Research Interests

areas goals interdisciplinary references

Professor
Paul G. Mezey Canada Research Chair Scientific Modelling and Simulation Department of Chemistry and Department of Physics and Physical Oceanography Memorial University of Newfoundland St. John's, NL, CANADA A1B 3X7 tel 1 709 737 8768 fax 1 709 737 3702 email pmezey@mun.ca |

Computer modeling and simulation are gaining exceptional importance in a growing range of fields of science and technology. Such fields are modern molecular science, biochemistry, and nanotechnology, where the objects studied often fall within a particular size-range, where direct observation is cumbersome, expensive, or hindered by physical or technical limitations. In these and related areas, computer modeling and simulation play an especially important role.

The research involves fundamental developments in computational quantum chemistry, molecular informatics, combinatorial quantum chemistry, and virtual reality simulation on the molecular level, as well as applications in biochemistry, biotechnology, nanotechnology, pharmacology, toxicological risk assessment, and a variety of non-chemistry fields. The four recent advances on which the research is partially built are (i) development of ab initio quality quantum chemistry computer modeling of large biomolecules, (ii) detailed molecular shape analysis methods, (iii) proof and applications of the "Holographic Theorem" of molecular informatics: any small volume of the charge density cloud contains the complete information about the molecule, and (iv) electron density fuzzy fragment approach to Combinatorial Quantum Chemistry.

- (i) Macromolecular Quantum Chemistry. This component of the research is based on earlier advances in ab initio quality macromolecular modeling, using linear-scaling macromolecular electron density and density matrix methods (the numerical Molecular Electron Density Lego Approach, MEDLA method [1,2], and the more advanced analytical Adjustable Density Matrix Assembler, ADMA method [3-7]). These are the first and still the only methods for which proven ab initio quality electron densities over the thousand atom limit have been published, although promising, but more expensive density functional methods may eventually provide similar results. The ADMA method, with linear dependence on the molecular size, is a macromolecular density matrix computational scheme suitable for the calculation of ab initio quality quantum chemistry information equivalent to that of a (still prohibitively expensive and inaccessible) macromolecular wavefunction. The ADMA method is a tool for the determination of ab initio quality approximate density matrices, electron densities, energies, and conformational forces of proteins and other large biomolecules, with promising applications in computer modeling and simulation in most fields of science which involve large molecules. In particular, the computation of ab initio quality macromolecular forces will find applications in the study of biomolecule conformations, geometry optimizations, and protein folding problems. This is the first opportunity to address the protein folding problem at a level of physically sound principles and reliability provided by ab initio quality quantum chemical calculations.
- (ii) Shape Analysis. The shape of a molecule is the shape of its electron density cloud (that also determines the electrostatic potential). This is the shape that is recognized by a reacting partner molecule. It is important to distinguish the actual electron density shapes from shapes of the commonly used Van der Waals surfaces of fused spheres, where the latter have systematic errors in the representation of pi-bonds and aromatic systems. The Molecular Shape Analysis techniques [8,9] and Potential Surface studies [10], two earlier developments in the laboratory of the applicant, are based on the computer implementation of topological shape analysis methods applied to fuzzy electron density clouds and molecular conformations. These methods, described in several publications and two books by the applicant, are efficient tools for molecular similarity and complementarity analysis, and for the simulation of molecular recognition. These shape analysis and similarity analysis methods can be applied to modeling and simulation in many non-chemistry fields, for example, in studies of plant shapes, in engineering design, and correlations between tumor shapes and diagnosis in medicine.
- (iii) The recently proven Holographic Electron Density Theorem [11,12], a new law of molecular informatics, establishes a fundamental property of all molecules: any nonzero volume piece of the (non-degenerate ground state) molecular electron density cloud contains the complete information about the entire molecule (that, being a quantum object, has no boundary). It is well known that molecules contain only nuclei and an electron density cloud, hence all molecular information is present within the electron density; according to the Hohenberg-Kohn Theorem the complete electron density determines the molecular energy, and through the Hamiltonian, all other properties. However, according to the Holographic Electron Density Theorem, all molecular information is also present already in any (nonzero volume) part of the electron density cloud, hence the new theorem is stronger than the Hohenberg-Kohn Theorem. According to the Holographic Electron Density Theorem, the part implies the whole, and a small piece of the electron density is already sufficient to determine the molecular energy and all other molecular properties. This theorem serves the goals of the emerging science of Molecular Informatics [13], and suggests a new, local approach to molecular modeling and electronic structure - molecular property correlations and predictions. It is now fully justified to seek correlations between biochemical activity and local molecular features.
- (iv) The combinatorial quantum chemistry modeling approach [14,15], based on the generation and combination of fuzzy molecular electron density fragments adjusted for local surroundings, is fully analogous with the synthetic combinatorial chemistry approaches. The approach involves the fundamentals of chemistry, molecular physics and also some of the modern aspects of applied mathematics. This provides an extremely rapid method for the computer modeling of a very large number of related molecules.

