Review
QM/MM methods: Looking inside heme proteins biochemisty

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Abstract

Mixed quantum mechanics/molecular mechanics methods offer a valuable computational tool for understanding biochemical events. When combined with conformational sampling techniques, they allow for an exhaustive exploration of the enzymatic mechanism. Heme proteins are ubiquitous and essential for every organism. In this review we summarize our efforts towards the understanding of heme biochemistry. We present: 1) results on ligand migration on globins coupled to the ligand binding event, 2) results on the localization of the spin density in compound I of cytochromes and peroxidases, 3) novel methodologies for mapping the electron transfer pathways and 4) novel data on Tryptophan 2,3-dioxygenase. For this enzyme our results strongly indicate that the distal oxygen will end up on the C3 indole carbon, whereas the proximal oxygen will end up in the C2 position. Interestingly, the process involves the formation of an epoxide and a heme ferryl intermediate. The overall energy profile indicates an energy barrier of approximately 18 kcal/mol and an exothermic driving force of almost 80 kcal/mol.

Introduction

The computational modeling, both at the software (methods) and hardware development, has evolved considerably since the early work in the 70s and 80s. Computational predictions are becoming significantly more accurate in predicting enzymatic mechanisms and rates, binding energies, docked structures, complex network pathways, gene annotation, etc. As a consequence, the level of confidence towards computational modeling is growing among scientists, and many experimental laboratories work in close collaboration with computational modelers. Furthermore, some experimentalists routinely use a computational modeling software themselves to analyze their results and obtain a detailed view of the mechanism in atomic resolution. In the near future one could expect that computational techniques would determine, at the initial stages of research projects, many aspects of the experimental work. Simulations will give a level of confidence to certain experiments, reducing cost and labor.

Understanding biochemical mechanisms at atomic and electronic detail is of crucial importance in industrial catalysis, in biomedical research, etc. Theoretical modeling can involve three main steps from a general point of view: 1) building the model, 2) projecting the conformational sampling and 3) mapping the enzymatic chemical process.

The first step involves the construction of a 3‐dimensional structure including all atoms needed to properly characterize the biological system. In enzymatic systems this often requires modeling the entire protein or catalytic domain. An alternative is to use a reduced model of the active site, including only dozens of atoms held together by means of harmonic constraints. The small size of the reduced system allows for a full quantum mechanical (QM) treatment of the model. While this has been shown to be a valid approach in many systems [1], the development of mixed quantum mechanics and classical mechanics (QM/MM) techniques has driven many theoreticians towards the description of the entire enzymatic system [2], [3], [4], [5], [6]. The computational cost of QM/MM techniques is similar to that of QM methods alone. Furthermore, by using the correct protein constraints, QM/MM methods might reduce significantly the number of theoretical assays. QM methods based on reduced models, however, are still quite useful to track the protein effects and perform comparison studies. When X‐ray or NMR 3‐dimensional coordinates are not available, it is also possible to use closely related structures to produce a model using comparative techniques, generally called homology modeling. However, when studying a chemical process, small differences in the active site model may produce significant changes in the potential energy surface. Thus, homology modeling in biochemistry should be restricted to systems with a very high level of sequence identity in the active site. Finally, the initial structure will often require extensive manual editing, as a comprehensive check on protonation states, hydrogen bond network, possible crystal contact artifacts, etc. is mandatory.

Once the model is chosen, it is generally not enough to perform the study on a single set of atomic coordinates. The crystal structure (respectively the homology model) may describe an intermediate of and enzymatic reaction with no specific interest for the researcher. Therefore, it might be needed to add some cofactor, protons or electrons to model the active state properly. As a consequence, these additions might result in conformational changes that need to be described. Furthermore, it is also possible that the enzymatic mechanism is enhanced by means of some low frequency collective motion of the system. To account for this conformational sampling effectively, one should discard the electronic degrees of freedom (due to computational expense) and model the system by means of molecular mechanics (MM), using a classical force field. There exist several common techniques such as molecular dynamics [7], [8], [9], [10], Monte Carlo [11], [12], [13], protein structure prediction algorithms [14], [15], robotic algorithms [16], etc. It is possible to speed up the sampling by using models with lesser atomic resolution. Several of these so-called coarse grained models have been introduced, where an entire residue is described by a reduced number of beads [17], [18]. Additionally, normal modes from a reduced system, where only the alpha carbon from each protein residue is included in a connectivity network matrix, have also been applied to obtain the low frequency conformational motion of the system [19]. However, performing conformational sampling different from an all atom representation may introduce too many changes in the active site.

