# Spatiotemporal expressions reflecting topological classes of repressor networks

## TL;DR

This paper classifies repressor gene networks into three topological classes, analyzing their complex spatiotemporal behaviors and relationships, especially in locally interacting network structures.

## Contribution

It analytically identifies three topological classes of repressor networks and explores their distinct spatiotemporal dynamics and relationships in locally interacting cases.

## Key findings

- Three topological classes with distinct dynamics
- Spatiotemporal complexity increases from homogeneous states
- Relationships between different network types are elucidated

## Abstract

A family of repressor networks is proposed as a simple model of gene regulatory networks. We analytically show three topological classes of the repressor networks, each of which exhibits distinctly growing complexity of spatiotemporal expressions starting from nearly homogeneous states. Further, by focusing on locally interacting cases such as chain networks, including a generalized repressilator, or feedforward(back)-loop networks, spatiotemporal expressions in the long time regime and elusive relationships between such different networks are discussed in detail.