Molecular Modeling

Molecular modeling is the term used to describe the use of computers to construct molecules and perform a variety of calculations on these molecules in order to predict their chemical and quantum characteristics and behaviour. It is often used with the term computational chemistry. Computational chemistry is a broader, referring to any use of computers to study chemical systems. Some chemists use the term computational quantum chemistry to refer to the use of computers to perform electronic structure calculations, where the electrons in a chemical system are calculated.

Medicinal chemists today are facing many complicated challenges. The most demanding one is the rational of new therapeutic agents for treating human disease. The concepts used are very simple. New molecules are built either on the basis of similarities with the known reference structure or more development of the of the same structure. Molecular modeling contributes to the understanding of these processes in a qualitative and quantitative way. It means analyzing the details of the molecular machinery involved in a known system and understanding the way it works.

At present, scientists can rely on an impressive number of tools allowing to give answer to a question: what to do with molecular calculations. Direct accurate property calculations of molecular systems of increasing complexity are now possible, often in competition with experimental methods. The use of molecular calculations as an aid to visualize complex molecular systems and their properties is a current practice in many laboratories not directly addressed to theoretical studies.

Molecular modeling allows the user to determine three fundamental items of interest of a molecule or system of molecules:

• the structure, or geometry of the molecule

• the property or properties of a molecule or system of molecules

• the activity, or reactivity, of a molecule or system of molecules.

These determinations can be used in experimental studies, or can be carried out to predict experimental results. With increased technologies, molecular modeling can be used to reduce dependence on wet, or traditional, chemical experimental procedures.

The term molecular mechanics was coined in the 1970s to describe the application of classical mechanics to determinations of molecular equilibrium structures. The method was previously known by two different names: the Westtheimer method and the force field method. The name and acronym MM are now established.

Andrews gave the idea of treating the molecules as balls joined by springs. Synder and Schachtschneider showed that transferable force constants could be obtained.

Force field should be treated as a set of constants fixed for more rigorous calculation. In MM we take account of non-bonded interactions; and also the chemical sense of each atom. a valence force field that contains non-bonded interactions is referred as a Urey-Bradley force field. The object of molecular mechanics is to predict the energy associated with a given conformation of a molecule. However, molecular mechanics energies have no meaning as absolute quantities. Only difference in energy between two or more conformations has meaning. A simple molecular mechanics energy equation is given by:

Energy = stretching energy + bending energy + torsion energy + non-bonded interaction energy.

Stretching Energy

Whenever a bond is compressed or stretched the energy goes up. The energy potential for bond stretching and compressing is described by an equation similar to Hooke's law for a spring. Each bond stretch between atom types A and B makes a contribution to the total molecular potential energy of

U_AB =1/2 k_AB (R_AB - R_e,AB)²

Parameter k_AB is the force constant, R_AB the instantaneous bond length and R_e,AB the equilibrium bond length.

Bending Energy

The bending energy equation is also based on Hooke's law. It is usual to write these as harmonic ones, for the connected atoms A-B-C

U_ABC = 1/2 k_ABC (ϑ_ABC -ϑ_e,ABC )²

where k is the force constant, and the subscript 'e' refers to equlibrium value where the molecule is at rest.

Torsion Energy

The torsion energy in molecular mechanics is primarily used to correct the remaining energy terms. The torsional energy represents the amount of energy that must be added to or subtracted from the Stretching Energy + bending Energy + Non Bonded Interaction Energy terms to make the total energy agree with the experiment or rigorous quantum mechanical calculation for a model dihaderal angle. It is given by:

U = ∑A [1+cos (nτ- φ)]

where A is the amplitude, n is the peridocity and φ is shift of rotation.

Non Bonded Energy

The non bonded energy represents the pair-wise sum of the energies of all possible non bonded atoms. The non bonded energy accounts for repulsion, van der Waals attraction and electrostatic interactions. van der Waals attraction occurs at short range, and rapidly dies off as the interacting atoms move apart by a few angstrons. Repulsion is modeled by an equation that is designed to rapidly blow up at close distances. The electrostatic contribution is modeled using a Coulombic potential. The electrostatic energy is a functionof the charge on the non-bonded atoms, their interatomic distance and molecular dielectric expression.

