Worm-like chain

The wormlike chain model ( WLC model, on German about, worm -like chain model '), rarely Porod -Kratky chain, is a model for the physical description of rigid polymers. It is more complex than the Freely - Jointed Chain model and is suitable for rigid polymers such as double-stranded DNA, double-and single-stranded RNA and proteins.

Properties

The WLC model approximately describes a flexible at defined locations, isotropic rod. In contrast to the Freely - Jointed Chain model of the rod is flexible only in some places. In the WLC model, the segments indicate approximately in the same direction. At room temperature, the polymer adopts a curved conformation, at absolute zero takes the rod a rigid conformation.

For a polymer of the length of the path of the polymer is as a parameterized with the unit tangent vector of the chain in, and as a position vector along the chain.

It can be shown that the correlation function of the orientation of a worm -like chain follows the exponential decay:

With a characteristic persistence length. A typical value is the square of the mean Endpunkteabstandes of the polymer:

In the limit is. This can be used to show that the length of the double - Kuhn persistence of a corresponding polymer WLC.

Stretching of polymers

At a given temperature, the distance between the two ends of the polymer will be significantly shorter than the length of the contour. This is caused by thermal fluctuations, which results in a spool-shaped, random conformation in the rest state. By stretching the polymer, the available range of fluctuations, which generates an entropic force against the externally applied extension reduced. The entropic force can be estimated by the following Hamiltonian equation:

.

With the contour length of the persistence length, the extension and the force.

By atomic force microscopes and optical tweezers, the force -dependent elongation of the polymer can be determined. The following interpolation was used to approximate the force - extension behavior was by JF Marko, ED Siggia (1995 ) developed:

With the Boltzmann constant and absolute temperature.

Extensible Worm -like chain model

With increasing stretching polymers are elastic. For example, in the stretch of DNA at neutral pH, an ionic strength of 100 mM, and the room temperature according to the model needs to be considered with reference to the enthalpic tensile modulus:

With the contour length of the persistence length, the extension and the external force. Inside is the entropic term, which considers the change in the conformation and the enthalpic term which considers the extension under external force. The enthalpic term is described here as a linear Hooke's spring.

Various approximations are based on the applied force. For the areas of small forces under ten piconewtons the following interpolation was formulated:

.

At higher forces, in which the polymers are clearly stretched, the following approximation applies:

.

A typical value for the tensile modulus of double-stranded DNA is about 1000 pN, and about 45 nm for the persistence.