The research plan for the Chair project involves fundamental development of the quantum chemistry basis of molecular modeling and molecular informatics, software development, and a wide range of modeling and simulation applications in many fields where the detailed molecular structure, electronic properties, structure-activity correlations, and large scale similarity and complementarity analyses are important. These applied fields, requiring powerful computer hardware, include biotechnology, nanomaterials, pharmaceutical drug design, medicinal chemistry, environmental toxicology, marine health research, polymer research, and molecular devices.

The research project has the dual goals of (i) fundamental development of methods and computer software, and (ii) applications of powerful modeling and simulation methods to a variety of fields.

Whereas both aspects are focusing on chemistry, neither the scope of the methods and software, nor the range of applications will be limited to chemistry. It is an explicit purpose of the research to seek and develop strong modeling and simulation capacity applicable to many fields beyond chemistry. In particular, the already existing shape analysis methodologies have been developed with various chemical and biochemical applications in mind, and the emphasis is often on molecules. Nevertheless, most of the shape analysis and similarity evaluation methodologies are very general, applicable to a variety of other modeling and simulation fields of interest, both at Memorial University of Newfoundland, and at various other Canadian and international research centers.

Within the central chemistry subject area, the earlier developments naturally suggest a systematic, new approach to macromolecular modeling and simulation, based on ab initio quality quantum chemistry, and the construction of an appropriate suite of computer programs, suitable for detailed, high resolution and high quality biomolecular modeling and simulation. The three interrelated components of the central, chemical modeling and simulation project are (a) high quality biomolecular modeling, (b) molecular level virtual reality simulation, and (c) combinatorial quantum chemistry.

(a) The novel, high quality biomolecular modeling will involve efficient and user-friendly computer implementation of already existing macromolecular quantum chemistry methodologies, fuzzy fragment electron density matrix databank generation, the implementation and further development of electron density deformation methods to provide simple tools to follow conformational changes, new software development for macromolecular force computation (for example, to address the protein folding problem), based on existing and proven methodologies introduced by the applicant. In addition, fundamentally new approaches will be developed based on post-Hartree-Fock generalizations of the underlying Additive Fuzzy Density Fragment (AFDF) principle, and an error reduction method suggested by the Holographic Electron Density Theorem.

(b) The software developments in component (a) will serve as the basis for the molecular level virtual reality simulation, a computer modeling approach relying on real-time or nearly real-time generation of dynamic representations of conformationally modified electron densities to simulate actual conformational changes and chemical reactions. This approach will provide a virtual window to view and manipulate models of interacting molecules, to study and model chemical reactions and other dynamic processes on the molecular level.

(c) The combinatorial quantum chemistry approach, using quantum chemical molecular fragment databanks such as those of fuzzy fragment density matrices, will enable the modeler to construct nearly simultaneously very large numbers of molecular models, using a combinatorial assembly of the molecular fragment models (and readjustment for precise nuclear geometry and for the effects of local surroundings, if required). The use of precalculated fragment density matrices, combined with efficient density deformation algorithms to account for the changed surroundings in new molecules [15-17], and the combinatorial, additive fragment assembly approach, provide very efficient computational means for the rapid construction of large numbers of molecular electron densities. This approach, fully analogous with synthetic combinatorial chemistry, will allow the computational screening of large numbers of molecular models for any desired feature, related to a specific biochemical or other type of activity [see ref. 15].

An underlying aspect of many of these research fields is conformational motions and reactions of the molecules involved, that places new emphasis on potential energy surface studies and the efficient treatment of large numbers of the possible rearrangements [10]. The research plan involves extensions of small molecule potential surface methods [10,18,19] to accommodate modeling the biochemically essential motions of macromolecules [20,21].

The basic concepts, approaches, methods, and computer algorithms used and to be developed within the project are highly interdisciplinary, involving mathematics, computer science, the fundamentals of physics and chemistry, biochemistry, biology, toxicology, and computer-aided drug discovery. In addition to application to chemistry, the Shape Analysis and Similarity Evaluation methods will be applicable to modeling and simulation in most of the other, non-chemistry fields where three-dimensional shapes, shape changes, and similarity measures are important. These fields include several research topics of interest in the Departments of Biochemistry, Physics and Physical Oceanography, Mathematics and Statistics, Computer Science and Earth Sciences, in the Faculty of Engineering and Applied Science, in the Faculty of Medicine, as well as within the interdisciplinary programs and institutions such as the interdisciplinary graduate programs in Environmental Science and Computational Science, and the Memorial University of Newfoundland Computation and Visualization Center (CVC).

