# Characterizing behavioural differentiation in gene regulatory networks with representation graphs

## TL;DR

This paper introduces a new way to visualize and understand gene regulatory networks using representation graphs, which help explain how cells differentiate into distinct behaviors.

## Contribution

The novel contribution is the introduction of representation graphs to compactly capture and analyze stable states and differentiation processes in gene regulatory networks.

## Key findings

- Representation graphs can capture differentiation processes into lytic and lysogenic states in phage viruses with consistent structure despite different mechanisms.
- The approach is effective for modeling myeloid cell differentiation from a common progenitor into distinct cell types.
- Representation graphs can derive and validate hypotheses about regulatory interactions necessary for biologically viable behaviors.

## Abstract

We introduce the formal notion of representation graphs, encapsulating the state space structure of gene regulatory network models in a compact and concise form that highlights the most significant features of stable states and differentiation processes leading to distinct stability regions. The concept has been developed in the context of a hybrid system-based gene network modelling framework; however, we anticipate that it can also be adapted to other approaches of modelling gene networks in discrete terms. We describe a practical algorithm for representation graph computation as well as two case studies demonstrating their real-world application and utility. The first case study presents models for three phage viruses. It shows that the process of differentiation into lytic and lysogenic behavioural states for all these models is described by the same representation graph despite the distinctive underlying mechanisms for differentiation. The second case study shows the advantages of our approach for modelling the process of myeloid cell differentiation from a common progenitor into different cell types. Both case studies also demonstrate the potential of the representation graph approach for deriving and validating hypotheses about regulatory interactions that must be satisfied for biologically viable behaviours.