  Cyclization of DNA with sticky ends is commonly used to construct DNA
minicircles and to measure DNA bendability. The cyclization probability of
short DNA (< 150 bp) has a strong length dependence, but how it depends on the
rotational positioning of the sticky ends around the helical axis is less
clear. To shed light upon the determinants of the cyclization probability of
short DNA, we measured cyclization and decyclization rates of ~100-bp DNA with
sticky ends over two helical periods using single-molecule Fluorescence
Resonance Energy Transfer (FRET). The cyclization rate increases monotonically
with length, indicating no excess twisting, while the decyclization rate
oscillates with length, higher at half-integer helical turns and lower at
integer helical turns. The oscillation profile is kinetically and
thermodynamically consistent with a three-state cyclization model in which
sticky-ended short DNA first bends into a torsionally-relaxed teardrop, and
subsequently transitions to a more stable loop upon terminal base stacking. We
also show that the looping probability density (the J factor) extracted from
this study is in good agreement with the worm-like chain model near 100 bp. For
shorter DNA, we discuss various experimental factors that prevent an accurate
measurement of the J factor.
