Probabilistic identification of cerebellar cortical neurones across species

Abstract

Despite our fine-grain anatomical knowledge of the cerebellar cortex, electrophysiological studies of circuit information processing over the last fifty years have been hampered by the difficulty of reliably assigning signals to identified cell types. We approached this problem by assessing the spontaneous activity signatures of identified cerebellar cortical neurones. A range of statistics describing firing frequency and irregularity were then used, individually and in combination, to build Gaussian Process Classifiers (GPC) leading to a probabilistic classification of each neurone type and the computation of equi-probable decision boundaries between cell classes. Firing frequency statistics were useful for separating Purkinje cells from granular layer units, whilst firing irregularity measures proved most useful for distinguishing cells within granular layer cell classes. Considered as single statistics, we achieved classification accuracies of 72.5% and 92.7% for granular layer and molecular layer units respectively. Combining statistics to form twin-variate GPC models substantially improved classification accuracies with the combination of mean spike frequency and log-interval entropy offering classification accuracies of 92.7% and 99.2% for our molecular and granular layer models, respectively. A cross-species comparison was performed, using data drawn from anaesthetised mice and decerebrate cats, where our models offered 80% and 100% classification accuracy. We then used our models to assess non-identified data from awake monkeys and rabbits in order to highlight subsets of neurones with the greatest degree of similarity to identified cell classes. In this way, our GPC-based approach for tentatively identifying neurones from their spontaneous activity signatures, in the absence of an established ground-truth, nonetheless affords the experimenter a statistically robust means of grouping cells with properties matching known cell classes. Our approach therefore may have broad application to a variety of future cerebellar cortical investigations, particularly in awake animals where opportunities for definitive cell identification are limited.

Figure 1. Activity patterns of cerebellar cortical cells in the rat.

A shows an ISIH and spike-shapes (band pass 0.3–10 kHz) from an example Purkinje cell - note the presence of two spike-shapes, complex (top) and simple (bottom). The right panel shows a bright-field micrograph of a Purkinje cell following juxtacellular labelling with neurobiotin - note the characteristic dendritic arbor in the molecular layer (ML). B–E follow the same format for an example Golgi cell, granule cell, a regular firing mossy fibre terminal and basket/stellate cell, respectively. Although each of these granular layer units have broadly similar mean firing rates (compare the ISIHs), their intrinsic irregularities are divergent. Note that the spike-shapes shown for the Golgi cell, granule cell and basket/stellate cell are highly similar due to being recorded in the juxtasomatic configuration, whilst the spike-shape for the mossy fibre terminal is composed of an early fast and later variable negative after wave (NAW). The micrographs show a typical Golgi cell, viewed in dark-field, with dendrites extending into the ML and profuse, highly arborised axon tree in the granular layer (GL: note GL dendrites are not visible). In contrast, the much smaller granule cell shown in bright-field has a soma with three short dendrites. The micrograph in D shows a neurobiotin deposit in the upper granular layer following a juxtacellular labelling attempt with a regular firing mossy fibre unit (indicated by the arrow). Example data from a basket/stellate cell are shown in E, with a cell visible in the lower third of the molecular layer (ML) with arborisations extending in the parasagittal plane and presumed dendrites ascending in the plane of the Purkinje cell dendrites. Micrographs shown in A & B reproduced with permission from .

Figure 2. Firing frequency and firing irregularity measures for granular layer and molecular layer neurones.

Three of the most useful statistics, CV of log ISIs (LCV), mean spike frequency (MSF) and log-interval-entropy (ENT), for classifying cells into distinct classes are plotted in A–C for the granular layer cells and I–K for the molecular layer cells. Each circle represents the spike train statistic of a single neurone (n = 120 cells and 41 cells, respectively). These data were used to build Gaussian Process Classifiers (D–F and L–N, respectively) using a single statistic to infer probabilities for each neurone belonging to a class and to delineate equiprobable decision boundaries between cell classes (solid black lines). Classification accuracy for each statistic is provided above each plot. G & H show the outcome of Gaussian Process Classifiers built using a twin-variate approach for the granular layer cells and O & P show the same analysis for the molecular layer cells (note inset labelled basket/stellate cell [cat]). Probability contours are superimposed for each class (probability levels = 0.25, 0.4, 0.6, 0.7, 0.8, 0.9 & 0.95) as well as the 2-dimensional decision boundaries and a resultant increase in classification accuracy (included in top right of each panel).

