Potential Energy Surface

The QM/MM method used in this chapter is slightly different than the one used in the previous chapter with ROAR. The set of atoms selected as QM zone are depicted in figure 4.2. The QM part will be treated with the PM3 semiempirical Hamiltonian, and it contains the mandelate substrate, the general acid-base catalyst Lys166 and His297 along with the charge stabilization residues Lys164 and Glu317. This selection of atoms has been labeled as model 2 in the gas phase calculation in page . The magnesium cation and its four other ligands are not included in the QM part anymore. The QM part has been shortened for several computational reasons. We encountered some problems to converge the SCF process with the bigger model. But mainly we decided to work with a QM model of 63 atoms because a 91 atoms model was too expensive for an appropriate sampling in the PMF calculation.

Figure 4.2: Atoms included in the QM part. The $\alpha$ mark indicates the boundary atom treated with GHO method.

Boundary Atoms:
The partition of covalent bonds in the QM/MM frontier has been treated with the Generalized Hybrid Orbital framework[91], in particular using the PM3(GHO) method published recently[93]. The boundary between the QM and MM zones is a specially delicate issue. The GHO method is a more refined strategy than the link atom used in previous sections. As we commented in the introductory section (section 1.2.3.1), in GHO no additional atoms are included, the boundary atom must be a sp3 carbon whose hybrid orbitals are locally optimized. The boundary atoms used in this model are displayed in figure 4.2 with the $\alpha$ mark. The rest of the enzyme will be represented with the all-atom CHARMM22 force field[54], while the solvent(not yet commented) with the three point charge TIP3P model[237].

Non-bonded interactions:
The van der Waals parameters for the quantum atoms have not been optimized with this new QM/MM selection. The optimization of parameters is recommended when the quantum part interacts directly with the MM part[77]. A particular example of this fact is the QM/MM study[6] of a S$_N$2 reaction in haloalkane dehalogenase where the enzymatic efficiency depends strongly on how a quantum chloride is stabilized by two MM triptophanes. In this case, the reproduction of an accurate non-bond interaction is crucial.

In our QM/MM partition the only problematic non-bonding interaction is between mandelate substrate and magnesium cation (not displayed in figure 4.2, see preceeding chapters, for example figure 2.12 in page ). We already commented that the magnesium cation stabilizes the transition state removing charge density from the substrate. However, after some tests, we have seen that the QM/MM interaction mandelate(PM3)-magnesium(CHARMM) using the standard parameters from CHARMM22 force field is very similar in energy and structure to the full PM3-SRP results.

The rest of classical ligands bound to the magnesium cation, including the water, is stable enough to keep its coordination over all our 2 nanosecond simulation.

The non-bonded interactions have been calculated with the following characteristics. The pairlist is built on the basis of a group based cutoff using a distance of 13.5 Å (both QM and MM regions). The pairlist is updated every 35 steps during the dynamics simulation. The van der Waals are calculated using a shifting function with a cutoff at 13 Å. The electrostatics have been calculated using a switching function (see introductory section 1.2.2.2 in page ) activated at 12 Å at which the smoothing function begins to reduce the potential and eliminated completely at 13 Å.