Gene regulatory network (GRN)-based morphogenetic models have recently gained an increasing attention. However, the relationship between microscopic properties of intracellular GRNs and macroscopic properties of morphogenetic systems has not been fully understood yet. Here we study a theoretical morphogenetic model using Kauffman's NK random Boolean network (RBN) as a GRN and spring-mass-damper kinetics for cellular movements , and reveal the relationship between criticality of GRNs and morphogenetic pattern formation. Our modelrepresents an aggregation of cells, where all the cells have identical GRNs in it. The properties of GRNs were varied from ordered, through critical, to chaotic by  node in-degree K. For cellular behaviors, we randomly assigned four cell fates to the attractors of RBNs  . By comparing diverse morphologies generated in our morphogenetic systems, we investigated what the role of the criticality of GRNs is in forming morphologies. We found that nontrivial spatial patterns were generated most frequently when GRNs were at criticality. Our finding indicates that the criticality of GRNs facilitates the formation of nontrivial morphologies in GRN-based morphogenetic systems.
Gene regulatory network (GRN)-based morphogenetic models have recently gained an increasing attention. However, the relationship between microscopic properties of intracellular GRNs and macroscopic properties of morphogenetic systems has not been fully understood yet. Here we propose a theoretical morphogenetic model representing an aggregation of cells , and reveal the relationship between criticality of GRNs and morphogenetic pattern formation. In our model, the positions of the cells are determined by spring-mass-damper kinetics. Each cell has an identical Kauffman's NK random Boolean network (RBN) as its GRN. We varied the properties of GRNs from ordered, through critical, to chaotic by adjusting node in-degree K. We randomly assigned four cell fates to the attractors of RBNs for cellular behaviors . By comparing diverse morphologies generated in our morphogenetic systems, we investigated what the role of the criticality of GRNs is in forming morphologies. We found that nontrivial spatial patterns were generated most frequently when GRNs were at criticality. Our finding indicates that the criticality of GRNs facilitates the formation of nontrivial morphologies in GRN-based morphogenetic systems.
R
study
propose
R
using Kauffman's NK random Boolean network (RBN) as a GRN and spring-mass-damper kinetics for cellular movements
representing an aggregation of cells
R
Our modelrepresents an aggregation of cells, where all the cells have identical GRNs in it. The
In our model, the positions of the cells are determined by spring-mass-damper kinetics. Each cell has an identical Kauffman's NK random Boolean network (RBN) as its GRN. We varied the
D
were varied
A
adjusting
R
For cellular behaviors, we
We
A
for cellular behaviors