Steady states in Boolean models of regulatory networks
Dr. Tomas Gedeon (Dept. of Mathematical Sciences, MSU)
09/11/2025 3:10 pm
Abstract:
Gene regulatory networks with more than a few genes can support different phenotypes
in different conditions. These conditions may be external inputs like intercellular
signaling, resource abundance or internal variability like abundance of ribosomes,
RNAP or even copy number of different enzymes. The different conditions can be modeled
as changes in parameters of a gene network model.
The mathematical challenge is to develop methods to describe, search and analyze behavior of models across large sets of parameters.
I will consider a collection of all monotone Boolean functions compatible with the network as a model for the network dynamics. I will discuss how to construct such models and show that they form lattices, which are a well-studied mathematical structure.
The main focus will be on the following question: given a state of the system, what is the collection of monotone Boolean models that have this state as a steady state. I will show that this set can be constructed from down-sets and up-sets of the corresponding lattices, which will allow us to completely describe prevalence of steady states and multi-stability in negative loop-free networks.
We apply our results to several examples, including EMT network that is implicated in cancer metastasis.
This is a joint work with Sarah Adigwe at MSU and a group of Mohit Kumar Jolly at Indian Institute of Science in Bangalore, India, which I visited during my sabbatical in March 2025.
The mathematical challenge is to develop methods to describe, search and analyze behavior of models across large sets of parameters.
I will consider a collection of all monotone Boolean functions compatible with the network as a model for the network dynamics. I will discuss how to construct such models and show that they form lattices, which are a well-studied mathematical structure.
The main focus will be on the following question: given a state of the system, what is the collection of monotone Boolean models that have this state as a steady state. I will show that this set can be constructed from down-sets and up-sets of the corresponding lattices, which will allow us to completely describe prevalence of steady states and multi-stability in negative loop-free networks.
We apply our results to several examples, including EMT network that is implicated in cancer metastasis.
This is a joint work with Sarah Adigwe at MSU and a group of Mohit Kumar Jolly at Indian Institute of Science in Bangalore, India, which I visited during my sabbatical in March 2025.
Some pictures from this trip may sneak into my presentation