Development of modified cable models to simulate accurate neuronal active behaviors.

In large network and single three-dimensional (3-D) neuron simulations, high computing speed dictates using reduced cable models to simulate neuronal firing behaviors. However, these models are unwarranted under active conditions and lack accurate representation of dendritic active conductances that greatly shape neuronal firing. Here, realistic 3-D (R3D) models (which contain full anatomical details of dendrites) of spinal motoneurons were systematically compared with their reduced single unbranched cable (SUC, which reduces the dendrites to a single electrically equivalent cable) counterpart under passive and active conditions. The SUC models matched the R3D model's passive properties but failed to match key active properties, especially active behaviors originating from dendrites. For instance, persistent inward currents (PIC) hysteresis, frequency-current (FI) relationship secondary range slope, firing hysteresis, plateau potential partial deactivation, staircase currents, synaptic current transfer ratio, and regional FI relationships were not accurately reproduced by the SUC models. The dendritic morphology oversimplification and lack of dendritic active conductances spatial segregation in the SUC models caused significant underestimation of those behaviors. Next, SUC models were modified by adding key branching features in an attempt to restore their active behaviors. The addition of primary dendritic branching only partially restored some active behaviors, whereas the addition of secondary dendritic branching restored most behaviors. Importantly, the proposed modified models successfully replicated the active properties without sacrificing model simplicity, making them attractive candidates for running R3D single neuron and network simulations with accurate firing behaviors. The present results indicate that using reduced models to examine PIC behaviors in spinal motoneurons is unwarranted.