Methodological Constraints In Cluster Analysis

The use of multiple criteria raises an interesting combinatorial issue. As illustrated in Figure 19.2, the assumption is made that all diversity of the repertoire should be found in a "hypercolumn cube" of 1 x 1 x 2 mm, which is a rough estimate of the volume of cortex required to process one point in visual space through both eyes and a complete preference set of orientation filters. The number of classes given in Figure 19.2 is based on the most recent studies performed in vitro (Toledo-Rodriguez et al. 2004). If the profiles observed for each classification type (anatomical, genomic, electrophysiological) were to be independent, the basic element of the neocortical microcircuit can be considered the cell itself and its singularity, since the number of neurons and potential categories are roughly comparable! Also, armies of postdoctoral fellows, working in vitro, might get depressed by the simple thought experiment of guessing the number of cells to be recorded before reaching statistical significance level.

Cluster analysis provides a quantitative method with which to measure in a multidimensional space how similar neurons are to one another. The group of Rafael Yuste has recently applied this approach to a population of neocortical interneurons from mouse primary visual cortex with the goal of examining how many distinct classes of interneurons exist (Dumitriu et al., submitted; Yuste 2005). The sample of interneurons included parvalbumin (PV)-positive, somatostatin (SS)-positive, and neuropeptide Y (NPY)-positive cells, as selected from transgenic animals expressing GFP under the control of these three promoters. These neurons were patched and their intrinsic electrophysiological parameters measured, as well as the time constants of the spontaneously received EPSPs and IPSPs. The neurons were also filled with biocytin and reconstructed morphologically after fixation. For each neuron, a series of ~100 different morphological parameters were measured. The morphological and physiological

1 mm

Criteria Anatomy

Electrophysiology Multiplex RT-PCR

# Classes Types 3 Subtypes 150 20 20

2 mm

1 mm

2 mm

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-100,000 cells

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Figure 19.2 Taxonomy and the hypercolumn: The volume of the cortical tissue chunk is the size of a functional hypercolumn (HubelandWiesel 1963). The number of neurons is roughly of the order of the number of classes (180,000) based on anatomical, electrophysiological, and genomic criteria (see text for the choice of parameters).

parameters were then used to generate two cluster trees: one based on the morphology and the other on the physiology. Interestingly, both trees had three major branches, which corresponded quite accurately to the three groups of PV, SS, and NPY interneurons.

From these results, it can be concluded that at least three distinct different classes of neocortical interneurons exist in mouse primary visual cortex. Further, there is a correspondence between the biochemical, morphological, and electrophysiological characteristics of the neurons within those groups, since the clusters found with the electrophysiological analysis can be used to predict the morphological clusters and they correspond to the expression of these three marker proteins.

One disadvantage of cluster analysis is that it always results in clusters and does not provide a natural cutoff in the classification, which in principle can be pursued with subsequent subdivisions until each cluster has a single individual. At the same time, the use of independent measurements with which to cluster a data set can help in distinguishing important clusters from the noise. Overall, the arguments in favor ofthe real existence of distinct classes of neocortical neurons are very compelling in the case of neocortical interneurons. There are striking correlations between the morphologies ofthe axon and dendrites, the firing patterns and spike and AHP characteristics, the EPSP and IPSPs kinetics, the synaptic dynamics, the coupling through gap junctions to neurons ofthe same class, and the expression of distinct protein markers. It is very probable, like the interneurons in the spinal cord, as demonstrated by Jessell and colleagues (Tsuchida et al. 1994), that different classes of neocortical interneurons could differentiate under the control of different promoters and play specific circuit roles. In general, if the circuit is built with specific elements, it appears absolutely essential to come to terms with this diversity in order to understand the function of the circuit.

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