The last step is to study the electronic states involved in the chemical process. Although it is possible to model a bond breaking event by parameterization of the classical force fields introducing, for example, coupling between different harmonic or Morse potentials [20], an accurate calculation will require the use of quantum chemistry calculations. As mentioned above, QM/MM methods allow the adequate description of large biological units, such as an enzyme. They join together a quantum and a classical representation of different sectors of a complex condensed phase system. The reactive region of the active site can be treated with a robust ab initio QM methodology, whereas the remainder of the protein can be modeled at the MM level, providing the appropriate structural constraints and electrostatic and van der Waals interactions with the reactive core.

The methodology used in the analysis of the chemical process would depend on the QM Hamiltonian chosen to describe the process. When using less expensive semiempirical QM methods (or small QM regions and basis sets), we can perform short molecular dynamic trajectories, build potential of mean force or free energy profiles for the chemical process [21], [22], [23]. If a more expensive Hamiltonian is used, for example at the Hartree–Fock (HF) or density functional (DFT) level of theory, the study will usually narrow down to one or several reaction coordinates. Recently, Thiel et al. applied QM/MM methods in studies on NMR chemical shifts [24] as well as on the stability of redox eliectronmers [25]. Further recent applications include excitation energies of rhodopsin [26] and on the reactive geometry of the HIV-1 protease [27]. Next to the QM/MM method, there exist approaches of utilizing divide-and-conquer algorithms within the QM calculations, firstly introduced by Yang et al [28], these approaches are able to compute large QM regions by iteratively calculating only fragments until convergence [29], [30], [31], [32]. Application of these methods are MP2 calculations of a synthetic protein [33] or structural refinement of the photosystem II [31], for example. Very interesting is the combination of accelerated dynamical sampling with DFT based methods, which has started to be used in mapping biochemical events with high accuracy [34]. These methods, however, involve large computational costs and it should be referred to only when necessary. Many times a simpler reaction coordinate will allow for a sufficient qualitative description of the process [2].

Of particular interest are heme proteins. These proteins are ubiquitous and essential for every organism [35], [36], [37], [38], [39], [40]. The complexity of the iron containing porphyrin, together with the different active site environments, gives to this group of metalloproteins multiple functions such as oxygen transport, oxidative catalysis, electron transport, etc. Theoretical methods offer a very valuable tool to study the electronic state of the metal center, to map the electronic delocalization and the energy barriers for the catalytic chemical reaction. Recent QM/MM studies focus on the structural and electronic state of compound I of cytochrome P450cam [41], [42], [43], [44], [45], of nitric oxide synthase[46], as well as cytochrome c peroxidase and ascorbate peroxidase [42], [47], for example. Godfrey et al. published a study on specifying the electronic state of taurine/α-ketoglutarate dioxygenase and predicting the presence of low reaction barriers within the catalytic cycle [48]. Furthermore, Crespo et al. applied QM/MM on identifying the NO detoxification mechanism of oxy-truncated hemoglobin N [49].

Within this context we would like to present recent results discovered by our group. We have studied multiple heme systems including globins, cytochromes and peroxidases, and pioneered the combination of protein structure prediction techniques with QM/MM methods. In this review we summarize some of our results and introduce some novel data on tryptophan 2,3-dioxygenase (TDO).

Section snippets

Methods

In the following section we summarize the methods employed for the studies reviewed below. We only give a general description of the most common methods used in the different systems, as it is possible to find more details on particular implementations in the corresponding publications.

Globin studies

We have performed various biophysical and biochemical studies on globin proteins, including myoglobin, hemoglobin and truncated hemoglobins, results of which we are showing in the following section.

Novel results on tryptophan 2,3-dioxygenase

QM/MM reaction mechanism in tryptophan 2,3-dioxygenase Heme. Tryptophan 2,3-dioxygenase (TDO) is a heme enzyme that catalyses oxidation of l-tryptophan to N-formyl-kynurenine,1-3, in a mechanism that involves binding of dioxygen to ferrous iron, shown in Fig. 7 [103]. Following recent studies by Raven et al. we have focused on the direct electrophilic addition to dioxygen [104]. The possibility of the indole proton abstraction using an active site base has also been investigated.

Starting with

Conclusions

We underlined here the possibilities of mixed quantum mechanics and molecular mechanics methods in addressing the enzymatic mechanisms in heme proteins. When combined with protein structure prediction techniques (or other sampling techniques), the coupling of the biochemical and biophysical processes in the enzyme can be studied.

The studies presented here include a wide diversity of enzymes with multiple specific findings. However we can draw some overall conclusions:

  • 1.

    Distal residues regulating

Acknowledgments

Computational resources were provided by the Barcelona Supercomputing Center. Work was supported by startup funds from the Barcelona Supercomputer Center and through the Spanish Ministry of Education and Science through the project CTQ2007-62122/BQU. We further want to thank all coworkers in the reviewed studies.

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