Hans Martin Senn

QM/MM Methods for Biomolecular Systems

Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.

QM/MM Methods for Biological Systems

Thirty years after the seminal contribution by Warshel and Levitt, we review the state of the art of combined quantum-mechanics/molecular-mechanics (QM/MM) methods, with a focus on biomolecular systems. We provide a detailed overview of the methodology of QM/MM calculations and their use within optimization and simulation schemes. A tabular survey of recent applications, mostly to enzymatic reactions, is given.

QM/MM Free-Energy Perturbation Compared to Thermodynamic Integration and Umbrella Sampling: Application to an Enzymatic Reaction

We used the free-energy perturbation (FEP) method in quantum mechanics/molecular mechanics (QM/MM) calculations to compute the free-energy profile of the hydroxylation reaction in the enzyme p-hydroxybenzoate hydroxylase (PHBH). k statistics were employed to analyze the FEP sampling including estimation of the sampling error. Various approximations of the free-energy perturbation method were tested. We find that it is adequate not only to freeze the density of the QM part during the dynamics at frozen QM geometry but also to approximate this density by electrostatic-potential-fitted point charges. It is advisable to include all atoms of a QM/MM link in the perturbation. The results of QM/MM-FEP for PHBH are in good agreement with those of thermodynamic integration and umbrella sampling.

The Fluorine-Iminium Ion Gauche Effect : Proof of Principle and Application to Asymmetric Organocatalysis

The gauche effect that is induced upon reversible formation of an iminium ion (see structure: green F, blue N) provides a powerful method for the preorganization of transient intermediates that are central to secondary amine catalyzed processes. This phenomenon has been exploited in the design of a novel organocatalyst and is showcased in the stereoselective epoxidation of alpha,beta-unsaturated aldehydes.

Metal−Metal and Metal−Ligand Bonding at a QTAIM Catastrophe: A Combined Experimental and Theoretical Charge Density Study on the Alkylidyne Cluster Fe3(μ-H)(μ-COMe)(CO)10

The charge density in the tri-iron methoxymethylidyne cluster Fe(3)(μ-H)(μ-COMe)(CO)(10) (1) has been studied experimentally at 100 K and by DFT calculations on the isolated molecule using the Quantum Theory of Atoms in Molecules (QTAIM). The COMe ligand acts as a nearly symmetric bridge toward two of the Fe atoms (Fe-C = 1.8554(4), 1.8608(4) Å) but with a much longer interaction to the third Fe atom, Fe-C = 2.6762(4) Å. Complex 1 provides a classic example where topological QTAIM catastrophes render an exact structure description ambiguous. While all experimental and theoretical studies agree in finding no direct metal-metal interaction for the doubly bridged Fe-Fe vector, the chemical bonding between the Fe(CO)(4) unit and the Fe(2)(μ-H)(μ-COMe)(CO)(6) moiety in terms of conventional QTAIM descriptors is much less clear. Bond paths implying direct Fe-Fe interactions and a weak interaction between the COMe ligand and the Fe(CO)(4) center are observed, depending on the experimental or theoretical density model examined. Theoretical studies using the Electron Localizability Indicator (ELI-D) suggest the metal-metal bonding is more significant, while the delocalization indices imply that both Fe-Fe bonding and Fe···C(alkylidyne) bonding are equally important. The source functions at various interfragment reference points are similar and highly delocalized. The potential-energy surface (PES) for the migration of the alkylidyne group from a μ(2) to a semi-μ(3) coordination mode has been explored by DFT calculations on 1 and the model complexes M(3)(μ-H)(μ-CH)(CO)(10) (M = Fe, 2; Ru, 3; and Os, 4). These calculations confirm a semi-μ(3) bridging mode for the alkylidyne ligand as the minimum-energy geometry for compounds 2-4 and demonstrate that, for 1, both Fe-Fe and Fe···C(alkylidyne) interactions are important in the cluster bonding. The PES between μ(2) and semi-μ(3) alkylidyne coordination for 1 is extremely soft, and the interconversion between several topological isomers is predicted to occur with almost no energy cost. Analysis of the density ρ(r) and the Laplacian of the density ▽(2)ρ(r(b)) in the methoxymethylidyne ligand is consistent with a partial π-bond character of the C-O bond, associated with an sp(2) hybridization for these atoms.

