Page - 91 - in Charge Transport in DNA - Insights from Simulations

7.1Creating theElectronicCouplings So, eachof theobtainedprobabilitydistributionsofECofall tenpossiblebase-pair stepswasfittedwitha functionof the following form: P(EC)= 1 σ √ 2π · ( exp [ −(EC−μ) 2 2σ2 ] +exp [ −(−EC−μ) 2 2σ2 ]) (7.1) Table 7.1 shows the resulting parameters σ, thewidth, and μ, themean value, of thedistributions. Table7.1: Mean values and standard deviations of the EC estimated for the different base-pair steps. X\Y – purine–pyrimidine step, X/Y – pyrimidine–purine step,X|Y–purine–purine step. See also figure5.6 for a graphical illustra- tion. base-pair step A|A A/A A\A A|G G|A G/A A\G G|G G/G G\G σ [eV] 0.0388 0.0204 0.0473 0.0428 0.0375 0.0180 0.0287 0.0297 0.0086 0.0218 μ [eV] 0.0480 0.0480 0.0497 0.0022 0.0008 0.0059 0.0002 0.0182 0.0089 0.0148 Now, time series of EC with these probability distributions have to be created, to be used in the parametrized model. The approach presented here is to draw random values from these distributions. Therefore, the following algorithm was implemented into theCTmodel. A standard linear congruential randomnumber generator is applied, which gen- erates series of uniformly distributed randomnumber in the interval (0,1). These uniformlydistributedrandomnumbersarenowtransformedtoanormaldistribu- tion. The cumulativedistribution functionof thenormaldistributionhas the form: Φ(x)= 1√ 2π ∫ x −∞ exp [ t2 2 ] dt= 1 2 [ 1+erf ( x√ 2 )] (7.2) The inverse of this function, called theprobit function, is used to get thedistribu- tion of the electronic couplings. The probit function can be expressed in terms of the inverse error function. Φ−1(x)= √ 2erf−1(2x−1) (7.3) 91