Autoregressive Point-Processes as Latent State-Space Models: a Moment-Closure Approach to Fluctuations and Autocorrelations

Modeling and interpreting spike train data is a task of central importance in computational neuroscience, with significant translational implications. Two popular classes of data-driven models for this task are autoregressive Point Process Generalized Linear models (PPGLM) and latent State-Space models (SSM) with point-process observations. In this letter, we derive a mathematical connection between these two classes of models. By introducing an auxiliary history process, we represent exactly a PPGLM in terms of a latent, infinite dimensional dynamical system, which can then be mapped onto an SSM by basis function projections and moment closure. This representation provides a new perspective on widely used methods for modeling spike data, and also suggests novel algorithmic approaches to fitting such models. We illustrate our results on a phasic bursting neuron model, showing that our proposed approach provides an accurate and efficient way to capture neural dynamics

Neural dynamics in cortical populations

Many essential neural computations are implemented by large populations of neurons working in concert. Recent studies have sought both to monitor increasingly large groups of neurons and to characterise their collective behaviour, but the standard computational approaches available to identify the collective dynamics scale poorly with the size of the dataset. We develop new efficient methods for discovering the low-dimensional dynamics that underlie simultaneously-recorded spike trains from a neural population. We use the new models to analyze two different sets of population recordings, one from motor cortex and another from auditory cortex. In motor cortex, we describe the nature of the trial-by-trial spontaneous fluctuations identified by the model and connect these fluctuations to behavioral events. The spatio-temporal structure of the spontaneous events was tracked by three trajectories identified by the model. These trajectories followed similar dynamics during hand reaches as they did when the hands were stationary. The structure of the models we developed allow them to be used as decoders of hand position from neural activity, significantly improving upon previous state-of-the-art methods. The decoders were able to predict information about the direction, onset time and speed profile of movements. In auditory cortex, we use the statistical models to identify population dynamics under different brain states. We report major differences in dynamics and stimulus coding between synchronized and desychronized brain states. Synchronized but not desynchronized brain states imposed constraints on neural dynamics such that a four-dimensional system accounted for most of the dynamical structure of population events. We used the low-dimensional representation of the data to construct network simulations that reproduced the patterns present in the recordings. The simulations suggest that the overall level of feedback inhibition controls the stability of each local cortical network, with unstable dynamics resulting in synchronized brain states. Finally we propose a functional role for dynamics in the representation of visual motion in visual cortex

Discovering structure in multi-neuron recordings through network modelling

Our brains contain billions of neurons, which are continually producing electrical signals to relay information around the brain. Yet most of our knowledge of how the brain works comes from studying the activity of one neuron at a time. Recently, studies of multiple neurons have shown that they tend to be active together. These coordinated dynamics vary across brain states and impact the way that external sensory information is processed. To investigate the network-level mechanisms that underlie these dynamics, we developed novel computational techniques to fit a deterministic spiking network model directly to multi-neuron recordings from different rodent species, sensory modalities, and behavioral states. We found that inhibition modulates the interactions between intrinsic dynamics and sensory inputs to control the reliability of sensory representations. We next recorded from awake mice using calcium imaging techniques, and acquired activity from 10,000 neurons simultaneously in visual cortex while presenting 2,800 different natural images. In awake mice, these intrinsic population-wide fluctuations were suppressed and responses to visual stimuli were reliable. The stimulus-related information was stored in a high-dimensional neural space: 1,000 dimensions of neural activity accounted for 90\% of the variance. Although awake mice lacked large population-wide fluctuations in activity, we observed several dozen dimensions of spontaneous activity. These dimensions of spontaneous activity were not spatially organized in cortex. Instead they were related to the orofacial behaviors of the mouse: over 50\% of the shared variability of the network could be predicted from the facial movements of the mouse. In simulations of high-dimensional network activity, flexible patterns of activity were reproduced only if the network contained multiple dimensions of inhibitory activity. We tested this hypothesis in our recordings and found that inhibitory neuron activity did track excitatory neuron activity across multiple dimensions