Extracting equilibrium constants from kinetically limited reacting systems

It has been known for some time that slow kinetics will distort the shape of a reversible reaction boundary. Here we present a tutorial on direct boundary fitting of sedimentation velocity data for a monomer-dimer system that exhibits kinetic effects. Previous analysis of a monomer-dimer system suggested that rapid reaction behavior will persist until the relaxation time of the system exceeds 100 s (reviewed in Kegeles and Cann, 1978). Utilizing a kinetic integrator feature in Sedanal (Stafford and Sherwood, 2004), we can now fit for the k(off) values and measure the uncertainty at the 95% confidence interval. For the monomer-dimer system the range of well determined k(off) values is limited to 0.005 to 10(-5) s(-1) corresponding to relaxation times (at a loading concentration of the Kd) of approximately 70 to approximately 33,000 s. For shorter relaxation times the system is fast and only the equilibrium constant K but not k(off) can be uniquely determined. For longer relaxation times the system is irreversibly slow, and assuming the system was at initial equilibrium before the start of the run, only the equilibrium constant K but not k(off) can be uniquely determined.