TY - JOUR
T1 - Maximal aggregation of polynomial dynamical systems
JF - Proceedings of the National Academy of Sciences
JO - Proc Natl Acad Sci USA
DO - 10.1073/pnas.1702697114
SP - 201702697
AU - Cardelli, Luca
AU - Tribastone, Mirco
AU - Tschaikowski, Max
AU - Vandin, Andrea
Y1 - 2017/09/06
UR - http://www.pnas.org/content/early/2017/09/05/1702697114.abstract
N2 - Large-scale dynamical models hinder our capability of effectively analyzing them and interpreting their behavior. We present an algorithm for the simplification of polynomial ordinary differential equations by aggregating their variables. The reduction can preserve observables of interest and yields a physically intelligible reduced model, since each aggregate corresponds to the exact sum of original variables.Ordinary differential equations (ODEs) with polynomial derivatives are a fundamental tool for understanding the dynamics of systems across many branches of science, but our ability to gain mechanistic insight and effectively conduct numerical evaluations is critically hindered when dealing with large models. Here we propose an aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion). A key feature of our proposal is to encode a polynomial ODE system into a finitary structure akin to a formal chemical reaction network. This enables the development of a discrete algorithm to efficiently compute the largest equivalence, building on approaches rooted in computer science to minimize basic models of computation through iterative partition refinements. The physical interpretability of the aggregation is shown on polynomial ODE systems for biochemical reaction networks, gene regulatory networks, and evolutionary game theory.
ER -