Ab initio simulations allow us to get atomic level insight into structure, behavior, and reaction mechanisms of metalloenzymes. Density-functional theory (DFT) based methods offer a compromise between feasibility and accuracy in the study of systems when a large portion of the system is directly involved in relevant reactions. However, it is still often required to include the effects such a large environment, that it is unpractical to treat the whole system quantum mechanically. One method to address this issue is to combine classical and ab initio techniques to so-called hybrid quantum mechanics and molecular mechanics (QM/MM) simulations with an appropriate electrostatic embedding.

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The protein farnesyltransferase (FTase), a Zn-metalloenzyme, catalyzes the transfer of the 15-carbon farnesyl group from the farnesyl diphosphate (FPP) to acceptor proteins that contain the so-called “CaaX” motif at the C-terminus. FTase activity is crucial in signal transduction pathways such as proliferation and apoptosis of cells. In fact, the Ras superfamily and small GTPases including Ras, Rho and Rab, are important examples of proteins that are activated by FTase function. Nowadays, FTase represents one of the promising targets for anti-cancer drug design, being involved in the activation of oncogene proteins such as mutated Ras, which are related to the development of ~20-30% of human cancers.

Several distinct hypotheses have been proposed based on various experimental findings in regard of the chemical reaction. A detailed picture of the reaction mechanism and its transition state would certainly improve our understanding of FTase enzymatic activity. Towards this aim, we focus on the chemical step of the catalytic cycle and present a theoretical investigation of the farnesylation mechanism. Our computations employ classical molecular dynamics (MD) and ab initio Car-Parrinello QM/MM calculations. Overall, our finding indicates that the reaction mechanism is an associative mechanism with dissociated character, which fits the experimental data well.

References:
M.-H. Ho, M. De Vivo, M. Dal Peraro, and M. L. Klein, J. Chem. Theory Comput., 5, 1657 (2009)

Contact: Ming-Hsun Ho Go back to research index.

Many biological processes (including respiration, protein cleavage and toxic particles removal) are catalyzed by transition-metal containing enzymes. While localized d-states of the transition-metal ions are central in these catalytic reactions, accurate descriptions of these states face great challenges when using DFT method. In this work, we adopt a QM/MM technique coupled with a DFT + Hubbard U scheme in order to study the transition metal enzyme called Superoxide Reductase (SOR), with an appropriate description of the d-state electrons.

SOR (see the protein and active site structure shown in the figure), found in several anaerobic bacteria, is important in toxic oxygen derivatives removal, by catalyzing the one-electron reduction of superoxide to hydrogen peroxide. It prevents the production of molecular oxygen and opens a new way for the therapeutic treatment of diseases related to the presence of superoxide, through the ideation of suitable SOR mimics. We study the structure and energetics of the iron-dioxygen intermediates at different stages of the reduction process. According to our results, the introduction of the Hubbard U correction leads to an improved description of the intermediate structures and the reaction mechanism. Finite temperature studies with better descriptions of structures and energetics allow us to obtain a reliable quantitative analysis of the enzymatic reaction rate and mechanism.

Contact: Ming-Hsun Ho, Patrick H.-L. Sit Go back to research index.

Electron-transfer reactions are ubiquitous processes in organic and inorganic redox reactions. In the diabatic limit, the transfer integral is small, and the system has to diffuse up to the intersection several times before an electron can tunnel. The reaction rate for such a weak coupling case can be written as

where H_if is the transfer integral between the initial and final states. ρFC is the density of states weighted by the Franck-Condon factor and thermally averaged. This term becomes

in the classical case. In the formula, λ is the reorganization energy and ΔG is the energy of the reaction.

To obtain quantitative descriptions of electron-transfer reactions fully from first-principles, we developed a novel method to calculate free-energy surfaces of electron-transfer reactions from ab initio molecular dynamics. Sampling of phase space is done with a penalty functional added to the standard density functional so that the oxidation states of ions can be controlled. This penalty functional opens up the possibility of performing out of ground state DFT calculations, and is also a practical way to correct for the self-interaction in DFT.

With this penalty functional technique, we calculated the free-energy surfaces of the self-exchange reaction between aqueous ferrous and ferric ions fully from first-princieples (see figure). We found that the free-energy curves are parabolic, validating the linear solvation model first proposed by Marcus. The reorganization energy obtained is 1.93 eV, which is in good agreement with the experimental value of 2.1 eV, and a big improvement over classical and semi-classical calculations in quantitatively describing electron-transfer reactions. A further improved value of 2.18 eV is obtained by including Hubbard U correction to accurately describe the strongly localized d-electrons.

We then calculated the transfer integral by adopting a recently developed ab initio method. Combining the reorganization energy and the transfer integral, we can estimate the ET reaction rate constant fully ab initio. The result of 8.4 × 10² s^-1 is in excellent agreement with the experimental estimate of 7.9 × 10² s^-1.

References:
A. Migliore, P. H.-L. Sit, and M. L. Klein., J. Chem. Theory Comput., 5, 307 (2009)
P. H.-L. Sit, M. Cococcioni, and N. Marzari. J. Electroanal. Chem., 607, 107 (2007)
P. H.-L. Sit, M. Cococcioni, and N. Marzari. Phys. Rev. Lett., 97, 028303 (2006)

Contact: Patrick H.-L. Sit Go back to research index.