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Chemoinformatics: Directions Toward Combating Neglected Diseases, 2012, 129-144 129 Antileishmaniasis Agents: Molecular Dynamics Simulations Tanos Celmar Costa França 1* and Alan Wilter Sousa da Silva 2 Teodorico C. Ramalho, Matheus P. Freitas and Elaine F. F. da Cunha (Eds) All rights reserved - © 2012 Bentham Science Publishers CHAPTER 5 1 Chemical Engineering Department, Military Institute of Engineering, Pça General Tibúrcio, 80, Urca, 22290-270, Rio de Janeiro/RJ, Brazil and 2 Department of Biochemistry, University of Cambridge, 80 Tennis Court Road, CB2 1GA, United Kingdom Abstract: Molecular dynamics simulations have showed to be powerful tools when applied to the preliminary investigations of the interactions of potential molecular targets with its natural subtracts or, eventually, with their potential inhibitors. When the 3D structure of a molecular target is yet unknown, sometimes it is possible to build a very consistent model using one of the several softwares available today for this purpose (see chapter on homology modeling) and, further, use it to analyze the overall structure of the target, the active site residues and their potential interactions with potential ligands, by performing MD simulations studies in order to afford additional information towards the rational design of inhibitors to the molecular target in focus. Literature has reported a few interesting studies using this approach on leishmaniasis. Those studies have afforded useful information for the experimentalists on new drug targets for the rational design of new, more selective and powerful antileishmiasis agents. Keywords: Molecular dynamics simulation, proteins, antileishmaniasis agents. 1. INTRODUCTION 1.1. Molecular Dynamics Simulations Molecular Dynamics (MD) is a technique developed to study the movements of a system of particles by simulation. This technique can be employed to electrons, atoms or molecules as well as to macromolecular systems. Its essential elements are the knowledge of the potential of interaction among the particles and the classic equations of movement ruling the dynamic of those particles. The potential can change from simple, like the gravitational star interactions, to the complex, with several terms, like the description of the interactions between atoms and molecules. For many systems, including the biomolecular, the equations of classic dynamics are suitable. However, for some problems, like the galaxy evolution, relativist terms are included, while for others, like chemical reactions involving tunneling effects, quantum mechanical corrections are needed [1]. The microscopic state of a system can be specified in terms of the positions and moments of its particles. Therefore, in classic mechanics, one can write the Hamiltonian H of a classic molecular system as the sum of the kinetic (C) and potential (U) energies in function of the series of generalized coordinates qi and generalized moments pi of all N atoms of the system, like in Eq. 1: H ( q , p ) C( p ) V( q ) (equation 1) Where: i i i i qi = q1, q2, ., qNat and pi = p1, p2,…, pNat The potential energy V(qi) contains the short and long distance inter and intramolecular interaction terms and can be replaced by the potential V(ri) in a way that the coordinates qi become the Cartesian coordinates and ri and pi its conjugated moments. The kinetic energy, on the other hand, can assume the form of Eq. 2: *Address correspondence to Tanos Celmar Costa França: Chemical Engineering Department, Military Institute of Engineering, Pça General Tibúrcio, 80, Urca, 22290-270, Rio de Janeiro/RJ, Brazil; Tel: +00552125467195; E-mail: tanos@ime.eb.br
130 Chemoinformatics: Directions Toward Combating Neglected Diseases França and Silva C( p ) i Nat p 2 i 2m i1 i where mi is the mass of the atom i. (equation 2) From Eq. 1 it is possible to construct the equations of movement ruling the temporal evolution of the system and their dynamical properties. As the potential energy is independent from velocities and time, H is the total energy of the system and Hamilton’s equations of motion (Eqs. 3 and 4): H qi p H pi q i i conduct to the Newton equations of motion (Eq. 5 and 6): pi ri vi m i V( ri) pi mr i i Fi r i (equation 3) (equation 4) (equation 5) (equation 6) In Eqs. 5 and 6, ri (or vi) and pi are the velocity and the acceleration of the atom i, while Fi is the force on the atom i [2-4]. The MD consists, therefore, in the numeric resolution of Eqs. 5 and 6 and their integration, step by step, in an efficient and accurate way. As a result, we have the energies and trajectories of all the particles (or atoms) for the system as a whole and from which several properties can be calculated. In systems with hydrogen, a time step of 5.0 x 10 -16 seconds is usually applied. In this procedure it is essential that the potential energy be a continuum function of the particle positions and that the positions change smoothly with time. The Fi forces on each atom, obtained from the spatial derivative of the potential energy, as shown in Eq. 6, can be considered constant in the gap between two steps. Once the dynamic stability is favored, the particles follow their classic trajectories more accurately and the total system energy tends to be conserved. A limitation of the MD simulation resides, therefore, in the fact that for each nanosecond of simulation, 2 million of steps are needed with the time step above. A simulation of 1 ns for a macromolecule with 200 atoms can take hours of CPU time in a supercomputer, when using an efficient algorithm. A description and analysis of the efficiency of algorithms for simulation and molecular dynamics can be found in Berendsen & van Gunsteren [3] and Allen & Tildesley [4]. The latter includes routines in FORTRAN for some simulation methods. 1.1.2. Molecular Mechanics Most of the systems in molecular modeling are too big to be treated by quantum mechanics or semi empirical methods. Because these methods consider the movements of the electrons and a large number of other particles in the system, they are so time consuming and unreliable for big systems. The force field methods or the molecular Mechanics Methods (MM) ignore the electron movements and calculate the energy of the system as a function of only the nuclear positions. This makes MM a suitable method to deal with systems containing a large number of atoms. In some cases, force fields can lead to answers as accurate as the top level of quantum mechanics, in much less computational time [5]. MM, however, is not able to predict properties depending on the electronic distribution in a molecule, like transition states or charge distributions but, still, it is a very useful and powerful technique for drug design.
Page 2 and 3: Chemoinformatics: Directions Toward
Page 4 and 5: CONTENTS Foreword i Preface ii List
Page 6 and 7: ii PREFACE Low-income populations i
Page 10 and 11: New Approaches to the Development C
Page 12 and 13: 34 Chemoinformatics: Directions Tow
Page 16 and 17: Antimalarial Agents Chemoinformatic
Page 18 and 19: 70 Chemoinformatics: Directions Tow
Page 22 and 23: Antileishmaniasis Agents Chemoinfor
Page 24 and 25: 146 Chemoinformatics: Directions To
Page 30 and 31: Molecular Modeling of the Toxoplasm

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