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Malti🧬 DNA Mechanics: Persistence Length & Worm-Like Chain
Interactive worm-like chain simulation of DNA under a virtual optical tweezer. Watch thermal writhing collapse into an extended molecule and compare the live force-extension curve to the Marko-Siggia formula.
About the DNA Mechanics Simulator
This simulation treats DNA as a semi-flexible polymer described by the worm-like chain (WLC) model. A bead-and-rod chain of 32 segments is propagated with overdamped Langevin dynamics: each joint carries a real Kratky-Porod bending penalty proportional to persistence length Lp divided by segment length, adjacent beads are held apart by a stiff stretching spring, and every bead receives a thermal kick drawn from the fluctuation-dissipation theorem at the chosen temperature. The result is a chain that writhes with the correct correlated-curvature statistics of a real semi-flexible polymer rather than a rigid rod or a fully random freely-jointed chain.
One end of the molecule is anchored; the other is held by a virtual optical tweezer that applies a constant pulling force. As force rises, the live force-extension point is plotted against the Marko-Siggia interpolation formula, F(x) = (kT/Lp)[¼(1−x/L)⁻² − ¼ + x/L], the textbook result that single-molecule biophysicists have verified directly with optical and magnetic tweezer experiments that stretch individual DNA molecules. At low force the chain resists extension entropically — thermal fluctuations, not chemical bonds, oppose straightening. Near full contour length the curve steepens sharply as the molecule approaches the enthalpic regime, where real backbone-bond stretching sets in.
Frequently Asked Questions
What is persistence length?
Persistence length Lp is the length scale over which a polymer's direction "forgets" its initial orientation due to thermal bending. For double-stranded DNA it is about 50 nm, roughly 150 base pairs — far stiffer than a floppy chain but far more flexible than a rigid rod at the scale of whole chromosomes.
What is the worm-like chain (WLC) model?
The WLC, or Kratky-Porod model, treats a polymer as a continuously flexible rod with a bending energy that resists curvature. It is the standard statistical-mechanics description of semi-flexible biopolymers like DNA, and it correctly predicts both the equilibrium coiling of an unstretched molecule and its response to an applied force.
What is the Marko-Siggia formula?
It is an interpolation formula, F(x) = (kT/Lp)[¼(1−x/L)⁻² − ¼ + x/L], that approximates the force needed to hold a worm-like chain at a given fractional extension x/L. It was derived by John Marko and Eric Siggia and has been confirmed directly by single-molecule stretching experiments on DNA.
Why does DNA act like entropic rubber at low force?
At low extension, pulling the two ends apart reduces the number of thermally-accessible bent configurations the chain can adopt. The restoring force comes from this loss of configurational entropy, exactly like stretching a rubber band, not from stretching any chemical bond. This is why the low-force portion of the curve is called the entropic regime.
What happens near full contour length?
As extension approaches the contour length L, nearly all thermal slack is gone and the force needed to stretch further diverges steeply — the (1−x/L)⁻² term in the Marko-Siggia formula. Very close to full extension, real DNA transitions into an enthalpic regime where the sugar-phosphate backbone bonds themselves begin to stretch.
How do optical and magnetic tweezers measure this in the lab?
Optical tweezers use a focused laser beam to trap a microscopic bead attached to one end of a single DNA molecule, while the other end is fixed to a surface or a second bead; moving the trap stretches the molecule and the laser's momentum transfer reports the force. Magnetic tweezers instead use a magnetic bead and field gradient to apply a controlled, constant pulling force. Both techniques can resolve piconewton forces and nanometre extensions directly on one molecule at a time.
How does temperature change the simulation?
Raising temperature increases the thermal kicks applied to every bead (the fluctuation-dissipation theorem ties noise strength directly to kT) while the molecule's intrinsic bending stiffness stays fixed. The net effect is a shorter effective persistence length at higher temperature — the chain writhes more for a given pulling force, exactly as real DNA becomes relatively floppier when heated.
Why is the bending energy proportional to Lp/l?
In the discretised Kratky-Porod model, the bending penalty between two adjacent segments of length l is set so the ensemble-averaged correlation between segment directions decays as exp(−l/Lp). That requires a stiffness of order kT·Lp/l per joint — the exact relation used to drive the segments in this simulation.
Is this simulation quantitatively accurate?
The bending potential, the Langevin thermostat, and the Marko-Siggia force law are all real, published physics used in polymer science and single-molecule biophysics. The bead spacing and pulling dynamics are simplified for real-time visualisation, but the qualitative and near-quantitative agreement between the simulated force-extension point and the theoretical curve is genuine, not scripted.
Interactive worm-like chain simulation of DNA under a virtual optical tweezer, comparing live simulated force-extension data against the experimentally-verified Marko-Siggia formula.
2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install