Merz Research Group-Research Summary

Merz Group Research

NMR Refinement

NMR chemical shifts are one of most important parameters for the study of biomolecular structure and function. We have developed a fast approach to accurately calculate NMR chemical shifts using âœdivide-and-conquerâ method at the semiempirical MNDO level. This approach enables us to study NMR properties for the system up to thousands of atoms. Specifically, we are interested in 1) the chemical shift perturbation (CSP) upon the ligand-binding. When a small molecule is bound to protein, NMR chemical shifts of protein as well as ligand can be changed at a wide range. Experimental 1HN and 15N chemical shift perturbations can be used to identify a binding site, which is the cornerstone of SAR by NMR technique for drug discovery. Theoretical understanding of these perturbations can provide detail insights of protein-ligand interaction at the molecular level.

For instance, a comparison of the calculated CSP at different ligand structures with experimental values is able to determine the binding mode of ligand inside the binding pocket. 2) the refinement and validation of protein structures. It is well known that NMR chemical shift is sensitive to protein conformations. However, the use of chemical shift information in protein structure determination is limited due to the complicated relationship between the chemical shifts and protein structures. Quantum chemical calculations for chemical shifts can give a better understanding of this relationship and facilitate the refinement and validation of protein structures.

QM/MM

Combining Quantum Mechanical(QM) methods with Molecular Mechanical(MM) methods to get so called QM/MM methods offers several advantages over using just one method or just the other. These QM/MM methods are significantly faster than a standard QM method, but offer a higher accuracy of just using MM.

Treating the active site of a protein with Quantum Mechanics allows charge transfer and other electronic effects upon ligand binding to be accounted for where it matters most. Treating the rest of the protein with Molecular Mechanics vastly reduces the computational cost, but allows the charge field around the active site to be included in the calculation. Using our linear scaled DivCon program we can do very large QM patches to model ligand binding and calculate the free energy for a particular ligand binding to a protein. Also, using a QM method allows us to take into account entropy changes in the ligand and active site upon binding, giving us a more accurate scoring function for the binding process. Typically these effects are accounted for using parameters such as surface area, but using this QM/MM method the vibrational frequencies in the active site can be determined so the entropy changes upon binding can be calculated accurately. These entropy terms have been found to add around 6kcal/mol to the free energy, which corresponds to approximately 1000x change in binding affinities, showing that this slight change in binding affinity is actually very important.

QSAR INTRODUCTION

There are currently nearly 1,300 drugs in clinical use in the United States, 25% of which target enzymes. The majority of enzyme-targeted drugs are enzyme-substrate based and most act via non-covalent interactions. Designing a new drug requires numerous steps from its inception to its introduction into the market. This process takes years and can cost millions of dollars. One of the oldest tools used to reduce this time is QSAR (Quantitative Structure Activity Relationships). QSAR is a technique that relates a drugÕs activity to some numerical property of its molecular structure by a mathematical model.

In 1969, Hansch, who is widely regarded as the father of QSAR, used three forces to describe ligandÐreceptor interactions in terms of steric, electronic, and hydrophobic effects: the Taft and Hammet parameters and the partition coefficient between 1-octanol and water. In recent years, 3D QSAR methods have been developed including CoMFA (Comparative Molecular Field Analysis), CoMSIA (Comparative Molecular Similarity Indices Analysis), and receptor-based methods such as COMBINE. 3D QSAR methods generate predictive models using a set of compounds for which some experimental data, e.g Ki, IC50, are available and also descriptors calculated from 3D structures of each compound that is presented in its active conformation. CoMFA and CoMSIA are grid-based methods where all the compounds in the data set are aligned on top of one another and steric and electrostatic descriptors are calculated at each grid point using a probe atom. The descriptors in receptor-based QSAR models are calculated from the steric and electrostatic interactions between the ligand and receptor. The descriptors used in traditional 3D-QSAR are usually divided into three categories 1) electronic descriptors, e.g. HOMO and LUMO energies, 2) topological descriptors, e.g. connectivity indices, and 3) geometric descriptors, e.g. moment of inertia. The models in all cases are often created using multivariate statistical tools due to the large number and high degree of collinearity of descriptors.

QUANTUM ALIGNMENT AND QSAR

Absent from CoMFA like approaches are quantum mechanically (QM) derived descriptors of electronic structure. The first principles approach of QM methods gives them an advantage over their empirical counterparts. QM-QSAR is a relatively new technique where semiempirical QM methods are used, to aid alignment using a molecular orbital overlap procedure, and to develop a quantum molecular field-based QSAR models.

SE calculations of molecules provide total electronic energies, heat of formation and orbital information. The resulting MOs can be viewed as frontier orbitals where the energies and phases of the HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) are provided. As we know, for example in pericyclic reactions, frontier orbitals are extremely important in chemical behavior (covalent bonding, ionization, polarization, etc.) and the basis of QM alignment involves pairwise alignment of these and other energetically similar MOs.

RECEPTOR-BASED DRUG DESIGN

With the advent of virtual screening techniques it is not uncommon to screen a library of tens of thousands virtual compounds against a well-defined target. The transition from a lead compound to a drug candidate involves optimizing structural and chemical complementarities with the receptor. Computational tools lend themselves to such a task. Molecular mechanics and semiempirical quantum mechanical methods have the ability to measure the effect of functional group substitution. Although this can also be done experimentally through combinatorial chemistry, the main reason of the computational approach is the reduction of cost and time.

A scheme to decompose the intermolecular interaction energy of a series of protein-ligand complexes at the semiempirical level of theory has been developed in our lab. Extending the work of Wade and Ortiz et al. (J. Med. Chem. 1995, 38, 2681-2691), and Raha et al. (J. Am. Chem. Soc. 2005, 127, 6583-6594), COMBINE and the semiempirical quantum mechanical method PairWise energy Decomposition (PWD) were coupled together to form SE-COMBINE. This approach calculates the residue pairwise electrostatic interaction energies, and QSAR models can be built with the energies as descriptors using partial least squares (PLS).

The application of SE COMBINE was used as an investigation of the intermolecular interactions between 88 benzamidine inhibitors and trypsin and to test the ability of this new method to predict binding free energies (J. Chem. Theory Comput., 2006, 2:383-399). The predictive capability of SE-COMBINE is shown to be comparable to those of other QSAR methods, and using graphical intermolecular interaction maps (IMMs) enhances the interpretability of receptor-based QSARs.

NDDO-DFT

Although our group has had success in the usage of traditional semiempirical methods to analyze large biological systems modern technology gives us an oppurtunity to develop a less approximate method than AM1 or PM3. Using the NDDO formalism, a gaussian basis and DFT we hope to develop a new more reliable semiempirical method for usage in biological systems. This method will be able to employ advances in integral technology provided by gaussians to be able to dispose of the need for multi-polar models used in MNDO based methods. The use of DFT will allow for the use of new and exciting functional methods to be incorporated easily as well. Current implementation is in an in-house program Quick and a partial implementation has also been done in the GAMESS package.

X-Ray Refinement

Structural biology is a vitally important field that combines a number of experimental and theoretical tools to investigate the structural basis of the activity and function of biological molecules. With the development of experimental approaches, such as synchrotron radiation sources and cro-cooling techniques, X-ray crystallography has become a major tool to determine the structures of macromolecules. But it is still difficult to obtain atomic level structural details from protein crystallography due to the poor observation-to-parameter ratios.

We developed a novel X-ray structure refinement scheme that improves the crystal structures. In our approach, we use a more accurate level of theory, a hybrid quantum mechanical/molecular mechanical (QM/MM) energy restraint in X-ray refinement in which the atoms of key region are treated quantum mechanically, while the other parts of proteins, solvent atoms and ions are treated using a force field. This method allows for the accurate characterization of the interactions in important regions and provides a more optimal compromise between experiment and theory. In another effort we are developing a fully QM refinement that can be applied to the refinement of proteins without the aid of more simplified molecular mechanical models. Our suite of refinement procedures are a set of powerful new approaches to the study of the geometry, properties and energies of biological macromolecules.

Applicability of Semiempirical Methods for Proteins

An investigation into the applicability of semiempirical (SE) methods for minimization of X-ray protein structures indicates several areas in which the minimization method needs to be refined. For the investigation 32 small globular proteins were chosen from the protein data bank (Berman, Westbrook et al. 2000) that were solved using X-ray crystallography and ranged in resolution from 1.5-2.5 Angstroms.

Minimizations at the SE level were performed in vacuo. The absence of solvation resulted in several artifacts, most notably proton transfer between charged groups. Without solvent screening, both Lys and Arg typically transferred a proton to nearby glutamate sidechains. The addition of solvation effects during the minimization procedure is expected to fix these problems. The internal geometries of the SE minimized proteins were analyzed and compared to the typical values found in X-ray structures. In general, bond lengths from structures minimized at the PM3 level were longer than those found in X-ray structures. Unlike the bond angles, the torsion angles in SE minimized structures do not match closely with X-ray structures. While a molecular-mechanics term has been added to constrain backbone torsions to match experimental structures, in many cases planar structures are puckered during the minimization process, such as the guanadyl group in Arg as shown below. This highlights the need for either a re-parameterization of SE methods for protein structures or the implementation of additional molecular-mechanics based terms to offset these problems.

