Thermodynamic linkage between the binding of protons and inhibitors to HIV-1 protease

The aspartyl dyad of free HIV-1 protease has apparent pK(a)s of approximately 3 and approximately 6, but recent NMR studies indicate that the aspartyl dyad is fixed in the doubly protonated form over a wide pH range when cyclic urea inhibitors are bound, and in the monoprotonated form when the inhibitor KNI-272 is bound. We present computations and measurements related to these changes in protonation and to the thermodynamic linkage between protonation and inhibition. The Poisson-Boltzmann model of electrostatics is used to compute the apparent pK(a)s of the aspartyl dyad in the free enzyme and in complexes with four different inhibitors. The calculations are done with two parameter sets. One assigns epsilon = 4 to the solute interior and uses a detailed model of ionization; the other uses epsilon = 20 for the solute interior and a simplified representation of ionization. For the free enzyme, both parameter sets agree well with previously measured apparent pK(a)s of approximately 3 and approximately 6. However, the calculations with an internal dielectric constant of 4 reproduce the large pKa shifts upon binding of inhibitors, but the calculations with an internal dielectric constant of 20 do not. This observation has implications for the accurate calculation of pK(a)s in complex protein environments. Because binding of a cyclic urea inhibitor shifts the pK(a)s of the aspartyl dyad, changing the pH is expected to change its apparent binding affinity. However, we find experimentally that the affinity is independent of pH from 5.5 to 7.0. Possible explanations for this discrepancy are discussed.