  Many chemical reactions in biological cells occur at very low concentrations
of constituent molecules. Thus, transcriptional gene-regulation is often
controlled by poorly expressed transcription-factors, such as E.coli lac
repressor with few tens of copies. Here we study the effects of inherent
concentration fluctuations of substrate-molecules on the seminal
Michaelis-Menten scheme of biochemical reactions. We present a universal
correction to the Michaelis-Menten equation for the reaction-rates. The
relevance and validity of this correction for enzymatic reactions and
intracellular gene-regulation is demonstrated. Our analytical theory and
simulation results confirm that the proposed variance-corrected
Michaelis-Menten equation predicts the rate of reactions with remarkable
accuracy even in the presence of large non-equilibrium concentration
fluctuations. The major advantage of our approach is that it involves only the
mean and variance of the substrate-molecule concentration. Our theory is
therefore accessible to experiments and not specific to the exact source of the
concentration fluctuations.
