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.