Writhe Wr
—
Twist Tw
—
Lk = Tw + Wr
—
Self-contact pts
—
Energy E
—
White's theorem: Lk = Tw + Wr (topological identity)
Kirchhoff rod: elastic energy
E = ∫[B(κ₁²+κ₂²)/2 + C·τ²/2] ds
DNA supercoiling: ~10 bp/turn → Tw=total turns. Over-twisting converts Twist→Writhe → plectonemes (supercoils).
Self-contact creates loops; topoisomerases cut & rejoin to change Lk.
Kirchhoff rod: elastic energy
E = ∫[B(κ₁²+κ₂²)/2 + C·τ²/2] ds
DNA supercoiling: ~10 bp/turn → Tw=total turns. Over-twisting converts Twist→Writhe → plectonemes (supercoils).
Self-contact creates loops; topoisomerases cut & rejoin to change Lk.