Biological Applications of QM/MM calculations with Polarized Embedding

David Řeha, Vasilina Zayats, Dhiraj Sinha, Rüdiger Ettrich

Institute of Nanobiology and Structural Biology of GCRC, Academy of Sciences of the Czech Republic

Zamek 136, Nove Hrady, 373 33, Czech Republic

Hybrid quantum mechanical/molecular mechanics (QM/MM) calculation can be widely used for the study of the biological systems. The effect of polarization on the charge distribution is usually included in the QM part only and MM part is often neglected due to difficulties of the implementation. The MM polarization can however play an important role. Therefore we have introduced simple approach to treat the polarization of the MM part of the model. The approach is based on the treatment of polarization by induced atomic charges instead of induced dipoles [1]. The main advantage of this approach is the easy implementation to the existing MM programs. We have implemented the method in various QM/MM programs and we have applied it for the theoretical study of the numerous biological systems.

We have applied the method for the study of the enzymatic reaction of chorismate to prephenate within the chorismate mutase. The polarization has stabilizing effect on the transition state and we have observed the decrease of the activation energy by 5-7 kcal/mol.

The method was also applied to study the mechanisms of NADH:quinone oxidation reduction reaction in flavoprotein WrbA. During the enzymatic reaction, the NADH is oxidized to NAD⁺ and quinone is reduced to hydroquionone. The reaction proceeds via FMN acting as an enzyme cofactor. We have used molecular docking improved by our approach based on QM/MM calculation with MM polarization to estimate the positions and relative binding energies of the substrates of the WrbA protein. The results of calculations supports the experimental evidence of the hopping mechanisms, where in the first step, the NADH is oxidized to NAD⁺ by FMN (which is reduced to FMNH₂) and in the second step (after the NAD⁺ leaves to active site), the quinone is reduced to hydro-quinone by FMNH₂ (which is oxidized back to FMN). Furthermore, our calculations helps to explain the unusual position of NAD in crystal structure of Andrade at al [2]. The crystal structure represents the product (NAD⁺) leaving the active site after the reaction.

Finally, the method was applied for the calculation of the conformational changes connected to the coupling of translocation and endonuclease activity in the restriction-modification system EcoR1241. We have calculated the binding energies of ATP with the aminoacid residues in the active site. The results showed that LYS313, ARG688 and ARG691 have major contributions in ATP binding. The strongest interactions are with the phosphate part, the adenine ring itself has a minor contribution to the overall binding energy. The contact with LYS220 has a negligible contribution in terms of the whole ATP binding itself, however it has some significance if just the interaction between adenine ring and protein is taken in to account.

The all applications of QM/MM calculation with polarized embedding demonstrated the importance of the implementation of our method to study the biological problems.

Authors gratefully acknowledge financial support from grant Kontakt ME09016 and the grant GACR P207/12/2323.

1. Ferenczy, G.G.; Reynolds, C.A. J. Phys. Chem. A 2001, 105, 11470–11479.

2. Andrade, S.L.; Patridge, E.V.; Ferry, J.G.; Einsle, O. J. Bacteriol. 2007, 189, 9101-9107.