Discussion U. Ryde Paper: Do Quantum Mechanical Energies Calculated for Small Models of Protein-Active Sites Converge?

We discussed the paper by Hu et al.

Bottom line:

• The paper discusses how the energy difference between an HIP state and an HID state is affected by the residues included in the respective model
• Let $E_B$ be the energy of the product state HIP for system $s$
• Let $E_A$ be the energy of the reactant state HID for system $s$
• Let $E_B'$ be the energy of the product state HIP for a system ($s$ + residue $i$), called $s'$
• Let $E_A'$ be the energy of the reactant state HID for a system ($s$ + residue $i$), called $s'$
• Reported is the $\Delta \Delta E := (E_B' - E_A') - (E_B - E_A)$
• Vacuum calculations are essentially worthless because even if the size of the system is set such that the difference in energy appears converged (above 15 residues, Fig. 2, 4, 5), still the energy differences obtained from such a system can change dramatically, once charged residues are added on top of this system (Fig. 7)

• This is less dramatic but still present when using continuum solvent models ($\epsilon =4$), Fig. 7
• It is now a question how much this effect could be further reduced with a higher dielectric constant
• It is however also possible that once the system reaches a certain size, the specific value of the dielectric constant does not affect the energy difference any longer (p.11796)
• One conclusion is that only including every position avoids convergence difficulties due to system size
• This however then most likely requires QM/MM approaches or linear scaling techniques
• If the study is to be carried out using only fragments of the protein back bone, charged residues should be included only together with their counter charge pair if available
• Charged residues in the interior of the protein are usually in counter-ion pairs
• Quantum only studies as the one presented however remain useful in mechanistic studies where one mechanism can be ruled out in favor for another mechanism because their respective activation energies are very different
• For such studies, it is recommended to include only a minimum model consisting of the groups immediately involved in the reaction