Borisyuk R et al. (2011), Modeling the connectome of a simple spinal cord.

XB-ART-44165

Front Neuroinform 2011 Sep 23;5:20. doi: 10.3389/fninf.2011.00020.

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Modeling the connectome of a simple spinal cord.

Borisyuk R , Al Azad AK , Conte D , Roberts A , Soffe SR .

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In this paper we develop a computational model of the anatomy of a spinal cord. We address a long-standing ambition of neuroscience to understand the structure-function problem by modeling the complete spinal cord connectome map in the 2-day old hatchling Xenopus tadpole. Our approach to modeling neuronal connectivity is based on developmental processes of axon growth. A simple mathematical model of axon growth allows us to reconstruct a biologically realistic connectome of the tadpole spinal cord based on neurobiological data. In our model we distribute neuron cell bodies and dendrites on both sides of the body based on experimental measurements. If growing axons cross the dendrite of another neuron, they make a synaptic contact with a defined probability. The total neuronal network contains ∼1,500 neurons of six cell-types with a total of ∼120,000 connections. The anatomical model contains random components so each repetition of the connectome reconstruction procedure generates a different neuronal network, though all share consistent features such as distributions of cell bodies, dendrites, and axon lengths. Our study reveals a complex structure for the connectome with many interesting specific features including contrasting distributions of connection length distributions. The connectome also shows some similarities to connectivity graphs for other animals such as the global neuronal network of C. elegans. In addition to the interesting intrinsic properties of the connectome, we expect the ability to grow and analyze a biologically realistic spinal cord connectome will provide valuable insights into the properties of the real neuronal networks underlying simple behavior.

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Species referenced: Xenopus
Genes referenced: dlc tbx2

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	Figure 1. Spinal cord anatomy and experimental measurements. (A) A short length of spinal cord shown in section and after cutting down the dorsal midline and opening flat. Rectangles containing neurons represent the two sides (RL and RR), separated by the ventral floor plate (dark gray rectangle, RF). Examples of the cell body positions (ellipses), dendrites (thick lines), and axon projections (thin lines) are illustrated. Neuron types are listed on the right: RB, Rohon Beard sensory neuron; dla, dlc, dorsolateral ascending and dorsolateral commissural sensory interneurons; dIN, cIN, aIN, descending, commissural, and ascending premotor interneurons; mn, motoneurons. (B) Longitudinal distributions of neuron cell body numbers (per 100 μm). The curves show smoothed, theoretical distributions based on current anatomical estimates and updated from Li et al. (2001). The color coding indicated for each cell type is used throughout this paper.
	Figure 2. The distribution of cIN neurons along the left side of the body. Bars indicate the connectome distribution (bin width is 175 μm); circles indicate the experimental estimate.
	Figure 3. Distributions of axon projections in the DV axis. There is a good match between distributions from experimental measurements (left, based on Li et al., 2007) and the connectome (right). In each case DV is divided into 10 bins.
	Figure 4. Visualizing the connectome. (A) A 300-μm long region of the connectome showing the network on one side of the spinal cord. Note: this is ∼10% of the longitudinal extent of the model. Vertical colored bars indicate the dendrites of individual neurons; horizontal curved lines indicate the trajectories of grown axons. Dendrites and axons are color coded for cell type as in Figure 1. Small colored ellipses indicate individual synaptic contacts. In each case, the contact is color coded according to the presynaptic cell type. (B) A small fragment of one side of the connectome, color coded as in (A).
	Figure 5. Visualization of individual axons with synapses. Each red marker shows the RC position of a soma and each horizontal line of black dots indicates the RC positions of individual synapses on each single axon. Synapses on the left of the soma are located on an ascending axon (toward the head) and synapses on the right side are located on a descending axon (toward the tail). (A) dlc. (B) aIN. (C) dIN; note that the ascending axons present on a few spinal cord dINs were not included in this connectome. (D) mn.
	Figure 6. Visualization of individual dendrites with synapses. Each vertical line of the figure corresponds to an individual dendrite. Dots indicate the DV positions of individual synapses. Dendrites and presynaptic contacts (dots) are color coded as in Figure 1. See text for details. (A) from cIN to mn. (B) from dIN to mn. (C) from cIN to dlc. (D) from dlc to dlc.
	Figure 7. Distribution of synapses in a single connectome model. (A) For each neuron type, the two stacked columns show outgoing synapses onto all other neuron types; post-synaptic neuron types (color coded as in Figure 1A) receive incoming synapses from descending axons (right columns) and ascending axons (left columns). (B) Like (A), but each stacked column shows the distribution of incoming synapses from all other cell-types, made via descending axons (left columns) and ascending axons (right columns). See Table 2 for data.
	Figure 8. Distributions of the number of connections as a function of distance. For each pair of neuron types, distance zero is the soma position of the post-synaptic neurons; the bars show the relative positions of the presynaptic neurons. Connections are shown: (A) from aIN to mn; (B) from dlc to dlc; (C) from cIN to dlc; (D) from dIN to mn. Colors (as in Figure 1) indicate the presynaptic neuron type. Bin widths: (A) = 111 μm; (B) = 67 μm; (C) = 90 μm; (D) = 55 μm.
	Figure 9. Properties of the connectome. Node degree distributions for the whole connectome (A) and one side of the connectome (B) show that only the network on one side shows a distribution similar to the power law, and is therefore scale-free. (C) The cumulative function from (B) (blue) and a linear approximation (red) plotted on a log scale. (D) The overall distribution of connection distances for synapses between neurons on a single side of the tadpole connectome.

References [+] :

Borisyuk, Stochasticity and functionality of neural systems: mathematical modelling of axon growth in the spinal cord of tadpole. 2008, Pubmed, Xenbase