The nucleic acid distribution function: Evaluation of the loop closure probability

We present a detailed theoretical study of nucleic acid distance distribution functions for chain lengths up to thirty‐five nucleotides. The distribution functions were found by the Monte Carlo techniques described previously and, where they are symmetric, by reconstruction from their even moments. A comparison of the two approaches allows an assessment of the utility of expansion procedures for stiff chains ( C ∞ ≈ 17), as a function of length and extension. It was found that for chains with fewer than fourteen nucleotides over seventy even moments were required to obtain a reliable function for extensions R ≥ (〈 R 2 〉) 1/2 . On the other hand at thirty‐five nucleotides the first ten even moments were sufficient to reconstruct the distribution for all but extreme extensions. The other feature of the calculation is the prediction of a loop weighting function. It was found that for a thirty‐five nucleotide chain, the form of the distribution function is very nearly gaussian for R < (〈 R 2 〉) 1/2 . Consequently a loop weighting function based on detailed crystallographic data is now known for all values of N . The first derivative of the function is within 8% of the Jacobson‐Stockmayer value at 170 nucleotides, but differs severely from the latter for chains with less than twenty nucleotides.