Page - 100 - in Charge Transport in DNA - Insights from Simulations

AParametrizedModel toSimulateCT inDNA Figure7.7: Relaxation functionof a fully localizedchargehopping fromonenucleobase to another. Function averaged over1000 simulations of100 fs each. Tomodel this behavior, two alternative functions are available so far. First, a sim- pleexponential functionmaymodel thechangeof IPof thenucleobases inapreset relaxation time. Second, toprevent a suddenchange in IPat theonsetof theexpo- nential function, aGaussian-shapedfunctionmaybe implemented to represent the changesofpolarization. As an alternative to such relaxation functions, an empirical relaxation has been implemented. 1000 simulations of 100 fs lengthwere performedwith the IP cal- culated in every time step. PolyA sequences equilibratedwith no charge on the nucleobaseswere simulated. Then, a chargewas introduced into the system, and MDsimulationswere commenced. The timeseriesof IPwere recorded inall these simulations, andameanvalueoutof the1000 simulationswascalculated forevery time step. Figure 7.7 shows the appearance of this averaged relaxation behav- ior. Averaging over 1000 simulations, the stochastic fluctuations of the systemare canceled, and the resultingfluctuationsof IPare aneffect of theCTevent. Theob- tained relaxation functionhas the formof a cosine functionwith an exponentially decreasing amplitude. There aremaxima, located at roughly 40 and 80 fs. Until now, there isnoarithmetical function for thisbehavior implemented, rathera table is read fromafile. This has the advantage that any desired function can be used for the relaxation, increasing theflexibilityof theapproach. The relaxation at a given timepoint is determined by an occupation history - the state of the charge is recorded for a chosennumber of stepspreceding the current step. Dependingon this occupationhistory, the value of the relaxation function is determinedand the IP is shiftedaccordingly. 100