Influence of data sampling methods on the representation of neural spiking activity in vivo

In vivo single-unit recordings distinguish the basal spiking properties of neurons in different experimental settings and disease states. Here, we examined over 300 spike trains recorded from Purkinje cells and cerebellar nuclei neurons to test whether data sampling approaches influence the extraction of rich descriptors of firing properties. Our analyses included neurons recorded in awake and anesthetized control mice, as well as disease models of ataxia, dystonia, and tremor. We find that recording duration circumscribes overall representations of firing rate and pattern. Notably, shorter recording durations skew estimates for global firing rate variability towards lower values. We also find that only some populations of neurons in the same mouse are more similar to each other than to neurons recorded in different mice. These data reveal that recording duration and approach are primary considerations when interpreting task-independent single-neuron firing properties. If not accounted for, group differences may be concealed or exaggerated.

Brain-Computer Interface

Launched in 2017 to widespread publicity due to the involvement of tech magnate and outspoken futurist Elon Musk, Neuralink Corp. aims to develop an advanced brain-computer interface (BCI) platform capable of assisting in the treatment of serious neurological conditions with longer-term goals of approaching transhumanism through nonmedical human enhancement to enable human-machine “symbiosis with artificial intelligence.” The first published description of a complete prototype Neuralink system, detailed by Muskin the company's only white paper to date, describes a closed-loop, invasive BCI architecture with an unprecedented magnitude of addressable electrodes. Invasive BCI systems require surgical implantation to allow for directly targeted capture and/or stimulation of neural spiking activity in functionally associated clusters of neurons beneath the surface of the cortex.

Efficient spline regression for neural spiking data

Point process generalized linear models (GLMs) provide a powerful tool for characterizing the coding properties of neural populations. Spline basis functions are often used in point process GLMs, when the relationship between the spiking and driving signals are nonlinear, but common choices for the structure of these spline bases often lead to loss of statistical power and numerical instability when the signals that influence spiking are bounded above or below. In particular, history dependent spike train models often suffer these issues at times immediately following a previous spike. This can make inferences related to refractoriness and bursting activity more challenging. Here, we propose a modified set of spline basis functions that assumes a flat derivative at the endpoints and show that this limits the uncertainty and numerical issues associated with cardinal splines. We illustrate the application of this modified basis to the problem of simultaneously estimating the place field and history dependent properties of a set of neurons from the CA1 region of rat hippocampus, and compare it with the other commonly used basis functions. We have made code available in MATLAB to implement spike train regression using these modified basis functions.

The role of rebound spikes in the maintenance of self-sustained neural spiking activity

In general, the mechanisms that maintain the activity of neural systems after a triggering stimulus has been removed are not well understood. Different mechanisms involving at the cellular and network levels have been proposed. In this work, based on analysis of a computational model of a spiking neural network, it is proposed that the spike that occurs after a neuron is inhibited (the rebound spike) can be used to sustain the activity in a recurrent inhibitory neural circuit after the stimulation has been removed. It is shown that, in order to sustain the activity, the neurons participating in the recurrent circuit should fire at low frequencies. It is also shown that the occurrence of a rebound spike depends on a combination of factors including synaptic weights, synaptic conductances and the neuron state. We point out that the model developed here is minimalist and does not aim at empirical accuracy. Its purpose is to raise and discuss theoretical issues that could contribute to the understanding of neural mechanisms underlying self-sustained neural activity.

Salience by Competitive and Recurrent Interactions: Bridging Neural Spiking and Computation

Decisions about where to move the eyes depend on neurons in Frontal Eye Field (FEF). Movement neurons in FEF accumulate salience evidence derived from FEF visual neurons to select the location of a saccade target among distractors. How visual neurons achieve this salience representation is unknown. We present a neuro-computational model of target selection called Salience by Competitive and Recurrent Interactions (SCRI), based on the Competitive Interaction model of attentional selection and decision making (Smith & Sewell, 2013). SCRI selects targets by synthesizing localization and identification information to yield a dynamically evolving representation of salience across the visual field. SCRI accounts for neural spiking of individual FEF visual neurons, explaining idiosyncratic differences in neural dynamics with specific parameters. Many visual neurons resolve the competition between search items through feedforward inhibition between signals representing different search items, some also require lateral inhibition, and many act as recurrent gates to modulate the incoming flow of information about stimulus identity. SCRI was tested further by using simulated spiking representations of visual salience as input to the Gated Accumulator Model of FEF movement neurons (Purcell et al., 2010; Purcell, Schall, Logan, & Palmeri, 2012). Predicted saccade response times fit those observed for search arrays of different set size and different target-distractor similarity, and accumulator trajectories replicated movement neuron discharge rates. These findings offer new insights into visual decision making through converging neuro-computational constraints and provide a novel computational account of the diversity of FEF visual neurons.

