昆蟲的中央複合體由位於腦部中央的4個神經氈所組成，擁有複雜但高度組織化的重複迴路構造。許多研究認為中央複合體參與廣泛的功能，包含空間工作記憶、感知到動作的轉換與運動的控制，然而中央複合體的複雜神經迴路如何執行實現這些功能仍是未解之謎。為了初步理解中央複合體神經迴路的功能，我們利用數學方法分析662個分佈於前腦橋的果蠅中央複合體神經細胞：每個神經細胞均表達為一個多維度向量，而各個維度則分別代表中央複合體的特定次區域。我們發現看似複雜的神經細胞端點分佈模式其實相當規律，大多數的神經細胞都可以藉由少數的初始神經細胞向量乘以產生器矩陣而預測得到。這個結果暗示中央複合體神經細胞的發育過程極具效率，可能僅由少數負責簡單規則(產生器矩陣)的基因所驅動。
然而少數神經細胞的分佈模式仍無法以產生器矩陣產生，為測試這些特殊神經細胞是否在資訊傳遞上扮演重要角色，我們將生物的神經細胞數據與數學模型所預測的神經細胞分別建構成實測網路與模型網路，並針對訊息如何由輸入細胞經過多個中間細胞傳遞至輸出細胞的情形加以比較。我們發現在特定的輸入輸出神經細胞對，實測網路的路徑數目，亦即神經網路運算的複雜程度，是模型網路的數倍之高。進一步的研究證實，只有一對特殊神經細胞能夠造成網路複雜度的大幅增加，且其獨特的端點分佈模式是最大化複雜度的關鍵原因。這個結果顯示少數特殊設計的神經細胞即可顯著增進網路的運算複雜度。整體而言，我們的工作對中央複合體神經網路的複雜結構給予新的見解，並提供特別的猜想以待未來實驗的證實。

The central complex (CX), which consists of four neuropils located in the central brain of insects, is characterized by a complex but highly organized and repetitive circuit architecture. Furthermore, CX has been suggested to participate in a range of functions including spatial working memory, sensory-motor transformation and motor control. However, how these functions are implemented and realized by the complex neural circuits in CX remains unclear. As a first step toward understanding of the functions of the CX neural circuits, we mathematically analyzed connectivity of 662 Drosophila neurons which innervate one of the CX neuropils, the protocerebral bridge. Specifically, each neuron is represented as a high-dimensional innervation vector with each dimension corresponding to a subregion of CX. We found that the seemly complex innervation patterns of the neurons are highly structured and the whole network can be generated or even predicted by applying a generator matrix on a small set of initial neurons. The result implies that the development of the complex CX neural network can be highly efficient because it can be driven by a small set of genes that encode the simple rules, or the generator matrices.
We further investigated a small set of observed neurons with innervation patterns that cannot be generated from the generator matrices. To determine whether these “special” neurons play specific roles in information transduction, we compared the network constructed by neurons from observed data and the network generated from the mathematical model (the generator matrices). Specifically, we studied how signals propagate from a given input neuron to a given output neuron through multiple intermediate neurons. We found that the observed network is characterized by large pathway numbers that are several folds larger than that of the model network for specific input-output neuron pairs. We further identified that only two specific neurons in EIP class are responsible for the major changes in the pathway numbers which greatly increase the complexity of network computation. Further analysis indicated that the unique innervation pattern of these neurons plays a key role in maximizing the processing complexity. The result suggests that a small number of specially designed neurons can greatly improve the processing complexity of network. Therefore, our work provides insights into the complex organization of CX neural circuits and may generate specific predictions that can be tested experimentally.

1. Lin, C.-Y., Chuang, C.-C., Hua, T.-E., Chen, C.-C., Dickson, B. J., Greenspan, R. J., and Chiang, A.-S. (2013). A Comprehensive Wiring Diagram of the Protocerebral Bridge for Visual Information Processing in the Drosophila Brain. Cell Reports 3, 1739–1753.
2. Loesel, R., Nässel, D. R., and Strausfeld, N. J. (2002). Common design in a unique midline neuropil in the brains of arthropods. Arthropod Struct. Dev. 31, 77–91.
3. Homberg, U. (2008). Evolution of the central complex in the arthropod brain with respect to the visual system. Arthropod Struct. Dev. 37, 347–362.
4. Power, M. E. (1943). The brain of Drosophila melanogaster. J. Morphol. 72, 517–559.
5. Hanesch, U., Fischbach, K.-F., and Heisenberg, M. (1989). Neuronal architecture of the central complex in Drosophila melanogaster. Cell Tissue Res. 257, 343–366.
