Autoregressive point-processes as latent state-space models

In 2016 I started a postdoc with the labs of Guido Sanguinetti and Matthias H. Hennig—and this is the first paper to result!

[get PDF]

A central challenge in neuroscience is understanding how the activity of single cells combines to create the collective dynamics that underlie perception, cognition, and behavior. One way to study this is to build detailed models, and "coarse grain" them to see which details are important. 

Our paper develops ways to relate detailed point-process models to coarse-grained quantities, like average neuronal firing rates and correlations. Point-process models are used for statistical modelling of spike train data. They can reveal effective neural dynamics by capturing how neurons in a population inhibit or excite each-other and themselves. 

Preview of figures: 

Figure 2: Moment closure of autoregressive PPGLMs combines aspects of three modeling approaches:

(A) Log-linear autoregressive PPGLM framework (e.g., Weber & Pillow, 2017). Dependence on the history of both extrinsic covariates x(t) and the process itself y(t) are mediated by linear filters, which are combined to predict the instantaneous log intensity of the process. (B) Latent state-space models learn a hidden dynamical system, which can be driven by both extrinsic covariates and spiking outputs. Such models are often fit using expectation- maximization, and the learned dynamics are descriptive. (C) Moment closure recasts autoregressive PPGLMs as state-space models. History dependence of the process is subsumed into the state-space dynamics, but the latent states retain a physical interpretation as moments of the process history (dashed arrow). (D) Compare to neural mass and neural field models, which define dynamics on a state space with a physical interpretation as moments of neural population activity

Optogenetic stimulation shifts the excitability of cerebral cortex from type I to type II

Our new paper, Heitmann et al. [get PDF], is finally out! It's a collaboration between the theoretical neuroscientists Stewart Heitmann and Bard Ermentrout at the University of Pittsburgh, and the Truccolo lab at Brown University. 

This work could help us understand what happens when we stimulate cerebral cortex in primates using optogenetics. Modeling how the brain responds to stimulation is important for learning how to use this new technology to control neural activity.

Optogenetic stimulation elicits gamma (~50 Hz) oscillations, the amplitude of which grows with the intensity of light stimulation. However, traveling waves away from the stimulation site also emerge. It's difficult to reconcile oscillatory and traveling-wave dynamics in neural field models, but Heitmann et al. arrive at a surprising and testable prediction: 

The observed effects can be explained by paradoxical recruitment of inhibition at low levels of stimulation, which changes cortex from a wave-propagating medium to an oscillator. 

At higher stimulation levels, excitation overwhelms inhibition, giving rise to the observed gamma oscillations. 

Many thanks to Stewart Heitmann, Wilson Truccolo, and Bard Ermentrout. The paper can be cited as:

Heitmann, S., Rule, M., Truccolo, W. and Ermentrout, B., 2017. Optogenetic stimulation shifts the excitability of cerebral cortex from type I to type II: oscillation onset and wave propagation. PLoS computational biology, 13(1), p.e1005349.