Computer Simulations in Molecular Biology by Hiqmet Kamberaj

Author:Hiqmet Kamberaj
Language: eng
Format: epub
ISBN: 9783031348396
Publisher: Springer Nature Switzerland

(7.8)

where 1/R can be written as

(7.9)

where is the unit tangent vector and s is the arc length.

The second term is given as

(7.10)

where is the angle between the unit vector and the z-axis. Then, the expression for the total energy is

(7.11)

where L is the contour length of the molecule.

The experimental data are analysed in terms of the persistence length , which is related to A as:

(7.12)

The partition function, is given via the path integral

(7.13)

Here, is the integration measure in functional space of the paths drawn on the unit sphere starting at the point and ending at . Following the discussion in Ref. Bouchiat et al. (1999), extending the integration along s in Eq. (7.13) in the imaginary axis, one obtains the action integral relative to a fictitious particle of unit charge moving upon a sphere under the influence of an electric field F with the time variable . This transforms the integral to the Feynman transition probability amplitude for the fictitious particle, initially localised at the coordinate , and at the point of coordinate at the final time . The amplitude is calculated by the matrix element:

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