Discriminating between Concerted and Sequential Allosteric Mechanisms by Comparing Equilibrium and Kinetic Hill Coefficients

Hill coefficients, which provide a measure of cooperativity in ligand binding, can be determined for equilibrium (or steady-state) data by measuring fractional saturation (or initial reaction velocities) as a function of ligand concentration. Hill coefficients can also be determined for transient kinetic data from plots of the observed rate constant of the ligand-promoted conformational change as a function of ligand concentration. Here, it is shown that the ratio of the values of these two Hill coefficients can provide insight into the allosteric mechanism. Cases when the value of the kinetic Hill coefficient is equal to or greater than the value of the equilibrium coefficient indicate concerted transitions whereas ratios smaller than one indicate a sequential transition. The derivations in this work are for symmetric dimers but are expected to have general applicability for homo-oligomers.