Computational analysis of a 9D model for a small DRG neuron.

Small dorsal root ganglion (DRG) neurons are primary nociceptors which are responsible for sensing pain. Elucidation of their dynamics is essential for understanding and controlling pain. To this end, we present a numerical bifurcation analysis of a small DRG neuron model in this paper. The model is of Hodgkin-Huxley type and has 9 state variables. It consists of a Nav1.7 and a Nav1.8 sodium channel, a leak channel, a delayed rectifier potassium, and an A-type transient potassium channel. The dynamics of this model strongly depend on the maximal conductances of the voltage-gated ion channels and the external current, which can be adjusted experimentally. We show that the neuron dynamics are most sensitive to the Nav1.8 channel maximal conductance ( $\overline {g}_{1.8}$ ). Numerical bifurcation analysis shows that depending on $\overline {g}_{1.8}$ and the external current, different parameter regions can be identified with stable steady states, periodic firing of action potentials, mixed-mode oscillations (MMOs), and bistability between stable steady states and stable periodic firing of action potentials. We illustrate and discuss the transitions between these different regimes. We further analyze the behavior of MMOs. As the external current is decreased, we find that MMOs appear after a cyclic limit point. Within this region, bifurcation analysis shows a sequence of isolated periodic solution branches with one large action potential and a number of small amplitude peaks per period. For decreasing external current, the number of small amplitude peaks is increasing and the distance between the large amplitude action potentials is growing, finally tending to infinity and thereby leading to a stable steady state. A closer inspection reveals more complex concatenated MMOs in between these periodic MMO branches, forming Farey sequences. Lastly, we also find small solution windows with aperiodic oscillations which seem to be chaotic. The dynamical patterns found here—as consequences of bifurcation points regulated by different parameters—have potential translational significance as repetitive firing of action potentials imply pain of some form and intensity; manipulating these patterns by regulating the different parameters could aid in investigating pain dynamics.