Biomod/2011/Caltech/DeoxyriboNucleicAwesome/Random Walk Formula

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Friday, July 11, 2014

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Random Walk Formula

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General Modeling Idea

The random walk on DNA origami can be modeled as one dimensional random walk with a reflecting and an absorbing barrier (Figure 1). Tracks in the same column are grouped into rectangles, and each step is defined as walking from one rectangle to the adjacent one. Various formulae had been developed to model this process, but none of them can perfectly match our situation (Weesakul, 1961; Hardin & Sweet, 1969; Alessandro Blasi, 1976; Ahmed El-Shehawy, 1992).


Figure 1. Modeling the random walk on DNA origami as one dimensional random walk. Cyan, markers. Blue, Track 1. Red, Track 2. White, DNA staples only. Five-pointed star, walker goal. Each step is modeled as walking from one rectangle to an adjacent one. SP 10, 22, 34 indicate different starting positions. Note that in the cases of SP22 and SP34, there are no tracks to the left of starting positions.
Figure 1. Modeling the random walk on DNA origami as one dimensional random walk. Cyan, markers. Blue, Track 1. Red, Track 2. White, DNA staples only. Five-pointed star, walker goal. Each step is modeled as walking from one rectangle to an adjacent one. SP 10, 22, 34 indicate different starting positions. Note that in the cases of SP22 and SP34, there are no tracks to the left of starting positions.


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