6. Young, J. m., and Armstrong, J. d. (2010). Structure of the adult central complex in Drosophila: Organization of distinct neuronal subsets. J. Comp. Neurol. 518, 1500–1524.
7. Renn, S. C. P., Armstrong, J. D., Yang, M., Wang, Z., An, X., Kaiser, K., and Taghert, P. H. (1999). Genetic analysis of the Drosophila ellipsoid body neuropil: Organization and development of the central complex. J. Neurobiol. 41, 189–207.
8. Young, J. m., and Armstrong, J. d. (2010). Building the central complex in Drosophila: The generation and development of distinct neural subsets. J. Comp. Neurol. 518, 1525–1541.
9. Bayraktar, O. A., Boone, J. Q., Drummond, M. L., and Doe, C. Q. (2010). Drosophila type II neuroblast lineages keep Prospero levels low to generate large clones that contribute to the adult brain central complex. Neural Develop. 5, 26.
10. Heinze, S., and Homberg, U. (2008). Neuroarchitecture of the central complex of the desert locust: Intrinsic and columnar neurons. J. Comp. Neurol. 511, 454–478.
11. Homberg, U. (1985). Interneurones of the central complex in the bee brain (Apis mellifera, L.). J. Insect Physiol. 31, 251–264.
12. Homberg, U. (1994). Flight-correlated activity changes in neurons of the lateral accessory lobes in the brain of the locust Schistocerca gregaria. J. Comp. Physiol. 175, 597–610.
13. Wessnitzer, J., and Webb, B. (2006). Multimodal sensory integration in insects—towards insect brain control architectures. Bioinspir. Biomim. 1, 63.
14. Strausfeld, N. J., and Hirth, F. (2013). Deep Homology of Arthropod Central Complex and Vertebrate Basal Ganglia. Science 340, 157–161.
15. Heinze, S., and Homberg, U. (2007). Maplike Representation of Celestial E-Vector Orientations in the Brain of an Insect. Science 315, 995–997.
16. Heinze, S., Gotthardt, S., and Homberg, U. (2009). Transformation of Polarized Light Information in the Central Complex of the Locust. J. Neurosci. 29, 11783–11793.
17. Heinze, S., and Homberg, U. (2009). Linking the Input to the Output: New Sets of Neurons Complement the Polarization Vision Network in the Locust Central Complex. J. Neurosci. 29, 4911–4921.
18. Homberg, U., Heinze, S., Pfeiffer, K., Kinoshita, M., and Jundi, B. el (2011). Central neural coding of sky polarization in insects. Philos. Trans. R. Soc. B Biol. Sci. 366, 680–687.
19. Ritzmann, R. E., Ridgel, A. L., and Pollack, A. J. (2008). Multi-unit recording of antennal mechano-sensitive units in the central complex of the cockroach, Blaberus discoidalis. J. Comp. Physiol. 194, 341–360.
20. Strauss, R., and Heisenberg, M. (1993). A higher control center of locomotor behavior in the Drosophila brain. J. Neurosci. 13, 1852–1861.
21. Martin, J. R., Raabe, T., and Heisenberg, M. (1999). Central complex substructures are required for the maintenance of locomotor activity in Drosophila melanogaster. J. Comp. Physiol. [A] 185, 277–288.
22. Strauss, R. (2002). The central complex and the genetic dissection of locomotor behaviour. Curr. Opin. Neurobiol. 12, 633–638.
23. Ridgel, A. L., Alexander, B. E., and Ritzmann, R. E. (2006). Descending control of turning behavior in the cockroach, Blaberus discoidalis. J. Comp. Physiol. 193, 385–402.
24. Strauss, R., and Pichler, J. (1998). Persistence of orientation toward a temporarily invisible landmark in Drosophila melanogaster. J. Comp. Physiol. 182, 411–423.
25. Kong, E. C., Woo, K., Li, H., Lebestky, T., Mayer, N., Sniffen, M. R., Heberlein, U., Bainton, R. J., Hirsh, J., and Wolf, F. W. (2010). A Pair of Dopamine Neurons Target the D1-Like Dopamine Receptor DopR in the Central Complex to Promote Ethanol-Stimulated Locomotion in Drosophila. Plos One 5, e9954.
26. Sakai, T., and Kitamoto, T. (2006). Differential roles of two major brain structures, mushroom bodies and central complex, for Drosophila male courtship behavior. J. Neurobiol. 66, 821–834.
27. Ueno, T., Tomita, J., Tanimoto, H., Endo, K., Ito, K., Kume, S., and Kume, K. (2012). Identification of a dopamine pathway that regulates sleep and arousal in Drosophila. Nat. Neurosci. 15, 1516–1523.
