Molecular organization and clustering of cell-wall-bound enzymes as a source of kinetic apparent co-operativity.

When fixed charges and enzyme molecules are not homogeneously distributed in a matrix, the degree of organization of charges, of enzyme molecules and of charges with respect to enzyme molecules modulate the enzyme reaction rate. The overall reaction velocity of the bound enzyme system may be expressed in terms of monovariate moments of the charge density distribution and of the bivariate moments of the charge and enzyme density distributions. With respect to the situation where fixed charges and enzyme molecules are randomly distributed in the matrix, the molecular organization, as expressed by the monovariate and bivariate moments results in an increase or a decrease, of the overall reaction rate, as well as in the appearance of a kinetic cooperativity. The degree of spatial organization of objects may be expressed quantitatively through the concept of minimal spanning tree. This concept may thus be applied to the quantification of the degree of order that may exist in the bidimensional distribution of enzyme molecules in a charged matrix. Primary walls of isolated plant cells in sterile culture behave as a polyanion and contain different enzymes. The spatial distribution in sycamore cell walls of an acid phosphatase has been studied through the concept of minimal spanning tree and shown to be non-randomly distributed in the polyanionic matrix, but clustered in that matrix. This spatial organization results in a modulation of the reaction rate of the cell-wall-bound phosphatase reaction. Both the theoretical and experimental results presented in this study leave little doubt as to the validity of the idea that in situ the organization of fixed charges and enzyme molecules modulate the overall dynamics of enzyme reactions.