Effect of nonlinear protein binding on equilibration times for different initial conditions

The dynamics in the equilibration of free drug in a two-compartment closed system, exhibiting nonlinear binding in one of the compartments, are elucidated. The dynamics of the free drug in the compartment containing the binding sites are first studied under the two initial conditions when the drug is added to the same and the other compartment; the dynamics of the drug in the compartment devoid of binding sites are then studied under the two initial conditions. Dynamic asymmetries are shown to exist among the four cases in the nonlinear region using an equilibrium limit which symmetrizes the dynamics for all four cases in the linear region. In the two cases where the dynamics are viewed in the compartment devoid of binding sites, the dynamic asymmetry is manifested by a reduction in the time required to reach the limit for the drug added to the compartment containing the binding sites compared with the other compartment. The time difference between these two cases becomes magnified when limits, reflective of the relative error in the estimate of the equilibrium value, are applied. In the linear region, application of these limits results in a time difference. This time difference again favors addition to the compartment containing the binding sites from a time-conservation perspective.