Near-critical phenomena in intracellular metabolite pools

The supply and consumption of metabolites in living cells are catalyzed by enzymes. Here we consider two of the simplest schemes where one substrate is eliminated through Michaelis-Menten kinetics, and where two types of substrates are joined together by an enzyme. It is demonstrated how steady-state substrate concentrations can change ultrasensitively in response to changes in their supply rates and how this is coupled to slow relaxation back to steady state after a perturbation. In the one-substrate system, such near-critical behavior occurs when the supply rate approaches the maximal elimination rate, and in the two-substrate system it occurs when the rates of substrate supply are almost balanced. As systems that operate near criticality tend to display large random fluctuations, we also carried out a stochastic analysis using analytical approximations of master equations and compared the results with molecular-level Monte Carlo simulations. It was found that the significance of random fluctuations was directly coupled to the steady-state sensitivity and that the two substrates can fluctuate greatly because they are anticorrelated in such a way that the product formation rate displays only small variation. Basic relations are highlighted and biological implications are discussed.