Effects of passive dendritic tree properties on the firing dynamics of a leaky-integrate-and-fire neuron

We study the effects of dendritic tree topology and biophysical properties on the firing dynamics of a leaky-integrate-and-fire (LIF) neuron that explicitly includes spiking dynamics. We model the dendrites as a multi-compartment tree with passive dynamics. Owing to the simplicity of the system, we obtain the full analytical solution for the model which we use to derive a lower dimensional return map that captures the complete dynamics of the system. Using the map, we explore how biophysical properties and dendritic tree architecture affect firing dynamics. As was first reported in earlier work by one of the authors, we also find that the addition of the dendritic tree can induce bistability between periodic firing and quiescence. However, we go beyond their results by systematically examining how dendritic tree topology affects the appearance of this bistable behavior. We find that the structure of the dendritic tree can have significant quantitative effects on the bifurcation structure of the system, with branchier topologies tending to promote bistable behavior over unbranched chain topologies. We also show that this effect occurs even when the input conductance at the soma is held fixed, indicating that the topology of the dendritic tree is mainly responsible for this quantitative change in the bifurcation structure. Lastly, we demonstrate how our framework can be used to explore the effect of biophysical properties on the firing dynamics of a neuron with a more complex dendritic tree topology.