In molecular modeling terms Eψ represents the total potential and kinetic energy of all the particles in the structure and H is the Hamiltonian operator acting on the wave function ψ. Operators are mathematical methods of converting one function into another function in order to find a solution or solutions of the original function.

Schrodinger equations for atoms and molecules use the sum of the potential and kinetic energied of the electrons and nuclei in a structure as the basis of a description of three dimensional arrangements of electrons about the nucleus. Equations are normally obtained using the Born-Oppenheimer approximation, which considers the nucleus to be stationery with respect to the electrons. This approximation means that one need not consider the kinetic energy of the nuclei in a molecule, which considerably simplifies the calculations. Schrodinger equation is not a single equation but represents a set of differential wave equations, each corresponding to an allowed energy level in the structure.

It is not possible to obtain a direct solution of a Schrodinger equation for a structure containing more than two particles. Solutions are normally obtained by simplifying by using Hartree-Fock approximation. This approximation uses the concept of an effective field to represent the interactions of an electron with all the other electrons in the structure.

Quantum mechanics is useful for calculating the values of ionization potentials, electron affinities, heats of formation and dipole moments and other physical properties of atoms and molecules. A knowledge of these properties are useful to access the nature of the binding of a possible drug to a target site.

Semi-empirical methods represent a “middle road” between the mostly qualitative results available from molecular mechanics and the computationally time-consuming quantitative results available from ab initio methods. Semi-empirical methods are particularly useful in the study of organic chemistry and the structure and reactions of organic molecules. Semi-empirical methods were developed specifically for this area of chemistry, and organic continues to be the primary target for this method. Semi-empirical methods also provide researchers with a relatively quick way of studying the structure and behavior of molecules.

PM3, or Parameterized Model number 3, is a semi-empirical method for the quantum calculation of molecular electronic structure in computational chemistry. It is based on the “Neglect of Differential Diatomic Overlap” integral approximation. It uses two Gaussian functions for the core repulsion function. The PM3 model has been widely used for rapid estimation of molecular properties and has been recently extended to include many elements, including some transition metals. PM3 calculations can be useful in many situations, such as

• computational modeling of structure-activity relationships to gain insight

• about reactivity or property trends for a group of similar compounds.

• development of hybrid quantum mechanics / molecular mechanics (QM/MM) methods for modeling of biochemical processes.

• preliminary optimization of geometries of unusual molecules and transition states that cannot be optimized with molecular mechanics methods

• in many applications where qualitative insight about electronic structure and properties is sufficient.

Hartree-Fock (HF) theory is a molecular orbital based approximation which has served as a corner stone is quantum chemistry. The idea of relating the electronic structure with molecular orbital is particularly intriguing for chemists because of its instructive and illustrative nature. It is is based on the assumption that every electron moves in the potential created by the nucleus plus the average potential of all the other electrons. It is an independent particle model in which the electron correlation is neglected. In restricted Hartree-Fock Theory, the electronic state is represented by a single configuration state function (CSF)

CSF = ∑i | i ›

where І i › are Slater determinants with coefficients Ci fixed by the spin symmetry of the wave function. each Slater determinant is constructed as a product of the canonical spin function (cs).

(CS) = ∏a+iα a+iβ | Vac ›

where | Vac › is the vacuum space and a+iα , a+iβ are the creation operators.

The Hartree-Fock equations are described as pseudo eigen value equations, to be solved in an iterative process where the Fock matrix is repeatedly constructed and diagonalized until a set of orbital that satisfy the canonical conditions is obtained.

The Fock operator is

F_pq = ½ ∑<CS|[ a+qσ ,{apσ M}]|CS›

The Hamiltonian operator may be written in the form

M = ĥ + ĝ + hnm = ∑pq hpq Epq + ½ ∑pqrs gpqrs epqrs + hnuc

The Hamiltonian contains the full set of electronic interactions and is independent of the electronic state studied. The Fock operator is by contrast an effective one-electron operator, designated with a particular state in mind.

