| The Santillan-Mackey model of the tryptophan operon was developed to characterize the anthranilate synthase activity in cultures of Escherichia coli. Similarly, the GABA reaction scheme was formulated to characterize the response of the GABAA receptor at a synapse, and the Hodgkin-Huxley model was developed to characterize the action potential of a squid giant axon. While the Hodgkin-Huxley model has been studied in great detail from a mathematical vantage, much less is known about the preceding two models in this regard. This work examines the stiffness of all three models; a novel perspective for both the Santillan-Mackey model and the GABA reaction. The characterization of the stiffness in these problems gives theoretical biologists insight into the dynamics of the reactions. It also enables them to select more computationally efficient methods for numerical simulations. The discovery of invariant manifolds in the Santillan-Mackey model and the GABA reaction in this work present experimentalists with concrete assays, against which the models can be tested. |
