End-to-end distribution for a wormlike chain in arbitrary dimensions

Shafigh Mehraeen, Bariz Sudhanshu, Elena F. Koslover, Andrew J. Spakowitz
2008 Physical Review E  
We construct an efficient methodology for calculating wormlike chain statistics in arbitrary D dimensions over all chain rigidities, from fully rigid to completely flexible. The structure of our exact analytical solution for the end-to-end distribution function for a wormlike chain in arbitrary D dimensions in Fourier-Laplace space ͑i.e., Fourier-transformed end position and Laplace-transformed chain length͒ adopts the form of an infinite continued fraction, which is advantageous for its
more » ... eous for its compact structure and stability for numerical implementation. We then proceed to present a step-by-step methodology for performing the Fourier-Laplace inversion in order to make full use of our results in general applications. Asymptotic methods for evaluating the Laplace inversion ͑power-law expansion and Rayleigh-Schrödinger perturbation theory͒ are employed in order to improve the accuracy of the numerical inversions of the end-to-end distribution function in real space. We adapt our results to the evaluation of the single-chain structure factor, rendering simple, closed-form expressions that facilitate comparison with scattering experiments. Using our techniques, the accuracy of the end-toend distribution function is enhanced up to the limit of the machine precision. We demonstrate the utility of our methodology with realizations of the chain statistics, giving a general methodology that can be applied to a wide range of biophysical problems.
doi:10.1103/physreve.77.061803 pmid:18643291 fatcat:oxhuqf5wybdupng4qrqes43bkm