Multivariate Autoregressive Modeling and Granger Causality Analysis of Multiple Spike Trains

Recent years have seen the emergence of microelectrode arrays and optical methods allowing simultaneous recording of spiking activity from populations of neurons in various parts of the nervous system. The analysis of multiple neural spike train data could benefit significantly from existing methods for multivariate time-series analysis which have proven to be very powerful in the modeling and analysis of continuous neural signals like EEG signals. However, those methods have not generally been well adapted to point processes. Here, we use our recent results on correlation distortions in multivariate Linear-Nonlinear-Poisson spiking neuron models to derive generalized Yule-Walker-type equations for fitting ‘‘hidden” Multivariate Autoregressive models. We use this new framework to perform Granger causality analysis in order to extract the directed information flow pattern in networks of simulated spiking neurons. We discuss the relative merits and limitations of the new method

Correlation-Based Analysis and Generation of Multiple Spike Trains Using Hawkes Models with an Exogenous Input

The correlation structure of neural activity is believed to play a major role in the encoding and possibly the decoding of information in neural populations. Recently, several methods were developed for exactly controlling the correlation structure of multi-channel synthetic spike trains (Brette, 2009; Krumin and Shoham, 2009; Macke et al., 2009; Gutnisky and Josic, 2010; Tchumatchenko et al., 2010) and, in a related work, correlation-based analysis of spike trains was used for blind identification of single-neuron models (Krumin et al., 2010), for identifying compact auto-regressive models for multi-channel spike trains, and for facilitating their causal network analysis (Krumin and Shoham, 2010). However, the diversity of correlation structures that can be explained by the feed-forward, non-recurrent, generative models used in these studies is limited. Hence, methods based on such models occasionally fail when analyzing correlation structures that are observed in neural activity. Here, we extend this framework by deriving closed-form expressions for the correlation structure of a more powerful multivariate self- and mutually exciting Hawkes model class that is driven by exogenous non-negative inputs. We demonstrate that the resulting Linear–Non-linear-Hawkes (LNH) framework is capable of capturing the dynamics of spike trains with a generally richer and more biologically relevant multi-correlation structure, and can be used to accurately estimate the Hawkes kernels or the correlation structure of external inputs in both simulated and real spike trains (recorded from visually stimulated mouse retinal ganglion cells). We conclude by discussing the method's limitations and the broader significance of strengthening the links between neural spike train analysis and classical system identification

Task specificity in mouse parietal cortex

Parietal cortex is implicated in a variety of behavioral processes, but it is unknown whether and how its individual neurons participate in multiple tasks. We trained head-fixed mice to perform two visual decision tasks involving a steering wheel or a virtual T-maze and recorded from the same parietal neurons during these two tasks. Neurons that were active during the T-maze task were typically inactive during the steering-wheel task and vice versa. Recording from the same neurons in the same apparatus without task stimuli yielded the same specificity as in the task, suggesting that task specificity depends on physical context. To confirm this, we trained some mice in a third task combining the steering wheel context with the visual environment of the T-maze. This hybrid task engaged the same neurons as those engaged in the steering-wheel task. Thus, participation by neurons in mouse parietal cortex is task specific, and this specificity is determined by physical context

Neural correlates of blood flow measured by ultrasound

Functional ultrasound imaging (fUSI) is an appealing method for measuring blood flow and thus infer brain activity, but it relies on the physiology of neurovascular coupling and requires extensive signal processing. To establish to what degree fUSI trial-by-trial signals reflect neural activity, we performed simultaneous fUSI and neural recordings with Neuropixels probes in awake mice. fUSI signals strongly correlated with the slow (<0.3 Hz) fluctuations in the local firing rate and were closely predicted by the smoothed firing rate of local neurons, particularly putative inhibitory neurons. The optimal smoothing filter had a width of ∼3 s, matched the hemodynamic response function of awake mice, was invariant across mice and stimulus conditions, and was similar in the cortex and hippocampus. fUSI signals also matched neural firing spatially: firing rates were as highly correlated across hemispheres as fUSI signals. Thus, blood flow measured by ultrasound bears a simple and accurate relationship to neuronal firing

Vision and locomotion shape the interactions between neuron types in mouse visual cortex

Cortical computation arises from the interaction of multiple neuronal types, including pyramidal (Pyr) cells and interneurons expressing Sst, Vip, or Pvalb. To study the circuit underlying such interactions, we imaged these four types of cells in mouse primary visual cortex (V1). Our recordings in darkness were consistent with a ‘‘disinhibitory’’ model in which locomotion activates Vip cells, thus inhibiting Sst cells and disinhibiting Pyr cells. However, the disinhibitory model failed when visual stimuli were present: locomotion increased Sst cell responses to large stimuli and Vip cell responses to small stimuli. A recurrent network model successfully predicted each cell type’s activity from the measured activity of other types. Capturing the effects of locomotion, however, required allowing it to increase feedforward synaptic weights and modulate recurrent weights. This network model summarizes interneuron interactions and suggests that locomotion may alter cortical computation by changing effective synaptic connectivity

Subcortical Source and Modulation of the Narrowband Gamma Oscillation in Mouse Visual Cortex

Primary visual cortex exhibits two types of gamma rhythm: broadband activity in the 30-90 Hz range and a narrowband oscillation seen in mice at frequencies close to 60 Hz. We investigated the sources of the narrowband gamma oscillation, the factors modulating its strength, and its relationship to broadband gamma activity. Narrowband and broadband gamma power were uncorrelated. Increasing visual contrast had opposite effects on the two rhythms: it increased broadband activity, but suppressed the narrowband oscillation. The narrowband oscillation was strongest in layer 4 and was mediated primarily by excitatory currents entrained by the synchronous, rhythmic firing of neurons in the lateral geniculate nucleus (LGN). The power and peak frequency of the narrowband gamma oscillation increased with light intensity. Silencing the cortex optogenetically did not abolish the narrowband oscillation in either LGN firing or cortical excitatory currents, suggesting that this oscillation reflects unidirectional flow of signals from thalamus to cortex