Fixing the location and dimensions of functional neocortical columns

Abstract

The quest to understand the way in which neurons interconnect to form circuits that function as a unit began when Ramon y Cajal concluded that axo-dendritic apposition were too conspicuous to be incidental and proposed that two neurons must be communicating through these points of contact (see Shepherd and Erulkar, 1997, Trends Neurosci., 20, 385–392). Lorente de Nó was probably the first to predict that a defined group of vertically displaced neurons in the neocortex could form functional units (Lorente de Nó, 1938, Physiology of the Nervous System, 20, OUP: 291–330) for which Mountcastle found experimental evidence (see Mountcastle, 1997, Brain, 120, 701–722) and which was ultimately demonstrated by Hubel and Wiesel in their elegant discovery of the orientation selective columns (Hubel and Wiesel, 1959, J. Physiol., 148, 574–591). Until today, however, it is still not clear what shapes functional columns. Anatomical units, as in the barrel cortex, would make it easier to explain, but the neocortex is largely a continuous slab of closely packed neurons from which multiple modules emerge that can overlap partially or even completely on the same anatomical space. Are the columns in fixed anatomical locations or are they dynamically assigned and what anatomical and physiological properties are operating to shape their dimensions? A recent study explores how the geometry of single neurons places structural constraints on the dimensions of columns in the visual cortex (Stepanyants et al., 2008, Cereb Cortex, 18, 13–24).

A recent article (Stepanyants et al., 2008) tries to explain the structural basis to explain the boundaries of neocortical columns (Lorente de Nó, 1938; Mountcastle 1997; Hubel and Wiesel, 1959) (Fig. 1). Synaptic connections can potentially form at any locations where axonal and dendritic segments come into apposition. All such close contacts together confer a maximal structural potential for functional circuits. Functional circuits correspond well with geometric constraints, but also display a wider range suggestive of a vast potential to configure functional circuits using plasticity mechanisms (Shepherd et al., 2005). Different models have been developed to systematically study structural connectivity (Uttley, 1956; Liley and Wright, 1994; Braitenberg and Schuz, 1998; Stepanyants et al., 2002; Kalisman et al., 2003). These studies assume that neurons cannot purposefully target their axons towards specific neurons which yields a unimodal distribution of the number of synapses per connection. Early on, such studies suggested that neurons form only one structural contact and very rarely many which lead to the notion of an ultra-weak highly distributed influence of each neuron on its neighbors (Braitenberg and Schuz, 1998).

Figure 1. Vertical chains of neurons were proposed by Lorente de Nó for form modular units [reproduced with permission from Oxford University Press from Lorente de Nó F, (1938) in Physiology of the nervous system. Fulton JF (ed) Oxford University Press, New York, 291–330].

“The hypothesis that such a vertically linked group of cells is the elementary unit for cortical function is not new. Such a conclusion was reached by Lorente de Nó from his extensive studies on synaptic linkages of cortical neurons.” Mountcastle (1997).

The first direct evidence that the actual emergent functional circuitry is not random came from data revealing selective innervation of domains and specific types of neurons (see Thomson and Morris, 2002). A second line of evidence for the pyramidal network comes from data revealing a bimodal distribution of the number of synapses deployed in connections with most neurons not being connected and the few that are connected, are connected with many synapses (range of 3–8, average around 5, Deuchars et al., 1994; Markram et al., 1997) which also predicts a sparse but much more powerful potential effect of a single neuron on the circuit than previously assumed. This bimodal functional connectivity is not because the single- and few-synapse connections are missed in experiments since electron microscopy has revealed the absence of synapses in physiologically unconnected neurons (Markram et al., 1997). The third line of evidence came from the finding that reciprocal connectivity is about three times higher than the unidirectional connection probability—a form of “nuclear recurrence or hyper-reciprocity” (Markram, 1997). How can one explain the discrepancy between a random structural and a non-random functional connectivity?

Hellwig (2000) began to systematically separate 3D neurons in 3D space and examine how structural connectivity changed with relative displacement. Examining pyramidal neurons, he found the highest structural connectivity when the somata of neurons were very close to each other with a tapering off of the connection probability to zero within the dimensions of a cortical column—not surprising since this more or less encompasses the dimensions of the highest density of overlap in the local arborizations of the axons and dendrites of these pyramidal neurons. Kalisman et al. (2003) developed a template approach, which uses the mean description of the arbors from many neurons to compute connection properties for a class of neurons. They generated contours of connection probabilities around the soma which, as in Hellwig’s study, were constrained to within the dimensions of a cortical column. This analysis, as the one by Stepanyants et al. (2002), predicted much higher connectivity in the column than earlier estimations. The template analysis led Kalisman et al. to suggest that the characteristic geometry of specific types of neurons could confer a large degree of invariance in connectivity across brain regions and species (Kalisman et al., 2003), which is also suggested by Stepanyants et al. (2008).

In all these studies, connectivity was examined between neurons from different experiments and, therefore, was only predictive of the actual structural principles of a given circuit. In the first combined anatomical and physiological study, Kalisman et al. (2005) discovered that the axon of virtually all the neurons in the same experiment came into close apposition with a dendrite of all other neurons regardless of whether the neurons were physiologically connected or not. This provided the first direct experimental proof for random structural connectivity and revealed the tabula rasa nature of the pyramidal network. The structural connectivity revealed experimentally is, however, greater than predicted by the theoretical models and 3D separation of neurons probably because of increased accuracy of the confocal reconstructions and direct, rather than computed, contact determination.

