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. 2006 Mar 21;103(12):4723-8.
doi: 10.1073/pnas.0506806103. Epub 2006 Mar 14.

Wiring optimization can relate neuronal structure and function

Beth L Chen  1 , David H Hall, Dmitri B Chklovskii
Affiliations

Wiring optimization can relate neuronal structure and function

Beth L Chen et al. Proc Natl Acad Sci U S A. .

Abstract

We pursue the hypothesis that neuronal placement in animals minimizes wiring costs for given functional constraints, as specified by synaptic connectivity. Using a newly compiled version of the Caenorhabditis elegans wiring diagram, we solve for the optimal layout of 279 nonpharyngeal neurons. In the optimal layout, most neurons are located close to their actual positions, suggesting that wiring minimization is an important factor. Yet some neurons exhibit strong deviations from "optimal" position. We propose that biological factors relating to axonal guidance and command neuron functions contribute to these deviations. We capture these factors by proposing a modified wiring cost function.

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Conflict of interest statement

Conflict of interest statement: No conflicts declared.

Figures

Fig. 1.
Fig. 1.
Actual and predicted neuronal cell body positions. (A) Neuronal layout in the worm, pharyngeal neurons excluded. Each color denotes a ganglion. (B) Actual placement of neuronal cell bodies projected onto anterior–posterior axis. Circles of the same color represent cell bodies belonging to the same ganglion. Plots for each ganglion are offset vertically to aid the eye. (Inset) Schematic example of biological network of three neurons and two fixed points: s, sensory ending; m, muscle. The blue neuron is bipolar, with one neurite attaching to the sensory ending and the other making two excitatory synapses onto the red neuron and one excitatory synapse onto the green neuron (circle represents the cell body). The red neuron makes an inhibitory synapse onto the blue neuron (line ending in circle) and a gap junction (bar) with the green neuron. The green neuron has a neuromuscular junction. (C) Neuronal layout predicted from minimization of quadratic wiring cost in dedicated-wire model. (Inset) Weighted dedicated-wire model. Each black line or wire corresponds to one synapse independent of polarity (excitatory vs. inhibitory), directionality, or modality (chemical vs. gap). (D) Neuronal layout predicted from the binary dedicated-wire model. (Inset) Binary dedicated-wire model. Each wire corresponds to a synaptic connection neglecting a multiplicity of synapses. (E) Neuronal layout predicted from the shared-wire model. (Inset) Shared-wire model. Neurons are represented as nonbranching wires (colored lines), which must overlap if a synaptic connection exists. Cell body location on the wire can be calculated by using different rules.
Fig. 2.
Fig. 2.
Neuron positions predicted by the quadratic dedicated-wire model vs. actual neuron positions. (Upper) Positions are normalized by the worm body length (0 = head; 1 = tail). Perfect predictions fall on the diagonal. Circles of the same color represent cell bodies belonging to the same ganglion. Three classes of pioneer neurons are labeled. (Lower) Schematics depicting the progression of pioneer neurons during worm development. Arrows indicate direction of neurite growth.
Fig. 3.
Fig. 3.
Analysis of cost-minimization outliers. (A) Histogram of absolute value of predicted-actual positions. (Top) Neurons with cell bodies in the head of the worm. (Middle) Neurons with soma in the midbody. (Bottom) Neurons with soma in the tail. Red vertical line in each plot marks the first standard deviation from the mean. Asterisks indicate neurons with ambiguous wiring (see text and Supporting Text for definitions). (B) Asymmetry of synapse position relative to the soma (1 = all synapses in the head and tail are located on opposite end of the worm as the cell body; 0 = all synapses in the head and tail are close to the cell body) vs. prediction error of wiring cost minimization. Bolded neurons above blue line (asymmetry >75%) are pioneer neurons. (C) Synaptic inputs near the cell body vs. prediction error of wiring cost minimization. Bolded neurons above the blue line (percent inputs >75%) are command interneurons for locomotion. The vertical red line is first standard deviation of wiring-cost model deviation.
Fig. 4.
Fig. 4.
Distribution of synapses by directionality and type along command interneurons. Neuronal outputs or presynaptic terminals are shown in blue, inputs or postsynaptic terminals are shown in red, and electrical junctions are shown in green. (Upper) AVAL. (Lower) PVCR.
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