@article {1236, title = {Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors.}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {106}, year = {2009}, month = {2009 Jul 28}, pages = {12536-41}, abstract = {

The shapes of dendritic arbors are fascinating and important, yet the principles underlying these complex and diverse structures remain unclear. Here, we analyzed basal dendritic arbors of 2,171 pyramidal neurons sampled from mammalian brains and discovered 3 statistical properties: the dendritic arbor size scales with the total dendritic length, the spatial correlation of dendritic branches within an arbor has a universal functional form, and small parts of an arbor are self-similar. We proposed that these properties result from maximizing the repertoire of possible connectivity patterns between dendrites and surrounding axons while keeping the cost of dendrites low. We solved this optimization problem by drawing an analogy with maximization of the entropy for a given energy in statistical physics. The solution is consistent with the above observations and predicts scaling relations that can be tested experimentally. In addition, our theory explains why dendritic branches of pyramidal cells are distributed more sparsely than those of Purkinje cells. Our results represent a step toward a unifying view of the relationship between neuronal morphology and function.

}, keywords = {Action Potentials, Algorithms, Animals, Axons, Dendrites, Haplorhini, Models, Neural Pathways, Neurological, Purkinje Cells, Pyramidal Cells, Rats, Synapses}, issn = {1091-6490}, doi = {10.1371/journal.pcbi.1001066}, author = {Wen, Quan and Stepanyants, Armen and Elston, Guy N and Grosberg, Alexander Y and Chklovskii, Dmitri B} } @article {1248, title = {Local potential connectivity in cat primary visual cortex.}, journal = {Cerebral Cortex}, volume = {18}, year = {2008}, month = {2008 Jan}, pages = {13-28}, abstract = {

Time invariant description of synaptic connectivity in cortical circuits may be precluded by the ongoing growth and retraction of dendritic spines accompanied by the formation and elimination of synapses. On the other hand, the spatial arrangement of axonal and dendritic branches appears stable. This suggests that an invariant description of connectivity can be cast in terms of potential synapses, which are locations in the neuropil where an axon branch of one neuron is proximal to a dendritic branch of another neuron. In this paper, we attempt to reconstruct the potential connectivity in local cortical circuits of the cat primary visual cortex (V1). Based on multiple single-neuron reconstructions of axonal and dendritic arbors in 3 dimensions, we evaluate the expected number of potential synapses and the probability of potential connectivity among excitatory (pyramidal and spiny stellate) neurons and inhibitory basket cells. The results provide a quantitative description of structural organization of local cortical circuits. For excitatory neurons from different cortical layers, we compute local domains, which contain their potentially pre- and postsynaptic excitatory partners. These domains have columnar shapes with laminar specific radii and are roughly of the size of the ocular dominance column. Therefore, connections between most excitatory neurons in the ocular dominance column can be implemented by local synaptogenesis. Structural connectivity involving inhibitory basket cells is generally weaker than excitatory connectivity. Here, only nearby neurons are capable of establishing more than one potential synapse, implying that within the ocular dominance column these connections have more limited potential for circuit remodeling.

}, keywords = {Animals, Cats, Cells, Cultured, Nerve Net, Neural Pathways, Synapses, Visual Cortex}, issn = {1460-2199}, doi = {10.1093/cercor/bhm027}, author = {Stepanyants, Armen and Hirsch, Judith A and Martinez, Luis M and Kisv{\'a}rday, Zolt{\'a}n F and Ferecsk{\'o}, Alex S and Chklovskii, Dmitri B} } @article {1250, title = {Geometric and functional organization of cortical circuits.}, journal = {Nature Neuroscience}, volume = {8}, year = {2005}, month = {2005 Jun}, pages = {782-90}, abstract = {

Can neuronal morphology predict functional synaptic circuits? In the rat barrel cortex, {\textquoteright}barrels{\textquoteright} and {\textquoteright}septa{\textquoteright} delineate an orderly matrix of cortical columns. Using quantitative laser scanning photostimulation we measured the strength of excitatory projections from layer 4 (L4) and L5A to L2/3 pyramidal cells in barrel- and septum-related columns. From morphological reconstructions of excitatory neurons we computed the geometric circuit predicted by axodendritic overlap. Within most individual projections, functional inputs were predicted by geometry and a single scale factor, the synaptic strength per potential synapse. This factor, however, varied between projections and, in one case, even within a projection, up to 20-fold. Relationships between geometric overlap and synaptic strength thus depend on the laminar and columnar locations of both the pre- and postsynaptic neurons, even for neurons of the same type. A large plasticity potential appears to be incorporated into these circuits, allowing for functional {\textquoteright}tuning{\textquoteright} with fixed axonal and dendritic arbor geometry.

