Numerical model for alginate block specificity of mannuronate lyase from Haliotis

Abstract

Purified preparations of alginate (mannuronate) lyase from Haliotis tuberculata have been investigated by recording the progress of product formation when acting on well-characterised alginates and alginate fragments. We have earlier shown that maximal conversion is affected by enzyme dose as well as by initial substrate concentration. This is related to a strong, reversible product inhibition, dominant in the enzymatic breakdown of the heteropolymeric (MG) fraction of the alginate compared to that of polymannuronic (MM) blocks. Polyguluronic (GG) structures were found to be inactive both as substrate and as inhibitor. A numerical two-substrate model is now presented in an attempt to analyse data by simply assigning different kinetic constants to each block fraction of the accessible substrate. Including reversible product inhibition, the general model is expressed by a set of six coupled nonlinear differential equations. If the steady-state assumption of the Michaelis-Menten initial rate analysis is accepted, these equations may be integrated directly. This approach could only adequately describe data for poly-M substrates showing no significant product inhibition. The steady-state assumption could not be maintained for results obtained with substrates rich in heteropolymeric MG blocks. Instead, the kinetic parameters were estimated by a nonlinear minimalisation of the sum squares of residuals. In this form, the model could fully describe our experimental observations.