Ligand-Induced Changes of the Apparent Transition-State Position in Mechanical Protein Unfolding

Force-spectroscopic measurements of ligand-receptor systems and the unfolding/folding of nucleic acids or proteins reveal information on the underlying energy landscape along the pulling coordinate. The slope Delta x(double dagger) of the force-dependent unfolding/unbinding rates is interpreted as the distance from the folded/bound state to the transition state for unfolding/unbinding and, hence, often related to the mechanical compliance of the sample molecule. Here we show that in ligand-binding proteins, the experimentally inferred Delta x(double dagger) can depend on the ligand concentration, unrelated to changes in mechanical compliance. We describe the effect in single-molecule, force-spectroscopy experiments of the calcium-binding protein calmodulin and explain it in a simple model where mechanical unfolding and ligand binding occur on orthogonal reaction coordinates. This model predicts changes in the experimentally inferred Delta x(double dagger), depending on ligand concentration and the associated shift of the dominant barrier between the two reaction coordinates. We demonstrate quantitative agreement between experiments and simulations using a realistic six-state kinetic scheme using literature values for calcium-binding kinetics and affinities. Our results have important consequences for the interpretation of force-spectroscopic data of ligand-binding proteins.