Page - 13 - in Charge Transport in DNA - Insights from Simulations

2.2MolecularDynamicsSimulation mental results and tabulated in advance for all relevant atoms and their different binding situations. Calculatingthenon-bondedparametersforallpairsofatomsinahugebiomolecule might slowdown the calculation significantly. To resolve this issue, simple cut-off schemes, like thoseused for thevan-der-Waals interactions, ormore sophisticated methods, like theparticle-meshEwald (PME)method [51–53] for theelectrostatics, canbeused tomake the computationof thenon-bonded termsmoreefficient. Withinitialcoordinatesandawell-definedforcefield, thetotalenergyofamolecule andgradientsarecalculated. Therefore, it ispossible toperformmoleculardynam- ics (MD) simulations. 2.2 MolecularDynamicsSimulation Moleculesandatomsarenotfixedon their equilibriumpositionsatfinite tempera- tures. Rather, atomsmoveandbondsoscillateoncertain timescales. Thus, it is not reasonable to investigateonly their static, energy-minimizingconformations, espe- ciallywhendealingwith largebiomolecules.Moleculardynamic (MD)simulations are performed to get an idea howmolecules behave in adefined time frame. The basic idea is to treat themotionsofatoms inaclassicalmanner inorder tocalculate positions ( ri(t)) andmomenta ( pi(t)) of all atoms in every time step. The result is a trajectory in thephase spaceof themolecule . TheMDsimulation is basedonNewton’s classical equationsofmotion [54] Fi=mi δ2 ri δt2 (2.2) where F is the force actingon theatom i and r is the three-dimensional coordinate of theatom i in thesystem.Asaresult, a systemconsistingofNatomsisdescribed by3N coordinates. The forces are calculatedas thenegativegradient of the energy. Fi=−δE( ri)δ ri (2.3) 13