Density functional theory (DFT) is a quantum mechanical theory used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms and molecules. With this theory, the properties of a many-electron system can be determined by using functional, i.e. functions of another function, which in this case are the spatially dependent electron density. Hence the name density functional theory comes from the use of functionals of the electron density. DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry. DFT was not considered accurate enough for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange and correlation interactions. DFT is now a leading method for electronic structure calculations in chemistry.

There are many sophisticated methods for solving the many-body Schrödinger equation based on the expansion of the wavefunction in Slater determinants. While the simplest one is the Hartree-Fock method, more sophisticated approaches are usually categorized as post-Hartree-Fock methods. However, the problem with these methods is the huge computational effort, which makes it virtually impossible to apply them efficiently to larger, more complex systems. The most significant advantage of DFT methods is a increase in computatinal accuracy without the additional increase in computing time. DFT methods such as B3LYP with basis sets are considered to be a standard model for many applications.

Computational methods have become increasingly important in drug discovery and design processes. Computational chemistry methods are used routinely to study drug complexes in atomic detail and to calculate properties of drug candidates. Tools from information technology are increasingly essential to organize and manage the huge chemical and biological activity databases.

In addition, computerized automation is highly amenable to generate chemical derivatives. A computer can rapidly generate and predict the binding of all potential derivatives, creating a list of best potential candidates. In essence, computer filters all weak binding compounds, allowing the chemist to focus, synthesize, and test only the most promising ligands. Thus, using the CADD software to aid in the refinement of lead molecules is the most effective manner in which these tools can be employed. The use of computer modeling to refine structures has become standard practice in modern drug design. So the current role of computer in drug design lies in:

a. Storing and retrieving information

1. Structures determined experimentally by IR methods for drug molecules.

2. Molecules and activities to test the affect of small structural changes on biological activity

b. Information about toxicity and its relationship to structure

c. Visualization of molecules

1. Similarities/differences between drugs and receptors.

2. Interaction between drugs and receptors

d. Calculations

1. Interaction strengths

2. Motion (dynamics)

CADD methods and bioinformatics tools offer significant benefits for drug discovery programs.

• Cost Savings. The Tufts Report suggests that the cost of drug discovery and development has reached $800 million for each drug successfully brought to market. Many researchers and biopharmaceutical companies now use computational methods and bioinformatics tools to reduce this cost burden. Virtual screening, lead optimization and predictions of bioavailability and bioactivity can help guide experimental research. Only the most promising experimental lines of inquiry can be followed and experimental dead-ends can be avoided early based on the results of CADD simulations.

• Time-to-Market. The predictive power of CADD can help drug research programs choose only the most promising drug candidates. By focusing drug research on specific lead candidates and avoiding potential “dead-end” compounds, biopharmaceutical companies can get drugs to market more quickly.

• Insight. One of the non-quantifiable benefits of CADD and the use of bioinformatics tools is the deep insight that researchers acquire about drug-receptor interactions. Molecular models of drug compounds can reveal intricate, atomic scale binding properties that are difficult to envision in any other way. When we show researchers new molecular models of their putative drug compounds, their protein targets and how the two bind together, they often come up with new ideas on how to modify the drug compounds for improved fit. This is an intangible benefit that can help design research programs.

CADD and bioinformatics together are a powerful combination in drug research and development.

Computer-Aided Drug Design (CADD) is a specialized discipline that uses computational methods to simulate drug interactions. CADD methods are heavily dependent on bioinformatics tools, applications and databases. Information Technology, Information Management, software applications, databases and computational resources all provide the infrastructure for bioinformatics. There are several key areas where bioinformatics supports CADD research. The activity prediction studies on the basis of shape of the molecule include : Fast and efficient clustering of molecules based on molecular shape, Field-based similarity computation of molecular structure, Flexible Quantitative Structure Activity Relationships (QSAR) analysis of molecules based on shape cluster. Various packages/ softwares used in the present work are:

Accelrys

• Accelrys, http://www.accelrys.com

• Product Summary: Accelrys is a computational science company that develops and delivers scientific software applications and services to solve R&D problems. They provide simulation and informatics software as well as a computational portfolio that combines modeling and visualization software to predict properties and interpret the behavior of molecules and materials and services. They adhere to an open, component-based software platform that can run across the network on Windows, Linux, or UNIX servers.

