On the Role of Magnesium Ions in the DNA-Scissoring Activity of the Restriction Endonuclease ApaI: Stochastic Kinetics from a Single Molecule to Mesoscopic Paradigm.

Abstract

Biochemical reactions occurring inside cells have significant stochastic signatures due to the low copy number of reacting species. Kinetics of DNA cleavage by restriction endonucleases are no exception as established by single-molecule experiments. Here, we propose a simple reaction scheme to understand the role of the cofactor magnesium ion in the action of the endonuclease ApaI. The methodology is based on the waiting time distribution of cleavage product formation that enables us to determine the corresponding rate both analytically and numerically. The theory is developed at the single-molecule level and then generalized to the biologically relevant case of a population of DNA-endonuclease complexes present inside a cell. The theoretical rate versus cofactor concentration curve is matched with relevant single-molecule experimental data that reveals positive cooperativity of cofactor binding and provides a reliable estimate of model parameters. Furthermore, a parameter range is identified where the dispersion of the waiting time, measured using the coefficient of variation, is significantly lower than the Poisson limit and becomes minimum at the in vivo magnesium ion concentration level. Such low dispersion can play a role in the robust DNA-scissoring activity of ApaI under in vivo conditions.