Capturing the Dynamical Repertoire of Single Neurons with Generalized Linear Models

Abstract

A key problem in computational neuroscience is to find simple, tractable models that are nevertheless flexible enough to capture the response properties of real neurons. Here we examine the capabilities of recurrent point process models known as Poisson generalized linear models (GLMs). These models are defined by a set of linear filters, a point nonlinearity, and conditionally Poisson spiking. They have desirable statistical properties for fitting and have been widely used to analyze spike trains from electrophysiological recordings. However, the dynamical repertoire of GLMs has not been systematically compared to that of real neurons. Here we show that GLMs can reproduce a comprehensive suite of canonical neural response behaviors, including tonic and phasic spiking, bursting, spike rate adaptation, type I and type II excitation, and two forms of bistability. GLMs can also capture stimulus-dependent changes in spike timing precision and reliability that mimic those observed in real neurons, and can exhibit varying degrees of stochasticity, from virtually deterministic responses to greater-than-Poisson variability. These results show that Poisson GLMs can exhibit a wide range of dynamic spiking behaviors found in real neurons, making them well suited for qualitative dynamical as well as quantitative statistical studies of single-neuron and population response properties.

Discrete stepping and nonlinear ramping dynamics underlie spiking responses of LIP neurons during decision-making

“…els to include autoregressive spike-history filters, like those in the generalized linear modeling (GLM) framework (Figure 1, Section 4). These filters capture non-Poisson spike-history dependencies (Truccolo et al, 2005;Weber and Pillow, 2017) and allow for a dissociation of latent dynamics from spiking activity that can be explained more parsimoniously by past spikes.…”

Poisson balanced spiking networks

“…Under this modified spiking rule, spiking is governed by an instantaneous probability of spiking λ t , also known as the conditional intensity, such that spiking is independent with probability ∆λ t in any small time window of width ∆. This results in an auto-regressive Poisson generalized linear model (GLM), also known as a Cox process [33][34][35]. This model has a quasi-realistic biophysical interpretation [32,36,37], and recent work has shown that it can capture a wide range of dynamical behaviors found in real neurons [35].…”

“…The local Poisson framework draws direct inspiration from the work of Plesser and Gerstner [32], which sought to approximate a noisy integrate-and-fire model with an inhomogeneous Poisson process via the so-called "escape-rate approximation", which refers to the instantaneous probability of noisy membrane potential crossing threshold in a small time window. Subsequent work on the spike response model [36,[65][66][67][68] and Poisson generalized linear model [33][34][35][69][70][71] further explored the connection between integrate-and-fire and conditionally Poisson spike train models. The latter are sometimes referred to as "soft-threshold" integrate-and-fire model [72], making the local Poisson model a natural extension of the original BSN model.…”

Spontaneous activity emerging from an inferred network model captures complex spatio-temporal dynamics of spike data

“…Although, quite surprisingly, the study of the dynamics of the inferred models has been largely neglected, we are not the first to address the issue. In 11 the authors demonstrated, on an in-vitro population of ON and OFF parasol ganglion cells, the ability of a GLM to accurately reproduce the dynamics of the network; 14 studied the response properties of lateral intraparietal area neurons at the single trial, single cell level; the capability of GLM to capture a broad range of single neuron response behaviors was analyzed in 13 . In all these works, however, the focus was on the response of neurons to stimuli of different spatio-temporal complexity; even where network interactions were accounted for, they proved to be, for the overall dynamics displayed by the ensemble, an important, yet not decisive correction.…”

“…In time, efforts have been made to make contact between the two approaches, e.g., in the case of neuroscience, by endowing the coupling structure of the inference model with features motivated by biological plausibility [10][11][12] ; it has also been recognized that a GLM is close to a stochastic version of the spike-response model. Recently, the repertoire of the driven dynamics of GLM models of single neurons has been explored 13 ; however, to our knowledge, a largely open issue is to endow network inference models with predictive power in terms of the system dynamics. Our approach to this problem is to explore the free, spontaneous dynamics of the inferred model in its relation with the one of the biological system generating the data and, in doing this, to identify the role of different elements of the inference model in determining the spontaneous dynamics of the neuronal network.…”