• Key capabilities and offerings: It has complete modeling and simulation product suite designed for structural and computational researchers to screen a wide variety of materials and process variables in silico. It provides simulation environments to create, view, and analyze molecules.

Acd Labs

• Advanced Chemistry Development Inc. (ACD Labs); http://www.acdlabs.com

• Product Summary: ACD/SpecManager product portfolio encompasses a number of technique-specific modules that handle a full range of analytical data (including Infrared, Raman) from all major instrument vendors. Compound Molecular Property Predictors is available as a Suite and separately, a set of integrated modules calculate physicochemical properties, such as boiling point, Log P, polar surface area, Log D as a function of pH, solubility as a function of pH, pKa, etc. ACD/Structure Design Suite builds on these predictions to suggest structural modifications that result in the desired physicochemical properties. ACD/ChemSketch Drawing Package is compatible with various chemistry file formats, is fully integrated and included with all ACD/Labs products and comes with several modules to expand its capabilities (e.g., ACD/Dictionary, ACD/Tautomers, ACD/3D Viewer, and more).

• Key capabilities and offerings: ACD/SpecManager software encompasses a number of modules for analytical data import and processing, a report editor (ACD/ChemSketch), and a databasing component for storage and retrieval of disparate forms of analytical information. All modules, each of which can be used separately, integrate into a single master interface that automatically provides appropriate technique-specific expert tools, such as spectral interpretation, baseline correction, and others, according to the context of the selected data set. ACD/Structure Elucidator combines the use of legacy data and ACD/Labs’ Computer-Assisted Structure Elucidation (CASE) algorithm to predict and elucidate chemical structures of unknown chemical entities. Compound Molecular Property Predictors module calculates acid-base ionization constants (pKa values at 25 C) and zero ionic strength in aqueous solutions, the octanol-water partition coefficient (log P), the distribution coefficient, log D, Calculates the aqueous solubility at any pH, as well as intrinsic solubility and solubility of the chemical dissolved in pure (unbuffered) water for almost any organic molecule. This software package helps medicinal chemists choose substituent modifications and evaluate the physicochemical properties of the new analogs in order to optimize their bioavailability.

Bio Byte

• BioByte, http://www.biobyte.com

• Product Summary: BioByte provides a variety of software solutions to the drug discovery scientist that range from a chemically-oriented database system to a unified driver for ClogP.

• Key capabilities and offerings: C-QSAR Package is their premier offering and is a comprehensive standalone drug discovery system. Dual databases of QSAR equations relating bio- and physicochemical activities to structural parameters. BIO currently contains more than 12,700 equations for different biological systems, which includes anticancer agents, anti-HIV agents, anti-bacterials, topoisomerase inhibitors, COX inhibitors, and QSAR for ADME (mainly absorption, metabolism, etc.). QSAR models are derived for different biological systems, which includes anticancer agents, anti-HIV agents, anti-bacterial, topoisomerase inhibitors, COX inhibitors, QSAR for ADME, mainly absorption, metabolism, etc.

CambridgrSoft

• CambridgeSoft, http://www.cambridgesoft.com

• Product Summaries: ChemDraw(9.0): http://www.chemdraw.com, ChemDraw is a widely used drawing package that is used to draw molecules, reaction schemes, and textual information in publication quality form. Information can easily be cut and pasted into word documents and other applications. Molecules can be converted into other molecular file formats

• Key capabilities and offerings: MS Word Numbering assigns reference numbers to ChemDraw structures that appear in MS Word documents to use as a eference. Structure CleanUp improves poor drawings. Online Menu allows one to draw a structure or model and immediately get online vendor information from chem. ACX.Com. ClogP property server calculates n-octanol/water partition coefficients. ChemProp/Draw allows one to compute physical properties such as Log P, BP, and MP.

