DETERMINATION OF MULTIPLE STEADY-STATES IN A FAMILY OF ALLOSTERIC MODELS FOR GLYCOLYSIS

To predict glycolytic oscillations, Goldbeter and Lefever [Biophys. J. 12, 1302 (1972)] proposed a complex allosteric model, consisting of 1 4 species and 32 reactions. Under the usual assumption of a quasistead y state for all the enzymatic forms, they simplified it to a two-varia ble model and ruled out the possibility of multiple steady states. In this work, the original network is determined to admit multiplicity of steady states by a zero eigenvalue analysis. It is shown that the exi stence of the multiplicity in the original network can be determined b y a subnetwork with five species and eight reactions. The fourteen-spe cies network can be treated as containing four such subnetworks. The a nalysis is extended to a general modified allosteric model, consisting of n active subunits. It can be shown that the general network has no steady-state multiplicity if all the four subnetworks follow the case of n=1; otherwise, multiple steady states can occur. (C) 1998 America n Institute of Physics. [S0021-9606(98)01143-X].