A European Informational Website
learn more
The worm-like chain (WLC) model in polymer physics is used to describe the behavior of semi-flexible polymers; it is sometimes referred to as the Kratky-Porod worm-like chain model.
The WLC model envisions an isotropic rod that is continuously flexible; this is in contrast to the freely-jointed chain model that is flexible only between discrete segments. The worm-like chain model is particularly suited for describing stiffer polymers. At room temperature, the polymer adopts a conformational ensemble that is smoothly curved; at K, the polymer adopts a rigid rod conformation.
For a polymer of length , parametrize the path of the polymer as , allow to be the unit tangent vector to the chain at , and to be the position vector along the chain. Then
and the end-to-end distance .
It can be shown that the orientation correlation function for a worm-like chain follows an exponential decay:
,
where is by definition the polymer's characteristic persistence length. A useful value is the mean square end-to-end distance of the polymer:
Several biologically important polymers can be effectively modeled as worm-like chains, including:
Laboratory tools such as atomic force microscopy (AFM) and optical tweezers have been used to characterize the force-dependent stretching behavior of the polymers listed above. An interpolation formula that describes the extension of a WLC with contour length and persistence length in response to a stretching force is
where is the Boltzmann constant and is the absolute temperature (Bustamante, et al, 1994).