameter limits and fitness optimization.

Findings

Successfully reduced a complex immune recognition model to a simple two-parameter model.

Identified multiple mechanisms for immune recognition through model reduction.

Automatically discovered similar modules across different models of the same process.

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.