Theoretical Modeling of Enzymatic Catalysis

We use accurate quantum chemical methods to model active sites of enzymes and to calculate properties and catalytic pathways. Quantum chemical methods have recently reached the level of speed and accuracy that makes them an indispensable tool in the study of enzyme mechanisms. This relies on several factors. Probably the most important one is the development of the density functional theory (DFT) approach. In the last decade, DFT has improved from being a method providing qualitative results to becoming a quantitatively highly accurate method, competing with the most accurate ab initio methods.
The favorable scaling of DFT compared to ab initio methods allows for the treatment of far larger systems, and has thus opened the door to much wider applications than ever before. Of course, the nearly exponential development in computer power also has a major impact on the field. Quantum chemistry has gone from being a quite expensive branch of science to a quite cheap one, where many problems can be addressed using a couple of ordinary personal computers.

One of the most useful aspects of quantum chemical methods is that short-lived species are treated with equal ease and accuracy as long-lived ones. This means that it is possible to obtain structures and energies for intermediates and transition states for chemical reactions. However, the systems studied experimentally are usually too large for a quantum chemical treatment. To test one or several reaction pathways and to find the transition states connecting the intermediates, a large number of calculations are usually required. With the computer power of today, using DFT methods, one is able to treat system of up to ca 100 atoms. This is a considerable improvement compared to just a couple of years ago. Still, with an active site of an enzyme containing 4-5 amino acids, we are immediately up to sizes on the limit of what can be handled within reasonable time. Necessity arises hence to employ as small models as possible of the active sites, in order to limit the computational time. At the same time, we have to ensure that the basic chemical features of the system are correctly accounted for.

For instance, to model metal centers, normally only the first coordination shell needs to be included. This usually defines the essential characteristics of the metal site. If some second shell residues are known from experiments, or can be suspected, to influence the reactions, they are included explicitly. In cases where the metal site is particularly large, including several metal centers, some of the ligands that do not directly participate in the chemistry can be replaced by simpler ligands, such as water or ammonia, as a first approximation.

The rest of the enzyme is usually considered as a homogenous polarizable medium and can normally be modeled by dielectric cavity techniques. In these methods, the solute cavity is determined from a surface of constant charge density around the solute molecule. The dielectric constant chosen for proteins is the standard epsilon = 4. The relative solvent effects between minima and transition states are normally calculated to be quite small (on the order of a few kilocalories/mol), which makes the particular choice of the dielectric constant less critical.

We have used this this strategy to model the active sites and catalytic mechanisms of a number of enzymes. These include Pyruvate-Formate Lyase (PFL), Galactose Oxidase (GO), Ribonucleotide Reductase (RNRs), Glyoxalase I (GlxI), and Benzylsuccinate Synthase (BSS). We are currently studyin several other enzymes, such as Nitrous Oxide Reductase (N2OR), Pyruvate-Ferredoxin Oxidoreductase (PFOR), and Spore Photoproduct Lyase (SPL). The chemistry involved in these reactions spans over the whole spectrum, including acid-base catalysis, electron and proton transfer reactions, transition metal assisted catalysis, and free radical chemistry.

Figure: An example of the imaginary frequency of a transition state, N-O bond cleavage step in Nitrous Oxide Reductase.

• Some representative papers
• Fahmi Himo's Homepage

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