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Near-Critical Phenomena in Intracellular Metabolite Pools

Johan Elf^*, Johan Paulsson, Otto G. Berg and Måns Ehrenberg^*

^* Department of Cell & Molecular Biology, Uppsala University, BMC, 751 24 Uppsala, Sweden, Department of Molecular Biology, Princeton University, New Jersey, 08544, USA, and Department of Molecular Evolution, EBC, 753 26 Uppsala, Sweden

Correspondence: Address reprint requests to ehrenberg{at}xray.bmc.uu.se or johan.elf{at}icm.uu.se.

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.

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