Seite - 92 - in Charge Transport in DNA - Insights from Simulations

AParametrizedModel toSimulateCT inDNA Figure7.2: Distribution of EC recorded during an MD simulation of 20 ns for six A|A base-pair steps (orange) and the fitted distribution function (blue). EC for oneA|Abase-pair step obtained fromoneCTmodel simulation of 20ns are shown in comparison (black). where x is in the interval (0,1). Finally, the randomvalue x is transformedwith the obtained parameters σ and μ, giving a randomvalue taken from the desired distribution: F−1(x)=μ+σ ·Φ−1(x) (7.4) The calculation of the probit function is donewith the algorithmbyP. J. Acklam. [129] This algorithmhasa relative errorof less than1.15 ·10−9. Figure 7.2 shows the distribution of recorded values of EC during anMD simu- lation of 20 ns for six adenine-adenine base-pair steps and the fitted distribution function (equation 7.1). EC for oneA|Abase-pair step obtained fromonemodel CTsimulationof20nsare shown in comparison. Drawingrandomnumbers inevery stepof the calculationhasa fatal consequence: The calculated time series are not continuous. To prevent these unrealistic sud- den changes, a newEC is generated in the described fashion only every 10 steps (10 fs). In between these steps, the EC is interpolated linearly. Thismight lead to distributions thatdeviate fromthedesiredoneslightly. Still, it is anacceptablefirst approach, andall test simulations aredonewith thispossibly inaccurate setup. 92