Metabolic profiling technologies for biomarker discovery in biomedicine and drug development

The state-of-the-art of nuclear magnetic resonance spectroscopy, mass spectrometry and statistical tools for the acquisition and evaluation of complex multidimensional spectroscopic data in metabolic profiling is reviewed in this article. The continuous evolution of the sensitivity, precision and throughput has made these technologies powerful and extremely robust tools for application in systems biology, pharmaceutical and diagnostics research. Particular emphasis is also given to the collection and storage of biological samples that are subjected to metabolite profiling. Selected examples from preclinical and clinical applications are paradigmatically shown. These illustrate the power of the profiling technologies for characterizing the metabolic phenotype of healthy, diseased and treated subjects. The complexity of disease and drug treatment is asking for an adequate response by integrated and comprehensive metabolite profiling approaches that allow the discovery of new combinations of metabolic biomarkers.

Terahertz underdamped vibrational motion governs protein-ligand binding in solution

Low-frequency collective vibrational modes in proteins have been proposed as being responsible for efficiently directing biochemical reactions and biological energy transport. However, evidence of the existence of delocalized vibrational modes is scarce and proof of their involvement in biological function absent. Here we apply extremely sensitive femtosecond optical Kerr-effect spectroscopy to study the depolarized Raman spectra of lysozyme and its complex with the inhibitor triacetylchitotriose in solution. Underdamped delocalized vibrational modes in the terahertz frequency domain are identified and shown to blue-shift and strengthen upon inhibitor binding. This demonstrates that the ligand-binding coordinate in proteins is underdamped and not simply solvent-controlled as previously assumed. The presence of such underdamped delocalized modes in proteins may have significant implications for the understanding of the efficiency of ligand binding and protein-molecule interactions, and has wider implications for biochemical reactivity and biological function.

Enzymatic hydroxylation in p-hydroxybenzoate hydroxylase: A case study for QM/MM molecular dynamics

We investigate the OH transfer step of the hydroxylation reaction of p-hydroxybenzoate in the enzyme p-hydroxybenzoate hydroxylase (PHBH) using QM/MM molecular dynamics methods. The QM region (49 atoms) is treated at the AM1 level, while the MM part (ca. 23 000 atoms) is described by the GROMOS force field. Performing pointwise thermodynamic integration from 10 starting structures, we have obtained an average value of the free-energy barrier for this reaction of 101 kJ mol(-)(1). The simulations provide insight into the dynamics of the hydrogen bonding network in the active site along the course of the reaction. In addition, we describe statistical techniques to analyze molecular dynamics data that assess the convergence of averages and yield an error measure. We discuss the effect of different error sources on the free energy.

Finite-temperature effects in enzymatic reactions — Insights from QM/MM free-energy simulations

We report potential-energy and free-energy data for three enzymatic reactions: carbon–halogen bond formation in fluorinase, hydrogen abstraction from camphor in cytochrome P450cam, and chorismate-t...

Exploiting QM/MM capabilities in geometry optimization: A microiterative approach using electrostatic embedding

We present a microiterative adiabatic scheme for quantum mechanical/molecular mechanical (QM/MM) energy minimization that fully optimizes the MM part in each QM macroiteration. This scheme is applicable not only to mechanical embedding but also to electrostatic and polarized embedding. The electrostatic QM/MM interactions in the microiterations are calculated from electrostatic potential charges fitted on the fly to the QM density. Corrections to the energy and gradient expressions ensure that macro- and microiterations are performed on the same energy surface. This results in excellent convergence properties and no loss of accuracy compared to standard optimization. We test our implementation on water clusters and on two enzymes using electrostatic embedding, as well as on a surface example using polarized embedding with a shell model. Our scheme is especially well-suited for systems containing large MM regions, since the computational effort for the optimization is almost independent of the MM system size. The microiterations reduce the number of required QM calculations typically by a factor of 2-10, depending on the system.