Mathematical models which simulate general biochemical kinetic reactions were studied by analytical means to determine regions of relative stability. Theorems were developed to determine whether the stability was a fixed point or a moving point kind. In addition, a theorem was produced which can be used to determine which models will or will not show oscillatory behavior in three dimensional systems. The technique could not be generalized to four dimensions. These theorems are useful in determining whether one has equilibrium points or regions of oscillation in biochemical kinetic models or other systems which may be modeled with differential equations. If there is a diseased state which is rhythmic and a normal state which is not, then these theorems are useful in establishing differences in the two model systems. In particular, these techniques were applied to a kinetic model for heme metabolism in acute intermittent porphyria and the normal, ruling out the possibility of oscillatory phenomena for a particular model used to represent the normal state.
NIH ExPorter
NIH ExPorter