DNA Stretching Mechanics: Worm-Like Chain Model Simulator

simulator intermediate ~10 min
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x/Lc = 0.83 — 83% of contour length

At 5 pN stretching force with Lp = 50 nm and Lc = 1000 nm, the DNA extends to 83% of its contour length. The worm-like chain model captures the nonlinear elastic response.

Formula

F = (kBT / Lp) × [1/(4(1-x/Lc)²) - 1/4 + x/Lc] (Marko-Siggia WLC interpolation)
x/Lc ≈ 1 - (kBT / (4 F Lp))^(1/2) + F/S (high-force regime)
R_rms = sqrt(2 × Lp × Lc) (random coil end-to-end distance)

DNA as a Mechanical Object

DNA is not just an information carrier — it is a physical polymer subject to stretching, bending, and twisting forces. In the cell, DNA is constantly pulled by molecular motors, bent around histones, and unwound by helicases. Single-molecule experiments have revealed that DNA's mechanical response follows the worm-like chain model with remarkable precision, connecting polymer physics to molecular biology.

The Worm-Like Chain Model

The WLC model describes a semi-flexible polymer using two parameters: contour length (Lc, the total stretched-out length) and persistence length (Lp, the bending stiffness). At low forces, the molecule resists extension entropically — pulling it straight reduces the number of available conformations. At high forces, the backbone itself begins to stretch elastically. The Marko-Siggia interpolation formula captures both regimes in a single elegant expression.

Force-Extension Experiments

Optical tweezers revolutionized DNA mechanics by enabling piconewton-precision force measurements on single molecules. The resulting force-extension curves show a characteristic nonlinear shape: gradual extension at low forces, rapid stiffening near full extension, and a dramatic overstretching plateau around 65 pN. This simulation reproduces these features, letting you explore how persistence length and temperature affect the mechanical response.

Biological Implications

DNA mechanics matters for gene regulation, chromosome organization, and viral DNA packaging. Nucleosomes bend DNA sharply, requiring ~50 kT of energy per wrap. Bacteriophages pack their genomes to near-crystalline density, generating internal pressures of ~60 atmospheres. Understanding DNA as a mechanical polymer connects physics to the most fundamental processes in biology.

FAQ

What is the worm-like chain model?

The worm-like chain (WLC) model treats a polymer like DNA as a continuously flexible rod characterized by its contour length (total length) and persistence length (stiffness). It predicts a nonlinear force-extension curve that matches single-molecule DNA stretching experiments remarkably well.

What is persistence length?

Persistence length (Lp) is the length scale over which a polymer maintains its direction. For double-stranded DNA, Lp ≈ 50 nm (~150 base pairs), meaning the molecule is essentially straight over this distance. Beyond Lp, thermal fluctuations bend the chain randomly.

How is DNA stretched experimentally?

Single-molecule techniques like optical tweezers, magnetic tweezers, and atomic force microscopy (AFM) can grab individual DNA molecules and measure force-extension curves with piconewton and nanometer precision.

What happens when DNA is overstretched?

At forces around 65 pN, B-form DNA undergoes an overstretching transition, extending to about 1.7× its normal length. The double helix partially melts or converts to an extended S-form. This transition is visible as a force plateau in stretching experiments.

Sources

Embed

<iframe src="https://homo-deus.com/lab/biophysics/dna-mechanics/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub