# DsDNA persistence length

## Persistence length of a double-stranded DNA

The example shows how to calculate a persistence length of a double stranded DNA molecule. dsDNA persistence length. The persistence length in this example is calculated using the following formula (see [1] for details):

<! ${\displaystyle \langle {\bf {n_{k}}}\cdot {\bf {n_{0}}}\rangle =\exp(-k\langle l_{0}\rangle /L_{ps}).}$

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In the EXAMPLES/PERSISTENCE_LENGTH directory, you will find a setup for calculating the persistence length of a 202 base pairs long dsDNA. Note that for calculating a persistence length of a dsDNA, one needs a large number of decorrelated states. To obtain the states (which will be saved into a trajectory file), run the simulation program using the prepared input_persistence file:

oxDNA input_persistence

The program will run a molecular dynamics simulation at 23 °C and record the individual configurations. They are saved in trajectory.dat file. To analyze the data, use the python script dspl.py:

dspl.py trajectory.dat init.top 10 50

This program will produce a table of correlations between helical vectors, ${\displaystyle \langle {\bf {n_{k}}}\cdot {\bf {n_{0}}}\rangle }$. Using an exponential fit to these data, one can find the persistence length.