Density-profile processes describing biological signaling networks: almost sure convergence to deterministic trajectories

We introduce jump processes called density-profile process, to model biological signaling networks. They describe the macroscopic evolution of finite-size spin-flip models with k types of spins interacting through a non-reversible Glauber dynamics. We show that the path of the empirical magnetization in any finite time-interval converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting.

Contacto: ebiomat@famaf.unc.edu.ar