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3 Molecular Dynamics Simulations of Peutides 43ferent conformations which are with<strong>in</strong> 1-2 kcals of each other. For this reasonvarious conformational search methods have been used to attempt to explore moreof conformational space without perform<strong>in</strong>g a full search. Two important methodsare those based on distance geometry [lo] and those based on <strong>molecular</strong> dynamics[I 1, 121. Distance geometry techniques essentially are non-energetic techniques whichset up random distance matrices, i.e. the matrix of all distances between all atompairs <strong>in</strong> the molecule, with constra<strong>in</strong>ts on certa<strong>in</strong> distances, e. g. bond lengths, NOEdata etc. and compute Cartesian coord<strong>in</strong>ates from these matrices. Moleculardynamics is a determ<strong>in</strong>istic simulation process where<strong>in</strong> the positions and velocitiesof atoms <strong>in</strong> a molecule are <strong>in</strong>tegrated forward <strong>in</strong> time us<strong>in</strong>g Newton’s laws of motion.The <strong>in</strong>itial velocities are randomly ascribed to atoms via a Maxwellian distributionconsistent with the temperature at which the simulation is be<strong>in</strong>g performed. Themovement of the atoms is then governed by the k<strong>in</strong>etic energy <strong>in</strong>put <strong>in</strong>to the systemand the restor<strong>in</strong>g forces that act on the molecule when its position from a m<strong>in</strong>imumenergy conformation is disturbed. The latter term is described by a forcefield fromwhich the potential energy of the system can be determ<strong>in</strong>ed. This term consists ofstra<strong>in</strong> energies such as bond length, bond angle deformations, torsional componentsetc. and van der Waals non-bonded <strong>in</strong>teractions and electrostatic terms. The ValenceForce Field (VFF) [13] AMBER [14] and CHARMM [15] are examples of forcefields<strong>in</strong> use to study peptide and prote<strong>in</strong> conformations.3.3 Applications of Molecular DynamicsAs seen from Table 3-1, the most common use of calculations on peptides at the momentis to aid <strong>in</strong> generat<strong>in</strong>g conformational hypotheses <strong>in</strong> association with data fromNMR studies. Many of these studies <strong>in</strong>volve NOE-restra<strong>in</strong>ed <strong>molecular</strong> dynamics, <strong>in</strong>which the experimental proton-proton distance constra<strong>in</strong>ts correspond<strong>in</strong>g to NOEcross-relaxation rates, obta<strong>in</strong>ed from 2D NOESY experiments, are directly used <strong>in</strong>the simulation [16]. Typically a harmonic term is <strong>in</strong>cluded <strong>in</strong> the forcefield topenalise for deviations from the observed proton-proton distances.Another application is the use of relative free energy to compare chemicallydist<strong>in</strong>ct systems us<strong>in</strong>g f<strong>in</strong>ite difference thermodynamic <strong>in</strong>tegration (FDTI) [17]. Inpractice, this is done by <strong>in</strong>troduc<strong>in</strong>g a coupl<strong>in</strong>g parameter A <strong>in</strong>to the forcefield whichchanges from 0 to 1 as the hamiltonians correspond<strong>in</strong>gly change from state A to stateB. Results from these calculations can be directly related to experimentally obta<strong>in</strong>edthermodynamic properties.A number systems have been studied <strong>in</strong> solvent, ma<strong>in</strong>ly water, but some have<strong>in</strong>volved other solvents commonly used <strong>in</strong> NMR studies of peptides.