# A computational approach to the structural analysis of uncertain kinetic systems

## TL;DR

This paper introduces a computational framework for analyzing uncertain kinetic systems, focusing on reaction graph structures within models where coefficients vary within a polytopic set, enabling efficient structural analysis.

## Contribution

It presents a polynomial-time method to compute the dense realization and all possible reaction graph structures of uncertain kinetic models.

## Key findings

- Dense realization contains the maximum number of reactions.
- Core reactions are present in all reaction graphs.
- Algorithm for enumerating all reaction graph structures.

## Abstract

A computation-oriented representation of uncertain kinetic systems is introduced and analysed in this paper. It is assumed that the monomial coefficients of the ODEs belong to a polytopic set, which defines a set of dynamical systems for an uncertain model. An optimization-based computation model is proposed for the structural analysis of uncertain models. It is shown that the so-called dense realization containing the maximum number of reactions (directed edges) is computable in polynomial time, and it forms a super-structure among all the possible reaction graphs corresponding to an uncertain kinetic model, assuming a fixed set of complexes. The set of core reactions present in all reaction graphs of an uncertain model is also studied. Most importantly, an algorithm is proposed to compute all possible reaction graph structures for an uncertain kinetic model.