How topological constraints facilitate growth and stability of bubbles in DNA

The bubbles in double-stranded DNA, essential for gene transcription and replication, occur in mechanically constrained situations. Through an elastic model incorporating topological constraint, we show that, when a stretched double helix is underwound above a critical value of twist, a bubble can spontaneously form, yielding extension and torque behaviors quantitatively in agreement with magnetic tweezers experiments. We find that, unlike thermal bubble in an unconstrained DNA, the bubbles in these constrained states can grow and stabilize, provided that tension and length of DNA are above critical values.