Transition in Writhe of a Small Circular DNA by Monte Carlo Simulation Campus Box 35 1 700 Monte Carlo simulations are employed to investigate the thermodynamics ofthe first transition in writhe ofa circular modeljlament corresponding to a 468 base-pair DNA. Parameters employed in these simulations are the torsionalrigidity, C = 2.0 X dyne cm2, andpersistence length, P = 500 A". Intersubunit interactions are modeled by a screened Coulomb potential.
For a straight line of subunits this accurately approximates the nonlinear Poisson-Boltzmann potential o f a cylinder with the linear charge density of DNA. Curves of relative free energy vs writhe atjixed linking diflerence (Al) exhibit two minima, one corresponding to slightly writhed circles and one to slightly underwrithedfigure-8 S, whenever Al lies in the transition region. The jkee energies ofthe two minima are equal when Al, = 1.35, which defines the midpoint of the transition. At this midpoint, thefree energy barrier between the two minima is found to be AGhor = (0.20) kBT at 298 K. Curves of mean potential energy vs writhe at fixed linking difference similarly exhibit two minima,for Al values in the transition region. and the two minimum mean potential energies are equal when Al = 1.50. At the midpoint writhe, Al, = 1.35, the difference in mean potential energy between the minimum free energyfigure-8 and circle states is (1.3) kBT, and the diference in their entropies is 1.3 kB. Thus, the entropy of the minimum,fiee energyfigure-8 state significantly exceeds that ofthe circle at the midpoint of the transition. The jrst transition in writhe is.found to occur over a rather broad range of A1 values.fiom 0.85 to I .85. The twist energy parameter (ET), which governs the overal1,free energy of supercoiling, undergoes a sigmoidal decrease, while the translational dijiusion coeficient undergoes a sigmoidal increase, over this same range. The static structure,factor exhibits an increase, which rejects a decrease in radius of gyration associated with the circle to ,figure-8 transition.