QM Continuum Solvent Model

Solvation effects are critical to serious molecular modeling simulation, especially for protein and other biosystem simulations.

The major obstacle for these simulations at the QM level is the costly calculation associated with the macromolecule itself, which increased a lot by considering solvation. We are using the Divide-Conquer semi-empirical QM method to cut the expense of the solute characterizing and developing Poisson-Boltzmann equation based implicit solvent model to address the solvation effects. The advantages of this model include:

Simulate macromolecules in solvent fast at QM level.
Real time QM solute charges for PB calculation.
Solute is polarizable by reaction field, via the self-consistent QM calculation.
No subjective solute dielectric constant, solute polarizibility is taken care of by QM.
Possible to address the charge transfer at the dielectric boundary

Urease Inhibition

Enzymes use a wide range of molecular mechanisms to facilitate reactions. Among the different effects that contribute to catalysis, the lowering of the free energy of activation plays a significant role. The energy lowering is measured relative to the reaction occurring in aqueous solution, and is quantified by the proficiency of the enzyme. Structural effects (enzyme flexibility), electrostatic interactions, and H-bonding, among others, act together in determining the proficiency. In this way, several different theoretical approaches have to be used simultaneously to understand key factors for enzyme reactivity. The ultimate goal is the design of inhibitors, and the most proficient enzymes are most sensitive to reversible inhibitors due to their high binding energy to the enzyme. Our research covers the different aspects related to enzyme reactivity by means of the application of different theoretical methodologies to the study of proposed reaction pathways:

Molecular dynamics simulation to study enzyme flexibility and how it contributes to substrate binding and reactivity
High level quantum chemical calculations of cluster models of the active site to analyze electrostatic interactions and bond formation/breaking when a ligand is coordinated in the active site.
High level quantum chemical calculations of synthetic bioinorganic mimics, to analyze the same interactions free of the uncertainties associated with the use of model clusters.
Mixed QM/MM calculations to combine both effects in a unique model system, simultaneously including the structural influence of the entire protein and the local interactions in the active site
High level QM calculations of the model reaction in aqueous medium, to further calculate the proficiency of the enzyme

This research strategy has demonstrated to be extremely successful in the study of the metalloenzyme urease. Urea amydohydrolase (urease) is a di-nickel enzyme that catalyzes the decomposition of urea to yield carbonic acid and ammonia. The theoretical study of this system is particularly challenging, as the MD simulations have to deal with 180 K atoms (Figure 1), and with a flexible mobile flap that has been found in close and open conformations, and holds key residues for catalysis (Figure 2). The QM calculations are complicated by open shell structures of multiplicity 5 (Figure 3). In addition, the force field has to be developed for the active site metallocenter, by means of geometry optimizations and second derivative calculations at high levels of theory. However, the activity of urease in agriculture and human health, associated with gastroduodenal diseases that include cancer, as well as with sickle cell anemia, justifies any theoretical effort.

We have found that urease is one of the most proficient enzymes
Contrary to what has been inferred from experiment, we have determined that urea coordinates to the active site in a mono-dentate manner,
Also at variance with experimental suggestions, we found that the elimination and hydrolytic pathways compete for the decomposition of urea in the active site, ultimately leading to CO2 and NH3.

In this way, our studies of the metalloenzyme urease demonstrate how theory can access details of the underlying mechanisms that are difficult for experimental studies to address.

Copper Metalloenzymes

Copper exists in both the cuprous and cupric states within the cell and is involved as a catalyst in several biological processes. Although these ions such are essential for normal cell behavior, the "free" existence of these ions in the cell is toxic. For example, cycling of copper ions between two oxidation states can catalyze the production of highly toxic hydroxyl radicals within the cellular environment which can result in damage to many intracellular macromolecules. Copper is sequestered and transported within the intracellular environment by a class of proteins known as copper chaperones. We have investigated Cu(I)-binding geometries by DFT in Gaussian98 and Gaussian03 and have performed MD simulations on the Human antioxidant protein (Hah1) in order to determine energetically favorable conformational transition states for the transfer of Hah1 to the Menkes Disease protein (Mnk4) in vivo.