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

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.