Figure 3. Comparison of irregularity measures, frequency measures and spike-train length on classification accuracy.

The bar chart shown in A plots the Gaussian Process Classifier LOO-CV accuracy for our rat dataset using a range of firing irregularity statistics combined with MSF. The worst combination was MSF vs SI offering 89% classification accuracy, whilst MSF vs. ENT performed at 99.2% accuracy. B shows a similar analysis with a variety of frequency measures combined with ENT. Median and Modal ISI offered ∼93% accuracy with a marginal difference between mean instantaneous frequency and mean firing rate (98% and 99.2%, respectively). C & D show Gaussian Process Classifiers built on the granular layer dataset but with 30 ISIs or 60 ISIs, respectively. The decision boundaries for the model built on all spikes are superimposed (black lines), along with the recomputed decision boundaries (green and red lines respectively). Note that the probability contours are specific to each model. Using 30 ISIs offered a prediction accuracy of 95% whilst the model built with 60 ISIs for all cells offered the same accuracy as the all-spikes model (99.2%; c.f. Figure 2H). This shows the model can be built and applied to spike trains containing as little as 60 ISI’s without a decrease in performance. This allows a prediction in the order of a few seconds for the slowest firing neurones (granule cells). E & F show Gaussian Process classifiers built on the molecular layer dataset following the same convention as above. Note that the probability contours are specific to each model. Using 30 or 60 ISIs offered prediction accuracy of 95.1% in both cases, comparable to the all-spikes model (92.7%; c.f. Figure 2P).

Figure 4. Decision-tree algorithm performance with identified neurones across mice, rats and cats.

Following the format used by Ruigrok et al. (2011), A compares the classifications our of GPC model with those of the decision-tree algorithm. The left and middle columns show the outcomes of our GPC classification taking all cells without probability-thresholding (left) or with an arbitrarily chosen probability threshold of (p>0.7; middle column) thus some cells were classified as 'unknown' cells (c.f. the Ruigrok decision-tree outputs). The right column shows the results of our datasets when classified using the Ruigrok decision-tree. The numbers within the pies indicate the number of cells that were classified correctly, incorrectly and as 'unknown' cells (i.e. cells for which no decision is taken). In general, the decision-tree algorithm was less accurate than our GPC model, although note that neither mossy fibres nor Purkinje cells were built in to the decision-tree algorithm. B shows data from a small set of identified granule cells recorded in the anaesthetised mouse, leading to 80% classification accuracy. C shows similar data for identified granule cells (inset shows confocal reconstructions of juxtacellularly labelled granule cells) and Golgi cells recorded in the decerebrate cat, leading to 100% classification accuracy. Following the same format as in A, we compare mouse and cat data using our GPC model and the decision-tree algorithm. Generally lower levels of accuracy were achieved by the decision-tree algorithm.

Figure 5. Putative classification of neurones in awake monkeys and rabbits.

A, C & E re-plot our GPC decision boundaries and probability contours, in each case with a selection of granular layer units (blue circles), from the ventral parafloculus of awake monkeys (A), alongside Purkinje cells in the nodulus uvula of awake monkeys (B) and alongside Purkinje cells in the lobule HVI of awake rabbits (E). Besides each plot, the pie charts (B, D, F) illustrate the classification decisions arising from the un-thresholded GPC (left column), the p>0.7 thresholded GPC (middle) and for comparison, the decision-tree algorithm (right) for both the granular layer units and where appropriate, the Purkinje cells (i.e. decision-tree algorithm cannot deal with Purkinje cells). For the granular layer, all classifications remain putative and in this setting the GPC highlights cells with, for example, the most Golgi-like firing patterns. In comparison, the decision-tree algorithm in all cases suggests that a subset of the granular layer neurones are molecular layer cells (c.f. Figure 5B, 5D & 5F).