Random coil

A random coil is a polymer conformation where the monomers are arranged at random. Many simple polymers such as polyethylene inhabit only this conformation, more complex polymers with varying chemical groups attached to its backbone, such as proteins, self-assemble into well defined structures.
Proteins, segments of proteins, and peptides that lack secondary structure inhabit the random coil conformation. In random coil, the only fixed relationship between amino acids is that between adjacent residues through the peptide bond. The conformation's name is derived from the idea that, in the absence of specific, stabilizing interactions, the polypeptide backbone will sample all possible conformations randomly. This is actually not the case, since the ensemble will be energy-weighted, with lower-energy conformations being present more frequently. For this reason, the term "statistical coil" is occasionally preferred.
The random coil conformation can be detected using spectroscopic techniques. The arrangement of the amide planes results in a distinctive signal by circular dichroism. By nuclear magnetic resonance (NMR), the chemical shift of amino acids in the random coil conformation is well known. Deviations from these values often indicates the presence of secondary structure and thus the absence of random coil. Furthermore, signals in multidimensional NMR experiment that indicate stable, non-local amino acid interactions are absent for polypeptides in the random coil conformation. Likewise in the images produced in crystallography experiments, pieces of random coil appear simply as an absence of "electron density" or contrast. The random coil state for any polypeptide chain can be attained through Denaturing of the system.
There is evidence that proteins perhaps never are truly random coils even when denatured (Shortle et al.).
Random flight model
By looking at the polymer as a freely jointed chain, one can look at each chain as doing random walk or more accurately constrained random walk and it can be shown that number of polymers with a any distance l between the ends of the chain will follow a normal distribution.