Theoretical studies of RNA catalysis: hybrid QM/MM methods and their comparison with MD and QM

Abstract

Hybrid QM/MM methods combine the rigor of quantum mechanical (QM) calculations with the low computational cost of empirical molecular mechanical (MM) treatment allowing to capture dynamic properties to probe critical atomistic details of enzyme reactions. Catalysis by RNA enzymes (ribozymes) has only recently begun to be addressed with QM/MM approaches and is thus still a field under development. This review surveys methodology as well as recent advances in QM/MM applications to RNA mechanisms, including those of the HDV, hairpin, and hammerhead ribozymes, as well as the ribosome. We compare and correlate QM/MM results with those from QM and/or molecular dynamics (MD) simulations, and discuss scope and limitations with a critical eye on current shortcomings in available methodologies and computer resources. We thus hope to foster mutual appreciation and facilitate collaboration between experimentalists and theorists to jointly advance our understanding of RNA catalysis at an atomistic level.

Fig 1

The free energy barriers of HDV ribozyme self-cleavage reaction corresponding to three different positions of Mg²⁺ ion: (A) hexacoordinated Mg²⁺ ion with one inner-shell bound phosphate, (B) pentacoordinated Mg²⁺ ion with two inner-shell bound phosphates, and (C) hexacoordinated Mg²⁺ ion with two inner-shell bound phosphates.

Fig. 2

Principle of QM/MM. (A) A typical QM/MM approach divides the studied system into a QM core and an MM surrounding. (B) The MM treated part of the HDV ribozyme is shown in wire representation, the QM core is highlighted in sticks. Water molecules and counter ions of the MM part are not shown for clarity.

Fig. 3

Basis set dependence of DFT results for the MPW1K DFT functional as applied to backbone self-cleavage by catalytic RNA (29). A medium basis set (6-31+G(d,p), red curve) yields results that are ~2 kcal/mol lower than those from a large basis set (MG3, green curve). For this particular functional the results for the smaller basis (MPW1K/6-31+G(d,p), red curve) are close to the reference (CCSD(T)/CBS, blue curve), because the MPW1K functional is parameterized for the 6-31+G(d,p) basis set.

Fig. 4

Reaction barriers of backbone self-cleavage by catalytic RNA (29) calculated using different methods in a medium 6-31+G(d,p) basis. The CCSD(T)/CBS reference data are in red. HF significantly overestimates barrier heights (blue). BLYP reproduces the reference data very poorly, especially the third TS (black).