The protein of silkworm pupae(PSP)is known for its nutritional value.The hydrolysates of PSP contained bioactive peptides with important bioactive activities

but enzymatic hydrolysis kinetics of PSP was less reported.This study applied lumping kinetics to the PSP-alcalase system.Solid-state PSP was the main substrate and soluble PSP was hardly responsive to alcalase.The molecular weight distribution of hydrolysates of solid-state PSP was analyzed by high performance size-exclusion chromatography(HPSEC)and the principle of lumping kinetics was built based on solubility of PSP and molecular weight distribution of hydrolysates.The lumped components of the complex reaction system were defined and a three-lumping reaction network was proposed.Reaction of the lumps was described with intrinsic kinetic equations

which contained product inhibition

substrate inhibition

enzyme inactivation and the variation of different lumped components in different times

and the system of differential equations for this reaction of lumps were established.The rate constant of each lump reaction was estimated by the Marquardt method.The reliability of the model was verified by comparing the computed values with the experimental values

and the average regression error was less than 5%.