A dynamical model for a co-operative enzyme

Abstract

Proteins partially immersed in the hydrophobic portion of a lipid bilayer interact by means of London-van der Waals non-bonding dispersion forces. Moreover, in certain organelles, enzymes are structured in a lattice or ordered matrix. These conditions may facilitate the establishment of long-range correlations between proteins. We studied the dynamical properties of a model for an enzyme endowed with a highly co-operative conformational transition between two reactive states. Two cases were considered, a closed system and an open system. In the closed system for different degrees of interaction among the proteins, it was found that for a substrate concentration greater than a certain threshold an abrupt change of enzymatic activity occurs. This biphasic behavior has been observed in the enzymatic activity of crystalline mitochondrial aspartate aminotransferase and for some other crystalline enzymes. In the analysis of the open system, for a specific input rate of the substrate, two different dynamics were found depending on the selected degree of interaction. For a certain value of a parameter phi, representing the degree of interaction among the reacting units, three steady states co-exist. This multiplicity confers excitable properties to the model. For larger values of phi, limit cycle type solutions were obtained. Thus, a sustained oscillatory product formation of the enzymatic reaction is observed. These results are compared with experimental observations of enzyme extracts detected by NMR.