Worm-Like Chain: DNA Stretching

Entropic elasticity of semiflexible polymers — how thermal fluctuations resist extension of a DNA molecule

Parameters

WLC Force-Extension (Marko-Siggia 1995)
F = (kT/Lp)[¼(1-x/L)⁻² - ¼ + x/L]

kT = 4.1 pN·nm at 300K
Lp(DNA) ≈ 50 nm (dsDNA)
L (contour) ~ 0.34 nm/bp

x/L → 0: F ≈ (3kT/2Lp)(x/L) [Gaussian]
x/L → 1: F → ∞ [entropic singularity]
The WLC treats DNA as a continuous elastic rod with bending stiffness kT·Lp. Thermal fluctuations create random bends that resist extension — the force diverges as the polymer approaches full extension. This was confirmed by optical tweezers experiments (Bustamante 1994).