Embedding optimization reveals long-lasting history dependence in neural spiking activity

Information processing can leave distinct footprints on the statistics of neural spiking. For example, efficient coding minimizes the statistical dependencies on the spiking history, while temporal integration of information may require the maintenance of information over different timescales. To investigate these footprints, we developed a novel approach to quantify history dependence within the spiking of a single neuron, using the mutual information between the entire past and current spiking. This measure captures how much past information is necessary to predict current spiking. In contrast, classical time-lagged measures of temporal dependence like the autocorrelation capture how long—potentially redundant—past information can still be read out. Strikingly, we find for model neurons that our method disentangles the strength and timescale of history dependence, whereas the two are mixed in classical approaches. When applying the method to experimental data, which are necessarily of limited size, a reliable estimation of mutual information is only possible for a coarse temporal binning of past spiking, a so-called past embedding. To still account for the vastly different spiking statistics and potentially long history dependence of living neurons, we developed an embedding-optimization approach that does not only vary the number and size, but also an exponential stretching of past bins. For extra-cellular spike recordings, we found that the strength and timescale of history dependence indeed can vary independently across experimental preparations. While hippocampus indicated strong and long history dependence, in visual cortex it was weak and short, while in vitro the history dependence was strong but short. This work enables an information-theoretic characterization of history dependence in recorded spike trains, which captures a footprint of information processing that is beyond time-lagged measures of temporal dependence. To facilitate the application of the method, we provide practical guidelines and a toolbox.

Quantifying Dynamical High-Order Interdependencies From the O-Information: An Application to Neural Spiking Dynamics

We address the problem of efficiently and informatively quantifying how multiplets of variables carry information about the future of the dynamical system they belong to. In particular we want to identify groups of variables carrying redundant or synergistic information, and track how the size and the composition of these multiplets changes as the collective behavior of the system evolves. In order to afford a parsimonious expansion of shared information, and at the same time control for lagged interactions and common effect, we develop a dynamical, conditioned version of the O-information, a framework recently proposed to quantify high-order interdependencies via multivariate extension of the mutual information. The dynamic O-information, here introduced, allows to separate multiplets of variables which influence synergistically the future of the system from redundant multiplets. We apply this framework to a dataset of spiking neurons from a monkey performing a perceptual discrimination task. The method identifies synergistic multiplets that include neurons previously categorized as containing little relevant information individually.

Embedding optimization reveals long-lasting history dependence in neural spiking activity

Information processing can leave distinct footprints on the statistical history dependence in single neuron spiking. Statistical history dependence can be quantified using information theory, but its estimation from experimental recordings is only possible for a reduced representation of past spiking, a so called past embedding. Here, we present a novel embedding-optimization approach that optimizes temporal binning of past spiking to capture most history dependence, while a reliable estimation is ensured by regularization. The approach does not only quantify non-linear and higher-order dependencies, but also provides an estimate of the temporal depth that history dependence reaches into the past. We benchmarked the approach on simulated spike recordings of a leaky integrate-and-fire neuron with long lasting spike-frequency-adaptation, where it accurately estimated history dependence over hundreds of milliseconds. In a diversity of extra-cellular spike recordings, including highly parallel recordings using a Neuropixel probe, we found some neurons with surprisingly strong history dependence, which could last up to seconds. Both aspects, the magnitude and the temporal depth of history dependence, showed interesting differences between recorded systems, which points at systematic differences in information processing between these systems. We provide practical guidelines in this paper and a toolbox for Python3 at https://github.com/Priesemann-Group/hdestimator for readers interested in applying the method to their data.Author summaryEven with exciting advances in recording techniques of neural spiking activity, experiments only provide a comparably short glimpse into the activity of only a tiny subset of all neurons. How can we learn from these experiments about the organization of information processing in the brain? To that end, we exploit that different properties of information processing leave distinct footprints on the firing statistics of individual spiking neurons. In our work, we focus on a particular statistical footprint: How much does a single neuron’s spiking depend on its own preceding activity, which we call history dependence. By quantifying history dependence in neural spike recordings, one can, in turn, infer some of the properties of information processing. Because recording lengths are limited in practice, a direct estimation of history dependence from experiments is challenging. The embedding optimization approach that we present in this paper aims at extracting a maximum of history dependence within the limits set by a reliable estimation. The approach is highly adaptive and thereby enables a meaningful comparison of history dependence between neurons with vastly different spiking statistics, which we exemplify on a diversity of spike recordings. In conjunction with recent, highly parallel spike recording techniques, the approach could yield valuable insights on how hierarchical processing is organized in the brain.