I have a pet lay-speculation that there’s a pretty mathematically interesting question here, which hasn’t been understood yet. I can’t formulate the question clearly, but it’s something like: “What sort of thing are these states?” We can abstractly talk about stable states of high-dimensional dynamical systems, but this probably isn’t very satisfying or helpful in this context. There’s some more practical or concrete or specific things we might want to know about the landscape of possible stable or quasi-stable states for gene regulatory networks, and how they transition, and how one could perturb them.
In the case of epigenetic memory based on freely-diffusing factors, the alternative “stable” states can probably be thought of as long-lived metastable states in “real” stochastic system, which become stable fixed points in the limit as the number of particles N goes to infinity. In models, the switching time often grows exponentially with the number of particles. You may enjoy https://arxiv.org/abs/q-bio/0410003 or https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.208101.
I have a pet lay-speculation that there’s a pretty mathematically interesting question here, which hasn’t been understood yet. I can’t formulate the question clearly, but it’s something like: “What sort of thing are these states?” We can abstractly talk about stable states of high-dimensional dynamical systems, but this probably isn’t very satisfying or helpful in this context. There’s some more practical or concrete or specific things we might want to know about the landscape of possible stable or quasi-stable states for gene regulatory networks, and how they transition, and how one could perturb them.
In the case of epigenetic memory based on freely-diffusing factors, the alternative “stable” states can probably be thought of as long-lived metastable states in “real” stochastic system, which become stable fixed points in the limit as the number of particles N goes to infinity. In models, the switching time often grows exponentially with the number of particles. You may enjoy https://arxiv.org/abs/q-bio/0410003 or https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.208101.
For memory based on chemical modifications embedded along the genome, like DNA methylation, there isn’t really a “large N” limit to take, and in my view things are less settled. You may enjoy https://pubmed.ncbi.nlm.nih.gov/17512413/ or (shameless plug) https://www.science.org/doi/10.1126/science.adg3053