Random sampling of ligand arrangements on a one-dimensional lattice

We introduce a transfer-matrix-based sequential sampling scheme for generating random samples of ligand arrangements on one-dimensional templates. The number of ligand types is arbitrary, the binding constants can have positional dependence, and cooperativity parameters are included. From the random arrangements, any (linear or nonlinear) observable can be calculated using sample averaging. As an example case study, we investigate the competitive binding of three ligand types (the sequence-specific binder netropsin, YOYO-1, and ethidium bromide) to a DNA molecule. We also employ our random sampling method of ligands to determine the quality of synthetically generated DNA barcodes as a function of concentration of a ligand (e.g., netropsin) in optical DNA mapping (ODM) experiments. We provide publically available softwares, with a computational time that scales linearly with the lattice size, for generating random ligand arrangements and for generating synthetic barcodes.