Figure 1. Illustration of how the rotational isomeric approximation of the Flory random coil model is constructed.

(A) This process begins with a detailed calculation of the free energy landscape (with free energies increasing from red to blue) for an individual amino acid (or Kuhn segment), shown here for alanine. The tiles represent a coarse graining of conformational space into discrete rotational isomers, and each isomer has a label and a statistical weight that is calculated using the energies associated with conformations that make up a rotational isomer. The assumption of independence / additivity allows the statistical weights for each combination of rotational isomers to be written as a product of individual weights. Panel (B) shows this procedure, whereby there are M conformations for a polypeptide of N residues and the statistical weight for each conformation z is a product of the weights for individual residues. The result is a weighted ensemble of all conformational possibilities where each “conformation” is denoted using a combination of the coarse grain rotational isomers. Panel (C) shows a schematic conformation for one of the conformations z.