A Phenomenological Theory of Spatially Structured Local Synaptic Connectivity

The structure of local synaptic circuits is the key to understanding cortical function and how neuronal functional modules such as cortical columns are formed. The central problem in deciphering cortical microcircuits is the quantification of synaptic connectivity between neuron pairs. I present a theoretical model that accounts for the axon and dendrite morphologies of pre- and postsynaptic cells and provides the average number of synaptic contacts formed between them as a function of their relative locations in three-dimensional space. An important aspect of the current approach is the representation of a complex structure of an axonal/dendritic arbor as a superposition of basic structures—synaptic clouds. Each cloud has three structural parameters that can be directly estimated from two-dimensional drawings of the underlying arbor. Using empirical data available in literature, I applied this theory to three morphologically different types of cell pairs. I found that, within a wide range of cell separations, the theory is in very good agreement with empirical data on (i) axonal–dendritic contacts of pyramidal cells and (ii) somatic synapses formed by the axons of inhibitory interneurons. Since for many types of neurons plane arborization drawings are available from literature, this theory can provide a practical means for quantitatively deriving local synaptic circuits based on the actual observed densities of specific types of neurons and their morphologies. It can also have significant implications for computational models of cortical networks by making it possible to wire up simulated neural networks in a realistic fashion

Blocking NMDAR Disrupts Spike Timing and Decouples Monkey Prefrontal Circuits: Implications for Activity-Dependent Disconnection in Schizophrenia

We employed multi-electrode array recording to evaluate the influence of NMDA receptors (NMDAR) on spike-timing dynamics in prefrontal networks of monkeys as they performed a cognitive control task measuring specific deficits in schizophrenia. Systemic, periodic administration of an NMDAR antagonist (phencyclidine) reduced the prevalence and strength of synchronous (0-lag) spike correlation in simultaneously recorded neuron pairs. We employed transfer entropy analysis to measure effective connectivity between prefrontal neurons at lags consistent with monosynaptic interactions and found that effective connectivity was persistently reduced following exposure to the NMDAR antagonist. These results suggest that a disruption of spike timing and effective connectivity might be interrelated factors in pathogenesis, supporting an activity-dependent disconnection theory of schizophrenia. In this theory, disruption of NMDAR synaptic function leads to dys-regulated timing of action potentials in prefrontal networks, accelerating synaptic disconnection through a spike-timing-dependent mechanism

Connectivity between Pyramidal Neurons in L2/L3 of Rat Visual Cortex

<div><p>(A–D) Images representing the average structures of axons (A and B) and dendrites (C and D) of pyramidal neurons originating from L2 (A and C) and L3 (B and D). Yellow dots depict cell somata. Ellipsoids capture the spatial extent of the synaptic clouds identified from these images. The dimensions and the displacementμ of each cloud were measured as illustrated in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010011#pcbi-0010011-g001" target="_blank">Figure 1</a>B. The images were created using dendritic and axonal arborization drawings based on data representations in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010011#pcbi-0010011-b22" target="_blank">22</a>] by kind permission of B. Hellwig. </p> <p>(E–H) Average number of contacts between pre- and postsynaptic neurons as a function of the distance between them. The type of axonal–dendritic connection is shown on each plot. Empirical curves [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010011#pcbi-0010011-b22" target="_blank">22</a>] are plotted in black. Fitted theoretical curves are plotted in blue and predicted curves are plotted in red. Dots show stochastic variations in the theoretical number of contacts.</p></div

Somatic Connections of Clutch Cells in L4 of Cat Visual Cortex

<div><p>(A) Radial distribution of the average number of postsynaptic somata contacted by the axon. Dots with drop-lines show empirical distribution obtained by pooling data from the two cells [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010011#pcbi-0010011-b26" target="_blank">26</a>]. Bars show theoretical distribution.</p> <p>(B) Image representing the average structure of the clutch cell axon. Yellow dot depicts cell soma. The ellipsoid captures the spatial extent of the synaptic cloud identified from the image. The dimensions and the displacement of the cloud were measured as illustrated in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010011#pcbi-0010011-g001" target="_blank">Figure 1</a>B. The image was created using axonal arborization drawings based on data representations in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010011#pcbi-0010011-b31" target="_blank">31</a>] by kind permission of Z. Kisvárday. </p></div

Connectivity between Pyramidal Neurons in L5 of Rat Somatosensory Cortex

<div><p>(A and B) Connectivity map showing the average number of contacts formed between the presynaptic cell positioned at the origin and the postsynaptic cell at location: (A) empirical map adapted from data representations in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010011#pcbi-0010011-b23" target="_blank">23</a>] by kind permission of H. Markram and G. Silberberg; (B) theoretical map. </p> <p>(C and D) Images representing the average structures of dendrites (C) and axons (D) of pyramidal neurons in L5. Yellow dots depict cell somata. Ellipsoids capture the spatial extent of the synaptic clouds identified from these images. The dimensions and the displacement of each cloud were measured as illustrated in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010011#pcbi-0010011-g001" target="_blank">Figure 1</a>B. The images were created using dendritic and axonal arborization drawings based on data representations in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010011#pcbi-0010011-b23" target="_blank">23</a>] by kind permission of H. Markram and G. Silberberg. </p></div

Decomposition of the Complex Structure of Arbors into Elementary Synaptic Clouds

<div><p>Synaptic density field of each cloud is illustrated by a set of concentric ellipsoids of different weights. An ellipsoid represents the equal-synaptic-density surface, whereas its weight represents the magnitude of the density. The outer ellipsoid, in addition, encloses the spatial extent of cloud ramifications. Yellow dots depict cell somata. The horizontal ℓ_|| and vertical ℓ_⊥ dimensions of one of the clouds as well as the displacement <b>r</b>₀ of its center from the soma are shown.</p> <p>(A) A drawing of the dendritic arbor typical for L3 pyramidal neurons.</p> <p>(B) A drawing of the axonal arbor typical for L2 pyramidal neurons.</p> <p>The drawings of arbors are based on data representations in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0010011#pcbi-0010011-b22" target="_blank">22</a>] by kind permission of B. Hellwig.</p></div