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.

 

 

A mechanism for persistent memory in oscillatory networks

I just finished the Methods in Computational Neuroscience "bootcamp". It was intense, but valuable—I can recommend that any student/postdoc who wants to get started in the field take it. 

For a course project, I extended previous work, which showed that oscillatory drive can excite patterned instabilities in visual cortex. These patterns constitute attractor states that are stabilized by an external oscillatory drive. The project explored the idea that similar oscillation-stabilized attractors might serve as a flexible working memory. 

(Unfortunately, these notes are rather brief and incomplete as I never had the time to write this up properly. )

Selective, short-term maintenance of attractor states is important for working memory in neural systems. Neural networks, however, are typically stabilized by feedback inhibition. The delays in this inhibition lead to unavoidable oscillations. 

This project demonstrate a scenario where the attractor dynamics associated with a working memory are not fixed points, but instead fixed limit cycles embedded within a population oscillation. 

External oscillatory drive, perhaps e.g. an attention signal, can switch such a network from a "read-in" mode, in which the system responds to external input, and a "hold" model, in which the system retains a memory of its past states. These concepts may underlie flexible working memory solutions that can coexist with population oscillations.

To better understand the mechanisms underlying this, we explored a switched piece-wise linear model that captured the qualitative dynamics of the original system. We found that firing-rate nonlinearities with positive curvature are important for allowing a synchronous (non-selective) external signal to excite the asymmetric network states associated with a memory trace. 

[get writeup PDF]

[get presentation slides]

Preview: Figure 4

Figure 4: Many-population generalization of the two-population model of Rule et al. (2011), serving as a working memory. Starting from rest, a stimulus is delivered to the first oscillator (green) for $t\in[300,500)$ ms. We test the stability of this stimulus-driven network response during a hold period $t\in[500,1500)$ ms. Without oscillatory drive (top), the memory fades in a few cycles. Periodic stimulation (bottom) preserves the memory. Rightmost plots show the phase-plane dynamics during the readout period $t\in[1000,1500)$. The top system, without drive, has returned to rest. The driven system shows a stable limit cycle, with higher firing rates in the population that initially received the stimulus.