Short note on the scaling behavior of communication by ‘slithering’ on a supercoiled DNA

The first passage time τ for two sites on a supercoiled DNA molecule is analyzed as a function of both overall molecule length N and the length between the two sites n, using a previously introduced theory [J.F. Marko, Physica A 244 (1997) 263]. This time is shown to have the scaling form τ(n,N)∝n2f(n/N) where f(x) smoothly runs from 5.6 to 1 as x runs from 0 to 0.5. Therefore τ(n,N) has a strong dependence on intersite distance n and a much weaker dependence on molecular length N.