Mathematical models for the action of alpha-amylase on amylose

Mathematical treatments have been developed to describe the action of alpha-amylases on amylose. The treatments are based on the unique properties of the exponential (or most-probable) distribution of molecular weights of the substrate, namely, that ( a) the principal averages are invariant to chain-end attack if the product molecules are ignored, and ( b) the ratio of the principal averages is invariant to random attack. The relations so developed allow published, qualitative data for the alpha-amylolysis of amylose to be interpreted in a quantitative manner. As a result, it appears that multiple attack is of little or no significance in the action patterns of alpha-amylases, with the exception of those derived from the pancreas.