Reading the Book of Memory: Sparse Sampling versus Dense Mapping of ConnectomesAdvances in Techniques for Measuring ConnectivityPairwise Models of ConnectivityC. elegansAn Invertebrate RetinaThe Vertebrate RetinaFunctional Properties as Cell LabelsThe Synaptic Chain Model of HVCOne-Dimensional Directed Graph LayoutStrengths of ConnectionIs Inhibition Less Specific than Excitation?Cognitive Maps and Hippocampal ConnectivityModel SelectionDiscussionExperimental ProceduresHidden Variables and Dependencies between ConnectionsAcknowledgmentsReferencesNeuronPerspectiveReading the Book of Memory: Sparse Samplingversus Dense Mapping of ConnectomesH. Sebastian Seung1,*1Howard Hughes Medical Institute, Brain and Cognitive Sciences Department, Massachusetts Institute of Technology, Cambridge,MA 02139, USA*Correspondence: [email protected] 10.1016/j.neuron.2009.03.020Many theories of neural networks assume rules of connection between pairs of neurons that are basedon their cell types or functional properties. It is finally becoming feasible to test such pairwise models ofconnectivity, due to emerging advances in neuroanatomical techniques. One method will be to measurethe functional properties of connected pairs of neurons, sparsely sampling pairs from many specimens.Another method will be to find a ‘‘connectome,’’ a dense map of all connections in a single specimen, andinfer functional propertie s of neurons through computational analysis. For the latter method, the mostexciting prospect wo uld be to decode the memories that are hypothesized to be stored in connectomes.In constructing a neural network model of brain function, it isstandard to start from a mathematical description of spikingand synaptic transmission, make assumptions about howneurons are connected by synapses and then numerically simu-late or analytically derive the activity patterns of the network.Success is declared if the model’s activity patterns reproducethose measured by neurophysiologists.Initially, the model neurons used in such networks were highlysimplified to the point of being naive. But they have becomemore sophisticated over the years, incorporating findings aboutintrinsic and synaptic currents in neurons. In contrast, manyassumptions about neural connectivity have been used by theo-rists for decades without revision, because they have been diffi-cult to test empirically.It has been popular to assume that the connectivity betweenany pair of neurons is a function of variables associated withthe neurons. These variables, which I dub cell labels, are attri-butes of a neuron that can be measured without determiningits connectivity directly. The cell label can include what neuro-anatomists call cell type, which is defined classically by shapeand location (Bota et al., 2003; Masland, 2004). In the retina,photoreceptors make connections onto horizontal cells, a ruleof connectivity based on cell type (Masland, 2001b). A cell labelcould also include some property that is determined by a neuro-physiologist through activity measurements. For example, somemodels of the primary visual cortex assume that excitatoryneurons with similar preferred orientations are connected (Som-ers et al., 1995; Ben-Yishai et al., 1995), so that the cell label ispreferred orientation.For testing such a pairwise model of neural connectivity, twostandard neuroanatomical methods are available. Sparse recon-struction relies on light microscopy and sparse labeling ofneurons, and dense reconstruction relies on electron micros-copy and dense labeling. Both methods have been problematic.Axons can be less than 100 nm in diameter (Shepherd andHarris, 1998), and dendritic spine necks can be even narrower(Fiala and Harris, 1999). Since 100 nm is less than the wavelengthof visible light, these structures cannot be resolved with a lightmicroscope if they are entangled in a densely stained neuropil(but see Hell [2007] for exceptions to this rule). However, onecan see a single neuron stained with dye, as long as thesurrounding neurons are unstained and hence remain invisible.This trick was employed by Golgi, who invented a stain thatmarked a sparse subset of neurons in the brain.Cajal used Golgi’s stain to reconstruct the branching patternsof neurons. If two neurons made contact with each other, Cajalinferred that they were connected. However, he could not rigor-ously prove this inference, because he could not see synapses.Contact suggests that a connection exists, but a synapse mustbe identified to prove it. In short, connection = contact +synapse.In the 1970s, neuroanatomists began to use electron micros-copy for dense reconstruction of neurons. In principle, thisimaging method has enough spatial resolution to see all of theaxons and dendrites in a densely labeled neuropil. It is alsopossible to identify synapses through telltale markers such asvesicles. Most famously, electron microscopy was used tomap every connection in the nervous system of the nematodeC. elegans (White et al., 1986). For every synapse between twoneurites, the presynaptic and postsynaptic neurons were identi-fied by tracing the neurites back to their parent cell bodies.Although the C. elegans nervous system is quite small (seehttp://wormatlas.org for about 300 neurons and 7000 synapses),mapping its connections consumed over a decade of effort.White et al. (1986) called the fruits of their labors a ‘‘reconstructednervous system.’’ Others dubbed it a ‘‘wiring diagram,’’comparing the branches of neurons with the wires of an elec-tronic device. Today we use the term connectome to refer tothe complete map of all connections in a brain or piece of brain(Sporns et al., 2005; Lichtman and Sanes, 2008). Because of theHerculean labor involved, dense reconstruction has not beenextended to more complex connectomes than that of C. elegans.To diagnose the problems succinctly, sparse reconstructionhas yielded contacts rather than connections, while densereconstruction has been too laborious to be practical. Fortu-nately, these deficiencies are being rectified by emergingNeuron 62, April 16, 2009 ª2009 Elsevier Inc. 17technical advances. The advent of genetic methods of fluores-cent labeling has improved the confidence with which sparsereconstruction can identify synaptically coupled pairs of neurons(Smith, 2007; Luo et al., 2008). And the automation of sectioning,electron microscopy, and image analysis is making the finding ofconnectomes more efficient (Briggman and Denk,