Although a complete description of neuronal circuits can only be achieved with EM, there are several reasons why other approaches must be pursued in parallel. First, the complete reconstruction of a complex circuit such as the mammalian cortical column is many years away, yet demand already exists for an approximate description of circuitry. Second, synaptic connectivity varies among animals and within one animal over time and EM cannot be applied in vivo and on a large enough scale to explore variability. Third, electron microscopy is not well suited to detect differential gene expression, an important marker of neuronal class and cell processes. This is why, in parallel with reconstructions from EM serial sections, we analyze light microscopy and electrophysiology data. Such description must necessarily be statistical, or probabilistic, because the presence of a synapse cannot be unequivocally established (in light microscopy) and because only a small subset of neurons can be probed in each experiment, meaning that data from different brains must be somehow combined.

We are assembling geometric connectivity maps using light microscopic 3D reconstructions of axonal and dendritic arbors. This approach is based on the concept of potential synapse (Stepanyants et al. 2002), a location in neuropil where an axon and a dendrite come within a certain distance so that a synapse can be formed by growing a spine or a bouton. The exact distance depends on the type of a synapse that can exist. If the dendrite is spiny, the distance is given by the spine length (~2um). Otherwise, the distance between the dendritic and axonal centroids is given by the sum of their radii. Using 3D reconstructions of neurons from different cortical layers, we calculate geometric input and output maps, Figure 5. Such maps show the number of potential synapses expected between neurons at given locations. As expected, these maps exhibit layer specificity in potential synaptic connectivity. Yet, the potential connectivity domain is rather wide, a few hundred microns, scale usually associated with the cortical column. Therefore, potential synaptic connectivity within a cortical column is close to all-to-all. In other words, any two neurons within a cortical column can make a synapse if they need to.

Figure 5. Geometric output map for a typical layer 3 pyramidal neuron from cat visual cortex calculated from 3D reconstructions of neuronal shape. Pixel color indicates the number of potential synapses expected between a given neuron and the neuron at the pixel location (Stepanyants et al. 2005).

Comparison of geometric connectivity maps with maps from photostimulation experiments. To understand how maps of potential synaptic connectivity are related to actual we collaborate with the Svoboda laboratory, who use laser scanning photostimulation to measure the spatial distribution of functional input to individual neurons in L2/3 (Shepherd et al. 2005). Photostimulation results were compared with geometrical maps obtained from quantitative morphological reconstructions of labeled neurons. With this approach we were able to test whether neuronal morphology and the overlap of dendrites and axons predicts functional circuits. It turns out that for most individual projections (e.g. between layer 4 and layer 2/3) geometry predicts functional inputs up to a single scale factor, synaptic strength per potential synapse. This factor, however, varies from projection to projection and, exceptionally within a projection.

As potential synapse is a necessary condition for an actual synapse, number of potential synapses provides an upper bound on the number of actual synapses. Geometric connectivity maps are particularly significant in view of the structural plasticity in adult neocortex: actual synapses can appear and disappear (Trachtenberg et al. 2002) while potential synapses stay put (Stepanyants et al. 2002). Therefore, an invariant description of synaptic connectivity should be done on the level of potential synapses.

Although potential synaptic connectivity provides a convenient description of neuronal circuits, activity of neurons is still determined by the currents injected at the actual synapses. To understand how potential synaptic connectivity is related to actual we combine geometric maps with multi-electrode recordings and laser-scanning photo-stimulation. Because the number of cells from which recordings can be made is limited, this approach is necessarily based on sampling.

Analysis of a large dataset of recordings has revealed that within a cortical column connectivity is highly non-uniform (Song et al. 2005). Distribution of connection strength, as measured by the average EPSP amplitude, has a heavy tail. We found that 17% of connections contribute 50% of synaptic weight. In addition, these connections are highly clustered forming a skeleton of stronger connections in the sea of weaker ones, Figure 6. This description contrasts strongly with the random or uniform connectivity assumptions made by many computational neuroscientists when analyzing network dynamics.

Figure 6. Local cortical circuits can be described as a skeleton of stronger connections (red) immersed in the sea of weaker ones (black). Strong connections are likely to influence network dynamics disproportionately (Song et al. 2005).

Section 1           Section 3