Description of systems

Figure 3.2: Schematic description of the studied molecular systems. The shaded zone in each picture corresponds to the quantum mechanical region. The left molecule is labeled DHAP and the right model is PHTAL.

Figure 3.3: Schematic description of the studied molecular systems. The shaded zone in each picture The upper left picture is called TIM, the upper right LDH and the central one ANTA.

To test our algorithm we have chosen several chemical or biochemical systems, taken from published works, from small to medium size. We have run both geometry minimization and transition state search on every molecular system. In what follows we will describe (see figures 3.2 and 3.3) the molecular systems we have chosen as a test.

The so called DHAP system is the deprotonated dihydroxyacetone phosphate (the dihydroxyacetone phosphate is the substrate of triosephosphate isomerase studied by Kollman and co-workers [247]). The reaction tested is a proton transfer between the hydroxy and the ketone group. DHAP has 14 atoms and we have partitioned it in a reactive part of 9 atoms treated with the PM3 Hamiltonian and a non-reactive part of 5 atoms treated with a molecular mechanics potential. Note that in all systems pictured in Figure 3.2 and 3.3 the shaded zone corresponds to the QM region. A link atom is required for each covalent bond that joins any atom belonging to the QM region with any atom lying in the MM (non-reactive) region. Then only one link atom has to be included in this case.

The PHTAL system is the phtalate anion. The reaction consists of a proton transfer between the two carboxylic groups. The whole system has 17 atoms. Seven of them, including both carboxylic groups, are treated with the AM1 semiempirical Hamiltonian, and the 10 atoms of the phenyl ring are in the MM part. Two link atoms are added.

The TIM system is again a model of the active site of triosephosphate isomerase studied by Cui and Karplus[127]. It is constituted by an enediolate emulating the deprotonated dihydroxyacetone phosphate. In all 19 atoms are included. 7 atoms are in the quantum part treated with the PM3 Hamiltonian, and a singly protonated imidazole ring modeling an histidine, that is 12 atoms, defines the MM part. No link atoms are required since there is no covalent bond crossing the QM/MM frontier. The reaction studied is a proton transfer between the two oxygen atoms, similarly to that studied in DHAP. In table 3.1 TIM1 and TIM2 stand for the reactant and the product of the reaction, respectively.

LDH is a model of the active site of lactate dehydrogenase enzyme studied by Andrés and co-workers [248]. The whole system is medium-sized and constituted by a total of 55 atoms. It includes a pyruvate and a nicotinamide ring involving 30 atoms in the reactive part treated with PM3, and a guanidino group and a methyl imidazole including 25 atoms for the MM part. As in the TIM system, no link atoms are required. The reaction studied is the transformation of pyruvate to lactate due to a hydride transfer between pyruvate and nicotinamide. In order to reproduce the system studied in the reference we have also performed an full QM calculation, including all 55 atoms in the quantum part.

The biggest system tested here is ANTA which is a decapeptide called antamanide, studied by Fischer and Karplus[146]. In that work the reaction studied was a conformational change in a proline ring. The fact that no bond is broken during this reaction enables us to study the whole system with a molecular mechanics force field. With the AMBER united atom model a total of 90 atoms are handled. When the whole system is treated classically the initial Hessian matrix has not the form shown in figure 3.1, but the full Hessian matrix is built.

In addition, a QM/MM partition has also been done on the ANTA system. The QM part includes the 14 atoms from the all-atom proline ring treated with the PM3 Hamiltonian (this partition takes into account that the frontier cannot be in the peptide bond due to the fact that it has some double bond character), whereas the molecular mechanics part is the rest of the decapeptide involving 83 united atoms. Two link atoms are also included.