Bifurcation analysis of motoneuronal excitability mechanisms under normal and ALS conditions

INTRODUCTION: Bifurcation analysis allows the examination of steady-state, non-linear dynamics of neurons and their effects on cell firing, yet its usage in neuroscience is limited to single-compartment models of highly reduced states. This is primarily due to the difficulty in developing high-fidelity neuronal models with 3D anatomy and multiple ion channels in XPPAUT, the primary bifurcation analysis software in neuroscience. METHODS: To facilitate bifurcation analysis of high-fidelity neuronal models under normal and disease conditions, we developed a multi-compartment model of a spinal motoneuron (MN) in XPPAUT and verified its firing accuracy against its original experimental data and against an anatomically detailed cell model that incorporates known MN non-linear firing mechanisms. We used the new model in XPPAUT to study the effects of somatic and dendritic ion channels on the MN bifurcation diagram under normal conditions and after amyotrophic lateral sclerosis (ALS) cellular changes. RESULTS: Our results show that somatic small-conductance Ca(2+)-activated K (SK) channels and dendritic L-type Ca(2+) channels have the strongest effects on the bifurcation diagram of MNs under normal conditions. Specifically, somatic SK channels extend the limit cycles and generate a subcritical Hopf bifurcation node in the V-I bifurcation diagram of the MN to replace a supercritical node Hopf node, whereas L-type Ca(2+) channels shift the limit cycles to negative currents. In ALS, our results show that dendritic enlargement has opposing effects on MN excitability, has a greater overall impact than somatic enlargement, and dendritic overbranching offsets the dendritic enlargement hyperexcitability effects. DISCUSSION: Together, the new multi-compartment model developed in XPPAUT facilitates studying neuronal excitability in health and disease using bifurcation analysis.