The Kalisman et al. study not only demonstrated a nearly all-to-all connection probability, but also a higher number of axo-dendritic appositions onto each neuron than previous predictions. This high structural connectivity provides the basis for multi-synaptic contacts found in most physiologically connected pairs of pyramidal neurons and, hence, explains the discrepancy between the random structural and nonrandom functional connectivity; when two pyramidal neurons “chose” to connect, they can switch on many contacts because multiple axonal and dendritic segments are already in apposition. A bimodal distribution of the number of synapses per connection therefore arises when a relatively small fraction of neurons interconnect using multiple synapses. An ordered functional circuitry can, therefore, emerge from the tabula rasa structural connectivity by switching connections on and off according to specific neuron-neuron interaction principles.

The Kalisman et al. study also showed that the connection statistics of axo-dendritic appositions were the same for connected and unconnected neurons and the key difference was simply the presence of boutons at the appositions, providing the first prediction of axonal (bouton) plasticity that could potentially reconfigure circuits without the axon having to grow towards the dendrite (Fig. 2).

Figure 2. The image shows two confocally reconstructed neurons overlaid on the continuous sheet of other pyramidal neurons in the rat somatosensory cortex.

The upper right image shows an axon passing by a dendrite without a bouton at the axo-dendritic apposition and, hence, does not form a synaptic connection onto the neurons, which is verified by paired recordings. The lower right image shows a bouton present at the axo-dendritic apposition which does form a functional synapses as verified by paired recordings. [Reproduced from Kalisman et al. (2003)Proc. Natl. Acad. Sci. U.S.A. 102, 880–885, copyright 2005 by the National Academy of Sciences.]

The proposed axo-dendritic plasticity complements a growing body of evidence for dendro∕spine plasticity (Lendvai et al., 2000; Trachtenberg et al., 2002; Holtmatt et al., 2005; see also Harms and Dunaevsky, 2007), both of which suggest that the wiring diagram of the circuit may also change (elimination of old and forming of new synapses). Dendro-spine plasticity may, however, also underly normal synaptic plasticity and even experimental evidence for changes in functional circuits could still be due to synaptic plasticity. The first direct experimental demonstration of circuit remodeling was obtained in the neocortex by recordings from multiple neurons in small clusters before and after stimulation (Le Be and Markram, 2006). This phenomenon was termed microcircuit plasticity and was observable in as little as four and pronounced in twelve hours. This form of plasticity, which would necessarily also require the forming and dissolving of boutons between structurally and functionally connected neurons, respectively, seems to follow a Darwinian-like process with a burst of excess synaptic connections followed by an elimination of the weaker ones. Although microcircuit plasticity was found in the young animal, this phenomenon does require an already developed circuitry where the axonal and dendritic arbors would need to be in readied apposition to allow rapid remodeling.

The Stepanyants et al. (2008) study is focused on the high connectivity tapering from the soma down toward zero within the dimensions of a column which is certainly a major factor shaping columns and provide a detailed description of the structural constraints that could underlie the invariance of the circuitry. There are, however, many other factors that are also likely to be very important in shaping functional neocortical columns such as the degree of stereotypy of neurons, mini-columnar arrangement (vertical alignment, which is more sloppy in rodents), nuclear reciprocity, microcircuit plasticity, and synaptic plasticity which could all favor clustered activity. Thomson has also found that pyramidal neurons tend to place their synapses higher up on the apical dendrites as they move apart (see Thomson and Bannister, 2003), which could even bring single neuron computation into the game. Top down control of dendritic tuft processing and interneuron tuft control by Martinotti cells are likely to shape an intense competition between pyramidal neurons to become the center of a functional column since there may not, in fact, be a fixed anatomical location for functional columns. Stepanyants et al. (2008) report very low connectivity onto interneurons which is not consistent with experimental findings.

Even with all these anatomical and functional facilitators of clearly demarcated functional columns, the continuous sheet of neurons so closely packed would make anatomically fixed functional columns very unlikely. What is critically required is punctuated input. In highly dedicated areas such as the barrel cortex, punctuating takes on an extreme anatomical form, but the computational power of the neocortex most likely arises from the generic capability to dynamically assign functional columns by punctuating the input across the neocortex. While punctuating would be hardwired to some degree in the thalamic bottom-up, associative top-down, and hemispheric and cortical horizontal input pathways, there may be considerable room for dynamic assignment of the anatomical center, and perhaps even the function of functional neocortical columns.

The prediction is simple—if one could inject punctuated stimulation at any point on the neocortex, a functional column would emerge with a diameter approximately that of the average dimensions of the overlapping basal axonal and dendritic arbors of the neurons at the center of the stimulation, and the dimensions of the column in each layer depends on the specific arborizations of the axons and dendrites in the respective layer and the function of the column would be determined by the nature of the input. The functional columns may, therefore, be dynamically fixed in anatomical locations and functionally assigned within the constraints imposed through the macro-anatomy of the brain and the functions being assigned to other areas. Such a relativistic theory of functional neocortical columns could explain the growing anatomical number of overlapping feature selective modules found in brain imaging as well as the emergent macroscopic organization of functional maps.