Effect of Temperature on Topological States of Circular DNA

The different topological states of circular double-stranded DNA can be defined by their linking number. The equilibrium distribution of linking number can be obtained by circularizing a linear DNA into a circle by ligase. Based on the recent experimental results that the DNA bending rigidity and twist rigidity strongly depend on temperature, the reduced bending rigidity can be approximated by $g=(3.19\times {10}^{-19}-T\cdot 4.14\times {10}^{-22})erg\cdot cm$ over the temperature interval (5 ∼ 53) °C, and the temperature dependence of twist rigidity can be fitted by $C\left(T\right)=\left(4588.89exp\right(-T/117.04)-251.33)$ nm. The temperature dependence of the linking number distribution of circular DNAs can be predicted by using Monte Carlo simulation. The variance of linking number distribution on temperature is in accordance with the previous experimental results. Compared with the temperature dependence of bending rigidity, the temperature dependence of twist rigidity causes a noticeable fluctuation in linking number distribution and mainly contribute towards the variance change of linking number distribution of circular DNA. The variance of the writhe number and twist number in the equation $⟨{\left(\Delta Lk\right)}^2⟩=⟨{\left(\Delta Tw\right)}^2⟩+⟨{\left(Wr\right)}^2⟩$ depends on the length of circular DNA. When the length of circular DNA is less than 230 nm, the variance of twist number $⟨{\left(\Delta Tw\right)}^2⟩$ is dominant over the variance of writhe number $(⟨{\left(Wr\right)}^2⟩)$, whereas for the condition that the length of the circular DNA is larger than 370 nm. (paper)