# Model rejection and parameter reduction via time series

## TL;DR

This paper introduces a graph-based method for validating dynamical system models using time series data, enabling model rejection and parameter reduction through pattern matching.

## Contribution

It presents a novel approach combining labeled path matching in graphs with model validation, applicable to biological regulatory networks.

## Key findings

- The method can invalidate models when no matching pattern is found.
- Application to yeast gene regulatory models demonstrates practical utility.
- Provides theoretical guarantees for model validation based on pattern matching.

## Abstract

We show how a graph algorithm for finding matching labeled paths in pairs of labeled directed graphs can be used to perform model validation for a class of dynamical systems including regulatory network models of relevance to systems biology. In particular, we extract a partial order of events describing local minima and local maxima of observed quantities from experimental time-series data from which we produce a labeled directed graph we call the pattern graph for which every path from root to leaf corresponds to a plausible sequence of events. We then consider the regulatory network model, which can be itself rendered into a labeled directed graph we call the search graph via techniques previously developed in computational dynamics. Labels on the pattern graph correspond to experimentally observed events, while labels on the search graph correspond to mathematical facts about the model. We give a theoretical guarantee that failing to find a match invalidates the model. As an application we consider gene regulatory models for the yeast S. cerevisiae.