Formation of loops in DNA under tension

We study the formation of loops along a DNA molecule under applied tension, as might occur in single-DNA micromanipulation experiments with proteins which are able to simultaneously bind two DNA sites. We consider the case of bare DNA in the loop, which forms a teardrop shape, and the case where a single DNA-bending protein produces a kink in the middle of the loop; the presence of a right-angle kink in the loop reduces its bending energy by a factor of 3. Using the bending energy plus an estimate of the free energies associated with fluctuations and the elasticity of the extended nonlooped DNA, we obtain a probability distribution for loops as a function of loop size and force. Force strongly suppresses formation of all loops, but suppresses large loops more severely than small ones. This quenching effect of force is reduced in the presence of a kink in the loop. We also calculate the speed at which length is absorbed into loops between arbitrary positions along the DNA (i.e., for non-sequence-specific loop forming proteins). The speed of retraction of the molecule decays as a stretched exponential function of the force with characteristic force scales depending on the geometry of the loops.