Conformational Flexibility in Jaguar pKa Calculations
Consider the case where there is only one relevant ionizable group in the molecule, but the protonated and deprotonated states can each exist in multiple conformations, which might be energetically competitive. There are several possible ways in which the conformational problem can be addressed, both of which are available in the current release.
| 1. | Perform calculations on one protonated and one deprotonated conformation, which are assumed to dominate the phase space due to being lowest in energy in their class. This is a reasonable assumption for many problems. Note that the lowest-energy conformation can be different for the protonated state and the deprotonated state. In many cases there are obvious electrostatic reasons why a conformational change on protonation or deprotonation would occur. The program can accept a different conformation for each species. |
The selection of the appropriate conformation can be nontrivial. Our recommendation is to do a solution phase conformational search in MacroModel, using the OPLS4 force field and the GB/SA continuum solvent model. This is a very fast procedure and gives a reasonable ordering of conformational free energies in solution. This procedure has been automated and can be used from Maestro. Alternatively, you can either construct the conformation by hand or use a gas-phase conformational search. Some results indicate that there are situations where a solution-phase conformational search is necessary to obtain accurate results.
| 2. | Perform quantum chemical calculations for multiple conformations, generated from a MacroModel solution phase conformational search, and use all of this information to compute the pKa. Two ways of doing this are: |
| a. | Pick the conformer that has the lowest solution-phase free energy for each protonation state and compute the pKa from this value. This method is analogous to (1) above but allows for imprecision in the conformational search protocol. It also takes more CPU time. |
| b. | Carry out a statistical mechanical average over conformations to determine the average (macroscopic) pKa. The assumption made if this option is chosen is that the midpoint of the pKa titration curve is achieved when the total population of the deprotonated state, summing over all deprotonated conformations, is equal to the total population of the protonated state, also summing over all conformations. This approach should be more accurate than that described in (a), although how important statistical effects are in practice remains to be ascertained. |
The macroscopic Ka value is given by
|
(1) |
where Nd and Np are the numbers of deprotonated and protonated conformers, dj and pi are the populations of these conformers, and Ka(i,j) is the Ka value for protonated conformer i going to deprotonated conformer j. The populations are calculated with the following expressions:
