The Denaturation and Renaturation Kinetics of β-Galactosidase by Chemical Denaturants in The Presence of Galactose, a Product Inhibitor

Abstract

In the present report, a quantitative characterization predicting functional allosteric states as a function of chemical denaturants (urea and Guanidine Hydrochloride) and ligand (galactose) concentrations has been presented for β-Galactosidase. The exact calculations predicting the apparent inactivation rate constant, _A_, and the product formed at infinite observable time, [P]∞, both as functions of protein unfolding studies in the presence of ligands are derived with implications of these derivations. These derivations, which are thermodynamic parameters, ultimately represent the apparent rate of enzyme/protein inactivation when an unfolded/unfolding protein interacts with ligand modifiers (_A_ is the rate at which the protein is inactivated under such conditions) and the accompanying [P]∞ which can translate to _Kcat_ (catalytic constant), _Kc_ the_ _enzyme turnover number which can translate – for example – to enzyme shuttling activities across membrane barriers, or even conversion efficiency from one enzyme form to the other on ligand binding to the unfolding/unfolded protein form as a result of allostery. Prior to these derivations, it has been impossible to quantify and characterize allosteric transition conditions via mathematical calculations. Simulation-based multiscale methods have been the way to make rough estimates-in-the-ball-park predictions of allosteric characterizations for quantitative purposes. Even though these derivations were made for β-galactosidase using chemical denaturants as the unfolding agents and galactose as the ligand modifier, it is expected that these equations will cut through different proteins, unfolding conditions, and ligand modifiers.