Analysis of neuronal ensemble activity reveals the pitfalls and shortcomings of rotation dynamics

Abstract

Back in 2012, Churchland and his colleagues proposed that “rotational dynamics”, uncovered through linear transformations of multidimensional neuronal data, represent a fundamental type of neuronal population processing in a variety of organisms, from the isolated leech central nervous system to the primate motor cortex. Here, we evaluated this claim using Churchland’s own data and simple simulations of neuronal responses. We observed that rotational patterns occurred in neuronal populations when (1) there was a temporal sequence in peak firing rates exhibited by individual neurons, and (2) this sequence remained consistent across different experimental conditions. Provided that such a temporal order of peak firing rates existed, rotational patterns could be easily obtained using a rather arbitrary computer simulation of neural activity; modeling of any realistic properties of motor cortical responses was not needed. Additionally, arbitrary traces, such as Lissajous curves, could be easily obtained from Churchland’s data with multiple linear regression. While these observations suggest that temporal sequences of neuronal responses could be visualized as rotations with various methods, we express doubt about Churchland et al.’s bold assessment that such rotations are related to “an unexpected yet surprisingly simple structure in the population response”, which “explains many of the confusing features of individual neural responses”. Instead, we argue that their approach provides little, if any, insight on the underlying neuronal mechanisms employed by neuronal ensembles to encode motor behaviors in any species.

Rotational dynamics versus sequence-like responses

“…Figure 2 in Churchland, Cunningham et al (2012) indeed illustrates ten neurons (selected from the data of four monkeys) whose responses are variable across conditions. Yet, we have already shown that, at population level, a consistent sequence of neuronal responses is present in Churchland's data (see Figure 2 in Lebedev, Ossadtchi et al (2019)). To examine this finding further, here we ranked the neurons in Churchland's population by how consistent the timing of their responses was across the conditions.…”

“…With this simple procedure, we found a temporal sequence of neuronal responses during the arm reaching task. This sequence persisted across 108 conditions with some variability (see Figure 2 in Lebedev, Ossadtchi et al (2019)). Based on this observation, we argued that sequence-like responses could be the cause of the rotational dynamics revealed with jPCA.…”

“…The matrix has imaginary eigenvalues, which corresponds to rotating around the center of coordinates (Garfinkel, Shevtsov et al 2017). Given that rotates, its coordinates are oscillating functions of time, and there is a temporal lag (or phase shift) between these functions, which led us to the hypothesis that similar temporal lags could be present in the neuronal population data before it has been processed with jPCA (Lebedev, Ossadtchi et al 2019). To test this hypothesis, we plotted population perievent time histograms (PETHs) for different conditions, where neurons were sorted by the time of peak activity taken from the cross-condition average PETHs.…”

“…We concluded that jPCA reveals sequence-like dynamics in neuronal population data, but we were skeptical regarding Churchland's claim that this method elucidates a fundamental mechanisms of cortical motor control. Recently, the Shenoy group published a new review on neural population dynamics (Vyas, Golub et al 2020) where they commented on our article: "While it is possible to obtain rotation-like features from non-dynamical models [e.g., sequencelike responses (Lebedev et al 2019)], such rotations are dissimilar from those observed empirically (Michaels et al 2016). Perhaps more critically, the hypothesis of sequence-like responses does not account for single-neuron responses, which are typically multiphasic and/or peak at different times for different conditions (e.g., Churchland et al 2012, figure 2).…”

“…In our previous study, we conducted an analysis (Lebedev, Ossadtchi et al 2019) of multichannel recordings from monkey motor cortex, which Churchland, Shenoy and their colleagues had made available online (https://www.dropbox.com/sh/2q3m5fqfscwf95j/AAC3WV90hHdBgz0Np4RAKJpYa?dl=0) and which they had originally used to substantiate the concept of rotational dynamics -a fundamental type of neuronal processing in many species according to their claim (Churchland, Cunningham et al 2012). In the rotational dynamics approach, multidimensional neuronal data are processed with a linear transform, called jPCA, designed to generates a set of curved trajectories, one trajectory per arm-movement condition.…”