  A hierarchy of timescales is ubiquitous in biological systems, where
enzymatic reactions play an important role because they can hasten the
relaxation to equilibrium. We introduced a statistical physics model of
interacting spins that also incorporates enzymatic reactions to extend the
classic model for allosteric regulation. Through Monte Carlo simulations, we
found that the relaxation dynamics are much slower than the elementary
reactions and are logarithmic in time with several plateaus, as is commonly
observed for glasses. This is because of the kinetic constraints from the
cooperativity via the competition for an enzyme, which has different affinity
for molecules with different structures. Our model showed symmetry breaking in
the relaxation trajectories that led to inherently kinetic transitions without
any correspondence to the equilibrium state. In this paper, we discuss the
relevance of these results for diverse responses in biology.
