End-to-end distance distribution of force stretched chains reconstruction by maximum-entropy method

Using the maximum-entropy method, the end-to-end distance distribution of the force stretched chain is calculated from the moments of the distribution, which can be obtained from the extension-force curves recorded in single-molecule experiments. If one knows force expansion of the extension through the (n - 1)th power of force, it is enough information to calculate the n moments of the distribution. The method is examined with force stretched chain models, Gaussian chain and excluded-volume chain on two-dimension lattice. The method reconstructs all distributions precisely. The method also is applied to force stretched complex chain molecules: the hairpin and secondary structure conformations. We find that the distributions of homogeneous chains of two conformations are very different: there are two independent peaks in hairpin distribution; while only one peak is observed in the distribution of secondary structure conformations. Our discussion also shows that the end-to-end distance distribution may discover more critical physical information than the simpler extension-force curves can give.