# Determinants of cyclization-decyclization kinetics of short DNA with sticky ends

## TL;DR

This study investigates how the length and rotational positioning of sticky ends influence the cyclization and decyclization kinetics of short DNA, revealing oscillatory behavior linked to helical turns and supporting a three-state looping model.

## Contribution

It provides detailed kinetic measurements of short DNA cyclization, demonstrating the impact of helical phase and proposing a three-state model for DNA looping behavior.

## Key findings

- Cyclization rate increases monotonically with DNA length.
- Decyclization rate oscillates with length, peaking at half-integer helical turns.
- The J factor aligns with the worm-like chain model near 100 bp.

## Abstract

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.