Control Analysis of the Action Potential and its Propagation in the Hodgkin-Huxley Model

The Hodgkin-Huxley model, created in 1952, was one of the first models in computational neuroscience and remains the best studied neuronal model to date. Although many other models have a more detailed system description than the Hodgkin-Huxley model, it nonetheless gives an accurate account of various high-level neuronal behaviours. The fields of computational neuroscience and Systems Biology have developed as separate disciplines for a long time and only fairly recently has the neurosciences started to incorporate methods from Systems Biology. Metabolic Control Analysis (MCA), a Systems Biology tool, has not been used in the neurosciences. This study aims to further bring these two fields together, by testing the feasibility of an MCA approach to analyse the Hodgkin-Huxley model. In MCA it is not the parameters of the system that are perturbed, as in the more traditional sensitivity analysis, but the system processes, allowing the formulation of summation and connectivity theorems. In order to determine if MCA can be performed on the Hodgkin-Huxley model, we identified all the discernable model processes of the neuronal system. We performed MCA and quantified the control of the model processes on various high-level time invariant system observables, e.g. the action potential (AP) peak, firing threshold, propagation speed and firing frequency. From this analysis we identified patterns in process control, e.g. the processes that would cause an increase in sodium current, would also cause the AP threshold to lower (decrease its negative value) and the AP peak, propagation speed and firing frequency to increase. Using experimental inhibitor titrations from literature we calculated the control of the sodium channel on AP characteristics and compared it with control coefficients derived from our model simulation. Additionally, we performed MCA on the model’s time-dependent state variables during an AP. This revealed an intricate linking of the system variables via the membrane potential. We developed a method to quantify