Qualitative investigation of dynamical equation system of hemoglobin (or allosteric enzymes)

Abstract

For the dynamical equation system (a three-dimensional autonomous system) of hemoglobin given in [1], we make the following qualitative investigations: (1) point out that all meaningful solutions should be in a tetrahedroid, and that its four surfaces are without contact; (2) find all singular points, and prove that only two of them are respectively situated on a pair of them are respectively situated on a pair of separate edges, and that other singular points are outside the tetrahedroid and meaningless; (3) prove that, among seven physical parameters of this system, only the sign of a parameter determines the properties of these two singular points; (4) clear up the relation between this system and MWC model^[3], The investigation shows that this system reflects the dynamical properties of hemoglobin satisfactorily.