[1] P.D. Walker and P.G. Mezey, "Ab initio Quality Electron Densities for Proteins: A MEDLA Approach", *J. Amer. Chem. Soc.*, 116, 12022-12032 (1994).

[2] P.D. Walker and P.G. Mezey, "Realistic, Detailed Images of Proteins and Tertiary Structure Elements: Ab Initio Quality Electron Density Calculations for Bovine Insulin", *Can J. Chem.*, 72, 2531-2536 (1994).

[3] P.G. Mezey, "Macromolecular Density Matrices and Electron Densities with Adjustable Nuclear Geometries", *J. Math. Chem.*, Vol. 18, pp. 141-168, (1995).

[4] P.G. Mezey, "Quantum Similarity Measures and Löwdin's Transform for Approximate Density Matrices and Macromolecular Forces", Int. J. Quantum Chem., Vol. 63, pp. 39-48, (1997).

[5] T.E. Exner and P.G. Mezey, "Ab Initio Quality Electrostatic Potentials for Proteins: an Application of the ADMA Approach", *J. Phys. Chem. A*, 106, 11791-11800 (2002).

[6] T.E. Exner and P.G. Mezey,
"Ab Initio Quality Properties for Macromolecules Using the ADMA Approach",
*J. Comput. Chem.*, 24, 1980-1986 (2003).

[7] T.E. Exner and P.G. Mezey,
"The Field-Adapted ADMA Approach: Introducing Point Charges",
*J. Phys. Chem.*, in press (accepted March 2, 2004).

[8] P.G. Mezey, "Shape Analysis", in __Encyclopedia of Computational Chemistry__, Eds. P. v. R. Schleyer, N.L. Allinger, T. Clark, J. Gasteiger, P.A. Kollman, H.F. Schaefer III, P.R. Schreiner, John Wiley & Sons, Chichester, UK, Vol. 4, pp. 2582 - 2589, (1999).

[9] P.G. Mezey, __Shape in Chemistry: An Introduction to Molecular Shape and Topology__, VCH Publishers, New York, 1993.

[10] P.G. Mezey, __Potential Energy Hypersurfaces__, Elsevier, Amsterdam, 1987.

[11] P.G. Mezey, "The Holographic Electron Density Theorem and Quantum Similarity Measures", *Mol. Phys., Vol.*, 96, 169-178, (1999).

[12] P.G. Mezey, "Holographic Electron Density Shape Theorem and Its Role in Drug Design and Toxicological Risk Assessment", *J. Chem. Inf. Comp. Sci.*, Vol. 39, pp. 224-230, (1999).

[13] P.G. Mezey, "Molecular Informatics and Topology in Chemistry", in __Topology in Chemistry__, Eds. R.B. King and D.H. Rouvray, Ellis Horwood Publ., U.K., pp. 316-332, (2002).

[14] P.G. Mezey, "Theory and Detailed Computer Modeling of Biomolecules", in __Fundamentals of Life__, Eds. G. Palyi, C. Zucchi, and L. Cagliotti, Elsevier (Paris), pp. 401-416, ( 2002).

[15] P.G. Mezey, "Computational Aspects of Combinatorial Quantum Chemistry", *Journal of Computational Methods in Sciences and Engineering (JCMSE)*, 1, 99-106, (2001).

[16] P.G. Mezey, "Averaged Electron Densities for Averaged Conformations", *J. Comput. Chem.*, 19, 1337-1344 (1998).

[17] P.G. Mezey, K. Fukui, and S. Arimoto, "A Treatment of Small Deformations of Polyhedral Shapes of Functional Group Distributions in Biomolecules", *Int. J. Quant. Chem.*, 76, 756-761 (2000).

[18] L.J. Wang, P. Warburton, and P.G. Mezey,
"Theoretical Prediction on the Synthesis Reaction Pathway of N_{6} (C_{2h})",
*J. Phys. Chem. A*, 106, 2748-2752 (2002).

[19] L.J. Wang and P.G. Mezey,
"Synthesis Reaction Pathway of Nitrogen-Rich Ionic Compound N_{4}H_{2}F^{+} and Stability of its Isomers",
*J. Phys. Chem. A*, 106, 10391-10395 (2002).

[20] T.E. Exner and P.G. Mezey,
"A Comparison of Nonlinear Transformation Methods for Electron Density
Approximation",
*J. Phys. Chem. A*, 106, 5504-5509 (2002).

[21] P.G. Mezey,
"Theory and Detailed Computer Modelling of Biomolecules",
in __Fundamentals of Life__, Eds. G. Palyi, C. Zucchi, and L. Cagliotti,
Elsevier (Paris), 2002, pp. 401-416.

This page was created by Peter Warburton. Please send comments to him at peterw@mun.ca.