Eran Stark

Dependence of neuronal correlations on filter characteristics and marginal spike train statistics

Correlated neural activity has been observed at various signal levels (e.g., spike count, membrane potential, local field potential, EEG, fMRI BOLD). Most of these signals can be considered as superpositions of spike trains filtered by components of the neural system (synapses, membranes) and the measurement process. It is largely unknown how the spike train correlation structure is altered by this filtering and what the consequences for the dynamics of the system and for the interpretation of measured correlations are. In this study, we focus on linearly filtered spike trains and particularly consider correlations caused by overlapping presynaptic neuron populations. We demonstrate that correlation functions and statistical second-order measures like the variance, the covariance, and the correlation coefficient generally exhibit a complex dependence on the filter properties and the statistics of the presynaptic spike trains. We point out that both contributions can play a significant role in modulating the interaction strength between neurons or neuron populations. In many applications, the coherence allows a filter-independent quantification of correlated activity. In different network models, we discuss the estimation of network connectivity from the high-frequency coherence of simultaneous intracellular recordings of pairs of neurons.

Spike sorting : Bayesian clustering of non-stationary data

Spike sorting involves clustering spikes recorded by a micro-electrode according to the source neurons. It is a complicated task, which requires much human labor, in part due to the non-stationary nature of the data. We propose to automate the clustering process in a Bayesian framework, with the source neurons modeled as a non-stationary mixture-of-Gaussians. At a first search stage, the data are divided into short time frames, and candidate descriptions of the data as mixtures-of-Gaussians are computed for each frame separately. At a second stage, transition probabilities between candidate mixtures are computed, and a globally optimal clustering solution is found as the maximum-a-posteriori solution of the resulting probabilistic model. The transition probabilities are computed using local stationarity assumptions, and are based on a Gaussian version of the Jensen-Shannon divergence. We employ synthetically generated spike data to illustrate the method and show that it outperforms other spike sorting methods in a non-stationary scenario. We then use real spike data and find high agreement of the method with expert human sorters in two modes of operation: a fully unsupervised and a semi-supervised mode. Thus, this method differs from other methods in two aspects: its ability to account for non-stationary data, and its close to human performance.

Distinct movement parameters are represented by different neurons in the motor cortex

Recent studies suggested that a single motor cortical neuron typically encodes multiple movement parameters, but parameters often display strong temporal interdependencies. To address this issue, we recorded single‐unit activity while macaque monkeys made continuous movements and employed an analysis that explicitly considered temporal correlations between several kinematic parameters; hand position, velocity, and acceleration. We found that while the activity of almost all motor cortical neurons was modulated during movement, most neurons were related only to a single dominant parameter. The activity of different neurons covaried with different parameters with similar strength, but neurons related to velocity were far more common than neurons related to any other parameter. These results were obtained for neurons recorded in the primary motor (M1) and dorsal premotor (PMd) cortices. Although neural activity tended to precede movement and PMd activity tended to precede M1 activity, time lags were widely dispersed. Shoulder and elbow muscles had the same properties as neurons, but their activity strictly preceded movement. These results demonstrate single neuron specificity and heterogeneity within a population of neurons with respect to movement parameters and time lags. Our results suggest that distinct subsets of motor cortical neurons are involved in computations related to distinct movement parameters.

Parabolic movement primitives and cortical states: merging optimality with geometric invariance

Previous studies have suggested that several types of rules govern the generation of complex arm movements. One class of rules consists of optimizing an objective function (e.g., maximizing motion smoothness). Another class consists of geometric and kinematic constraints, for instance the coupling between speed and curvature during drawing movements as expressed by the two-thirds power law. It has also been suggested that complex movements are composed of simpler elements or primitives. However, the ability to unify the different rules has remained an open problem. We address this issue by identifying movement paths whose generation according to the two-thirds power law yields maximally smooth trajectories. Using equi-affine differential geometry we derive a mathematical condition which these paths must obey. Among all possible solutions only parabolic paths minimize hand jerk, obey the two-thirds power law and are invariant under equi-affine transformations (which preserve the fit to the two-thirds power law). Affine transformations can be used to generate any parabolic stroke from an arbitrary parabolic template, and a few parabolic strokes may be concatenated to compactly form a complex path. To test the possibility that parabolic elements are used to generate planar movements, we analyze monkeys’ scribbling trajectories. Practiced scribbles are well approximated by long parabolic strokes. Of the motor cortical neurons recorded during scribbling more were related to equi-affine than to Euclidean speed. Unsupervised segmentation of simulta- neously recorded multiple neuron activity yields states related to distinct parabolic elements. We thus suggest that the cortical representation of movements is state-dependent and that parabolic elements are building blocks used by the motor system to generate complex movements.

Applying resampling methods to neurophysiological data.

Standard statistical techniques do not always provide answers to complex physiological questions because often there are no parametric or non-parametric distributions on which significance can be estimated. Resampling methods provide a battery of tests that can be used in such circumstances. In the past few years these methods have been explored theoretically and are now employed frequently. In this paper we describe a unified framework for the use of such methods in the context of neurophysiological data analysis. We construct specific tests for placing confidence limits on estimates of mutual information and on parameters of circular data, and we present procedures for testing hypotheses on circular and on partitioned data. These tests are explained in detail and illustrated with real data from experiments with behaving monkeys.

Motor cortical activity related to movement kinematics exhibits local spatial organization

While it is generally accepted that multiple neurons cooperate to generate movement, the precise mechanisms are largely unknown. One way to generate a robust local control signal is for nearby neurons to share similar properties. To study this possibility, we recorded neural activity from the macaque motor cortex during two drawing tasks: free scribbling, and tracing given paths. We analyzed neural activity in relation to three kinematic parameters - position, velocity, and acceleration - while explicitly considering temporal correlations between them. Single-unit (SU) activity was typically related to one parameter, most often velocity, and tended to precede movement. Different SUs encoded different parameters, but nearby units tended to prefer the same parameter. Moreover, while SUs covered a wide range of positions, velocity directions, and acceleration directions, SUs recorded by the same electrode tended to prefer similar values of the same parameter. Nevertheless, some nearby units exhibited marked differences. Multi-unit activity (MUA), estimating the spiking activity of many neurons around the recording electrode, also tended to be related to one parameter and precede movement. However, overall correlations between MUA and movement were more than twice as strong as SU correlations. Finally, SUs and MUAs recorded by the same electrode tended to share similar properties. These two lines of evidence converge to suggest that activity of motor cortex neurons within approximately 200 micrometers is accumulated in a manner useful for representing a single parameter. However, even within a small region there are also neurons related to other parameters, potentially facilitating coordination between distinct parameters.

Spike-centered jitter can mistake temporal structure

Jitter-type spike resampling methods are routinely applied in neurophysiology for detecting temporal structure in spike trains (point processes). Several variations have been proposed. The concern has been raised, based on numerical experiments involving Poisson spike processes, that such procedures can be conservative. We study the issue and find it can be resolved by reemphasizing the distinction between spike-centered (basic) jitter and interval jitter. Focusing on spiking processes with no temporal structure, interval jitter generates an exact hypothesis test, guaranteeing valid conclusions. In contrast, such a guarantee is not available for spike-centered jitter. We construct explicit examples in which spike-centered jitter hallucinates temporal structure, in the sense of exaggerated false-positive rates. Finally, we illustrate numerically that Poisson approximations to jitter computations, while computationally efficient, can also result in inaccurate hypothesis tests. We highlight the value of classical statistical frameworks for guiding the design and interpretation of spike resampling methods.