CAS Scifinder

• CAS, ChemistryAbstract Services, www.cas.org, http://www.cas.org, and http://www.cas.org.prod.html

• Product Summaries: It contains data from over 200 databases covering chemistry, life sciences, engineering, patents, physics, and many other scientific fields that can be searched using command line searching,

• Key capabilities and offerings: Over 200 databases are accessible through STN, for a full listing with the details see: http://www.cas.org/ONLINE/DBSS/dbsslist.html. STN uses CA Lexicon for searching and permits structure-based searches similar to those available through SciFinder. STN Database Summary sheets are produced for every file on STN. Each sheet describes file content, sources of the file, file data, and producer. SciFinder provides access to more than 23 million abstracts, over 26 million organic and inorganic substances, and over 56 million sequences. SciFinder is one of several interfaces for access to the voluminous information in the CAS databases. SciFinder can be searched by structure, concepts, reaction and other parameters and searches may be further refined.See: http://www.cas.org/SCIFINDER/scicover2.html

ChemAxon

• ChemAxon; http://www.chemaxon.com/

• Product Summary : General: ChemAxon provides Java based chemical software evelopment platforms for the biotechnology and pharmaceutical industries. ChemAxon creates web-based cross platform solutions for chemoinformatics and chemical communication. Marvin is a collection of Java tools for drawing, displaying and characterizing chemical structures, substructures and reactions. It features advanced molecule (isotopes, radicals, lone pairs, templates, abbreviated groups, multiple groups, attached data, 3D sketching), reaction (manual and automatic mapping, reaction stereo, curved electron flow arrows) and query drawing (generic atoms/bonds, atom lists/notlists, pseudo atoms, link nodes, other query properties, recursive SMARTS, R-groups) capabilities. Marvin contains 2D cleaner for presentation quality molecule display and a proprietary geometry optimizer able to create 3D geometry from connectivity and perform conformational search. Marvin Applets: Tools for building chemical web pages, which are compatible with most browsers (Internet Explorer, Netscape, Mozilla, Firefox, Safari, Opera, etc.) and have two GUIs: AWT and Swing. They offer access from/to JavaScript and are customizable by applet parameters. The signed versions of the applets support access to local files (open/save molecule files, save structure images). Marvin Beans: A set of classes for building applications. It provides an API with low and high level classes, and JavaBeans. Marvin Beans support copy and paste to/from several other structure handling software, import/export various formats (SMILES, Molfile, SDfile, etc.), and can generate images (BMP, PNG, JPG, SVG, etc.) MarvinSketch/MarvinView: Applications for end users which are built from Marvin Beans. MarvinSketch is a tool for drawing molecules/reactions. MarvinView displays a set of structures. Calculator Plugins are an open technology, custom chemical calculation platform for Marvin and other JChem tools. Default calculations are provided as dynamically loading- plugins. Currently available tools from ChemAxon include:

1. pKa

2. log P, log D

3. polar surface area (PSA)

4. charge distribution

5. Hückel analysis

6. polarizability prediction

7. H-bond acceptors/donors

8. major microspecies

9. refractivity

10. isoelectric point

11. tautomers

12. resonance

13. elemental analysis

14. topology analysis

http://www.chemaxon.com/marvin/chemaxon/marvin/help/calculatorplugins html provides the theory behind the programs used for the calculations.

• • • Key capabilities and offerings:

      • • • Marvin is a Java based chemistry software that is available in various forms. Marvin Applets are created for the web developer who builds chemical Internet/Intranet sites. Marvin can handle molecules in various file formats including MDL mol, Compressed mol, unique SMILES, SMARTS, Sybyl mol, PDB, CML, XYZ, POV-Ray. MarvinView can display a 2D or 3D molecule, or many molecules in a table. Marvin can be equipped with custom chemical calculation tools by the integrated plugin services.

          • Marvin contains a framework for integrating chemical computations into the drawing/viewing application environment. These tools – called plugins – are loaded dynamically upon request. ChemAxon provides various tools for calculating charge, pKa, log P, etc. The available calculator plugins are located in the Tools menu. The corresponding calculation parameters can be set in the parameter panel accessible from the Options submenu. Some plugins (charge, polarizability, polar surface area and hydrogen bond donor-acceptor) optionally perform their computation on the physiological microspecies of the input molecule taken at a specified pH. This option together with the corresponding pH can also be set in the parameter panel. JChem is a development tool written in Java for manipulating mixed chemical and corporate data for web-based applications. Java supports most operating systems, database handlers, and web servers. JChem is a tool for developing distributed custom chemical applications that can be accessed by web browsers.

