Hierarchical Linear-Nonlinear Cascade Models of Dendritic Integration and Somatic Membrane Potential

Daniel Strouse, Princeton University

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Accumulating evidence suggests that dendritic trees play a crucial role in single-neuron information processing, yet there exists no simple, canonical formalization of dendritic computation. At one extreme, multi-compartmental models retain as much biophysical detail as possible, enabling them to exhibit the spatial and temporal dendritic nonlinearities observed in experiments, but sacrificing ease of fitting, mathematical tractability, and computational interpretability. At the opposite extreme, heuristic “two-layer network” models [Poirazi et al., Neuron 2003, Polsky et al., Nat. Neuro. 2004], which assume that the somatic membrane potential is produced by passing the instantaneous synaptic inputs through a two-layer linear-nonlinear cascade, are easy to analyze mathematically and interpret computationally. However, they were designed to work only with static inputs and outputs, restricting their experimental application to artificial stimulus protocols involving brief, intense stimulation rather than extended spike trains with realistic statistical properties. Moreover, because of this restriction, the associated metrics for judging nonlinear dendritic behavior were based only on either instantaneous firing rates or peaks/means of somatic membrane potentials, rather than predictiveness of dynamically changing firing rates or full membrane potential traces.

Here we propose a model class consisting of a hierarchical cascade of linear-nonlinear stages (hLN model) that retains the simplicity and interpretability of the two-layer network model class but generalizes it to handle dynamic inputs, model dendritic trees of arbitrary complexity, and be judged by its predictiveness of full somatic membrane potential traces. By fitting the hLN model to data generated from a biophysically realistic multi-compartmental model of a cortical pyramidal neuron, we demonstrate how the nonlinear dendritic properties discovered depend on the stimulation protocol and synapse locations. In particular, we find that over a wide range of synaptic input statistics and in marked contrast to previous findings using static inputs and outputs, two-layer models offer little to no improvement over one-layer models in capturing the behavior of cortical pyramidal neurons.

Abstract Author(s): D.J. Strouse, Balázs Ujfalussy, Máté Lengyel