}, keywords = {Animals, Axons, Brain Mapping, Cell Shape, Dendrites, Electric Stimulation, Excitatory Postsynaptic Potentials, Image Cytometry, Lasers, Lysine, Neural Pathways, Neuronal Plasticity, Organ Culture Techniques, Photic Stimulation, Pyramidal Cells, Rats, Somatosensory Cortex, Sprague-Dawley, Synapses, Synaptic Transmission, Ultraviolet Rays}, issn = {1097-6256}, doi = {10.1016/j.tins.2005.05.006}, author = {Shepherd, Gordon M G and Stepanyants, Armen and Bureau, Ingrid and Chklovskii, Dmitri and Svoboda, Karel} } @article {1249, title = {Neurogeometry and potential synaptic connectivity.}, journal = {Trends in Neurosciences}, volume = {28}, year = {2005}, month = {2005 Jul}, pages = {387-94}, abstract = {

The advent of high-quality 3D reconstructions of neuronal arbors has revived the hope of inferring synaptic connectivity from the geometric shapes of axons and dendrites, or {\textquoteright}neurogeometry{\textquoteright}. A quantitative description of connectivity must be built on a sound theoretical framework. Here, we review recent developments in neurogeometry that can provide such a framework. We base the geometric description of connectivity on the concept of a {\textquoteright}potential synapse{\textquoteright}{\textendash}the close apposition between axons and dendrites necessary to form an actual synapse. In addition to describing potential synaptic connectivity in neuronal circuits, neurogeometry provides insight into basic features of functional connectivity, such as specificity and plasticity.

}, keywords = {Animals, Axons, Dendrites, Imaging, Models, Neural Pathways, Neurological, Neuronal Plasticity, Neurons, Synapses, Synaptic Transmission, Three-Dimensional}, issn = {0166-2236}, doi = {10.1016/j.tins.2005.05.006}, author = {Stepanyants, Armen and Chklovskii, Dmitri B} } @article {1255, title = {Class-specific features of neuronal wiring.}, journal = {Neuron}, volume = {43}, year = {2004}, month = {2004 Jul 22}, pages = {251-9}, abstract = {

Brain function relies on specificity of synaptic connectivity patterns among different classes of neurons. Yet, the substrates of specificity in complex neuropil remain largely unknown. We search for imprints of specificity in the layout of axonal and dendritic arbors from the rat neocortex. An analysis of 3D reconstructions of pairs consisting of pyramidal cells (PCs) and GABAergic interneurons (GIs) revealed that the layout of GI axons is specific. This specificity is manifested in a relatively high tortuosity, small branch length of these axons, and correlations of their trajectories with the positions of postsynaptic neuron dendrites. Axons of PCs show no such specificity, usually taking a relatively straight course through neuropil. However, wiring patterns among PCs hold a large potential for circuit remodeling and specificity through growth and retraction of dendritic spines. Our results define distinct class-specific rules in establishing synaptic connectivity, which could be crucial in formulating a canonical cortical circuit.

}, keywords = {Animals, Axons, Computer-Assisted, Dendrites, gamma-Aminobutyric Acid, Image Processing, Imaging, Interneurons, Neocortex, Neural Pathways, Neurons, Pyramidal Cells, Rats, Synapses, Three-Dimensional, Wistar}, issn = {0896-6273}, doi = {10.1016/j.tins.2005.05.006}, author = {Stepanyants, Armen and Tam{\'a}s, G{\'a}bor and Chklovskii, Dmitri B} } @article {1257, title = {Power-law for axon diameters at branch point.}, journal = {BMC Neuroscience}, volume = {4}, year = {2003}, month = {2003 Aug 28}, pages = {18}, abstract = {

Axon calibers vary widely among different animals, neuron classes, and even within the same neuron. What determines the diameter of axon branches?

}, keywords = {Animals, Axons, Biological Evolution, Humans, Models, Neural Conduction, Neurological, Predictive Value of Tests, Reaction Time}, issn = {1471-2202}, doi = {10.1016/j.tins.2005.05.006}, author = {Chklovskii, Dmitri B and Stepanyants, Armen} } @article {1259, title = {Geometry and structural plasticity of synaptic connectivity.}, journal = {Neuron}, volume = {34}, year = {2002}, month = {2002 Apr 11}, pages = {275-88}, abstract = {

Changes in synaptic connectivity patterns through the formation and elimination of dendritic spines may contribute to structural plasticity in the brain. We characterize this contribution quantitatively by estimating the number of different synaptic connectivity patterns attainable without major arbor remodeling. This number depends on the ratio of the synapses on a dendrite to the axons that pass within a spine length of that dendrite. We call this ratio the filling fraction and calculate it from geometrical analysis and anatomical data. The filling fraction is 0.26 in mouse neocortex, 0.22-0.34 in rat hippocampus. In the macaque visual cortex, the filling fraction increases by a factor of 1.6-1.8 from area V1 to areas V2, V4, and 7a. Since the filling fraction is much smaller than 1, spine remodeling can make a large contribution to structural plasticity.

}, keywords = {Animals, Macaca fascicularis, Male, Models, Neural Pathways, Neurological, Neuronal Plasticity, Synapses}, issn = {0896-6273}, doi = {10.1016/j.tins.2005.05.006}, author = {Stepanyants, Armen and Hof, Patrick R and Chklovskii, Dmitri B} }