Stochastic point process models for multi-compartment dendritic-tree input-output transformations in spiking neurons

We extend stochastic point-process generalized linear models (PPGLMs) to the estimation of input-output transformations in dendritic trees and their contribution to the generation of soma action potentials in multi-compartmental models of single neurons. We used simulations of a model enthorinal cortex pyramidal neuron, with known dentritic tree and soma spatial organization, including active compartments defined in terms of standard cable and standard Hodgkin-Huxley equations. Each dendritic compartment (391 total) was endowed with either excitatory (E) or inhibitory (I) synaptic inputs whose strength was randomly specified. We examined the cases of both homogeneous and inhomogeneous spatial distributions for E and I synaptic inputs. The times for synaptic inputs followed a Poisson process with different mean rate regimes varying from 50 to 600 inputs/s. The soma membrane potential received also a background noise in the form of an Ornstein-Uhlenbeck process. Our main findings are: (1) Power spectra of soma membrane potentials revealed subthreshold resonances at ~40 Hz and ~80 Hz; (2) The contribution of different dendritic compartments, under the examined input ranges and spatial distributions, depended not only of the dendrite-soma path distance, but also on the number of compartments in the dendritic segment. (3) Estimated conditional intensity functions (CIFs) with PPGLMs successfully predicted spiking activity based on given E-I input times; area under ROC curves computed on test data varied from 0.8 - 0.95. (4) The CIF models identified compartments and regions receiving E-I synaptic inputs; Estimated temporal filters were consistent with dendrite-soma path distances and input weights. We expect this type of PPGLMs to contribute to data-driven identification of input-output transformations in dentritic trees based on single-neuron Ca²⁺ and voltage indicator imaging data.