Schrodinger, LLC

• Schrödinger, LLC (http://www.schrodinger.com/)

• Product Summaries: Schrödinger provides its FirstDiscovery software suite to address and aid in the discovery process in industry. First Discovery runs under Unix and Linux and it includes several programs: Glide, Jaguar, Liaison, LigPrep, MacroModel, Maestro, Mopac 2002, pKa predictor, Phase, Prime, QikPro, Qsite, and Strike. For the Microsoft Windows platform Schrödinger offers CAChe, BioMedCAChe, ChemFrontier, MaterialsExplorer, QikPro, Titan, and WinMOPAC.

• Key capabilities and offerings: Mopac 2002. Mopac is used to carry out semiempirical calculations to predict chemical properties and reactions in gas, solution or solid-state. Mopac 2002 can use several semiempirical Hamiltonian methods including MNDO, MINDO/3, AM1, PM3, MNDO-d, and PM5. Mopac 2002 comes with the MOZYME algorithms integrated for the fast calculations of electronic properties of proteins, polymers, semiconductors, and crystals.

Spartan

• http://www.wavefun.com/products/spartan.html

• Product Summaries: It is an "Electronic Model Kit". Making use of computer technology, SpartanModel replaces the "plastic models" used by past generations of organic chemistry students, and extends the utility of molecular models in chemistry education. is the most sophisticated version offered. The latest Spartan'10 release offers offers all features and methods included in the Spartan Essential Edition, and in collaboration with Q-Chem, provides a full range of post-Hartree-Fock methods including Density Functional, Moller Plesset, Theremochemistry recipes

• Key capabilities and offerings: Spartan'10 provides a wide range of computational methods, addressing the needs of educators, bench chemists, and professional modelers. All methods are easily accessed via Spartan's seamless graphical interface. Molecular mechanics is presently the only practical method for calculations on very large molecules or for conformational searching on highly flexible molecules. MMFF94, in particular, has proven to be a reliable and fast tool for conformational analysis. There are no atom limits for molecular mechanics calculations. Semi-empirical models are the simplest of the quantum chemical schemes, and are useful for equilibrium and transition-state structure calculations. PM3, in particular, has proven to be a reliable tool for geometry calculations on transition metal inorganic and organometallic compounds. MNDO, AM1, RM1, PM3, and PM6 methods are supported. MNDO/d extensions for heavy main-group elements have been implemented and PM3 parameters for most transition metals are available. Hartree-Fock models useful for predicting structure, energy and property calculations, in particular for organic molecules. A variety of standard basis sets are supported: STO-3G, 3-21G, 6-31G*, 6-311G*, cc-pVDZ, cc-pVTZ and cc-pVQZ, with extensions including (d), (d,p), (2d), (2d,2p), (2df, 2dp), (3d, 3p), (3df, 3dp) and diffuse functions and/or additional polarization functions. Determine total energy (Hartree-Fock, density functional, Møller-Plesset, advanced correlated), heat of formation (semi-empirical or thermochemical recipes) or strain energy (molecular mechanics). Determines local energy minimum. Calculate and Plot IR Spectra. It can calculate Atomic Charges, Thermodynamics, dipole moment, polarizabilities, Weight, Area, Volume, Symmetry Group, HOMO and LUMO Energies, Polar Surface Area, LogP, Ovality, Q-Minus, Q-Plus, Electronegativity and Hardness Vibrational spectra available from IR calculations including plotting and animation of vibrational modes.

Molinspiration

• Molinspiration, http://www.molinspiration.com/

• Product Summaries: Molinspiration offers broad range of cheminformatics software tools supporting molecule manipulation and processing, including SMILES and SDfile conversion, normalization of molecules, generation of tautomers, molecule fragmentation, calculation of various molecular properties needed in QSAR, molecular modelling and drug design, high quality molecule depiction, molecular database tools supporting substructure and similarity searches.

• Key capabilities and offerings: It calculates molecular physicochemical properties relevant to drug design and QSAR, including logP, molecular polar surface area (PSA), and the Rule of 5 descriptors.

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