28. Wu, C.-L., Xia, S., Fu, T.-F., Wang, H., Chen, Y.-H., Leong, D., Chiang, A.-S., and Tully, T. (2007). Specific requirement of NMDA receptors for long-term memory consolidation in Drosophila ellipsoid body. Nat. Neurosci. 10, 1578–1586.
29. Liu, G., Seiler, H., Wen, A., Zars, T., Ito, K., Wolf, R., Heisenberg, M., and Liu, L. (2006). Distinct memory traces for two visual features in the Drosophila brain. Nature 439, 551–556.
30. Neuser, K., Triphan, T., Mronz, M., Poeck, B., and Strauss, R. (2008). Analysis of a spatial orientation memory in Drosophila. Nature 453, 1244–1247.
31. Rubinov, M., and Sporns, O. (2010). Complex network measures of brain connectivity: Uses and interpretations. NeuroImage 52, 1059–1069.
32. Watts, D. J., and Strogatz, S. H. (1998). Collective dynamics of “small-world” networks. Nature 393, 440–442.
33. Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., and Alon, U. (2002). Network Motifs: Simple Building Blocks of Complex Networks. Science 298, 824–827.
34. Albert, R., Jeong, H., and Barabási, A.-L. (2000). The Internet’s Achilles’ Heel: Error and attack tolerance of complex networks. Nature 406, 200–0.
35. Felleman, D. J., and Essen, D. C. V. (1991). Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex, 1–47.
36. Klausberger, T., and Somogyi, P. (2008). Neuronal Diversity and Temporal Dynamics: The Unity of Hippocampal Circuit Operations. Science 321, 53–57.
37. Compte, A., Brunel, N., Goldman-Rakic, P. S., and Wang, X.-J. (2000). Synaptic Mechanisms and Network Dynamics Underlying Spatial Working Memory in a Cortical Network Model. Cereb. Cortex 10, 910–923.
38. Wang, X.-J. (2008). Decision Making in Recurrent Neuronal Circuits. Neuron 60, 215–234.
39. Chiang, A.-S., Lin, C.-Y., Chuang, C.-C., Chang, H.-M., Hsieh, C.-H., Yeh, C.-W., Shih, C.-T., Wu, J.-J., Wang, G.-T., Chen, Y.-C., et al. (2011). Three-Dimensional Reconstruction of Brain-wide Wiring Networks in Drosophila at Single-Cell Resolution. Curr. Biol. 21, 1–11.
40. Homberg, U. (1991). Neuroarchitecture of the central complex in the brain of the locust Schistocerca gregaria and S. americana as revealed by serotonin immunocytochemistry. J. Comp. Neurol. 303, 245–254.
41. Peters, A., and Payne, B. R. (1993). Numerical Relationships between Geniculocortical Afferents and Pyramidal Cell Modules in Cat Primary Visual Cortex. Cereb. Cortex 3, 69–78.
42. Shepherd, G. M. G., Stepanyants, A., Bureau, I., Chklovskii, D., and Svoboda, K. (2005). Geometric and functional organization of cortical circuits. Nat. Neurosci. 8, 782–790.
43. Douglass, J. K., and Strausfeld, N. J. (2003). Anatomical organization of retinotopic motion-sensitive pathways in the optic lobes of flies. Microsc. Res. Tech. 62, 132–150.
44. Tanaka, N. K., Endo, K., and Ito, K. (2012). Organization of antennal lobe-associated neurons in adult Drosophila melanogaster brain. J. Comp. Neurol. 520, 4067–4130.
45. Tejedor, F. J., Bokhari, A., Rogero, O., Gorczyca, M., Zhang, J., Kim, E., Sheng, M., and Budnik, V. (1997). Essential Role for dlg in Synaptic Clustering of Shaker K+ Channels In Vivo. J. Neurosci. 17, 152–159.
46. Cook, P. B., and McReynolds, J. S. (1998). Lateral inhibition in the inner retina is important for spatial tuning of ganglion cells. Nat. Neurosci. 1, 714–719.
47. Olsen, S. R., Bhandawat, V., and Wilson, R. I. (2010). Divisive Normalization in Olfactory Population Codes. Neuron 66, 287–299.
48. Lin, Y.-N. (2012). How network architectures and hubs affect efficiency of vertical and horizontal information propagations in neural circuits — a theoretical analysis.
49. Biggs, N. (1993). Algebraic Graph Theory (Cambridge University Press).
50. Kaiser, M. (2011). A Tutorial in Connectome Analysis: Topological and Spatial Features of Brain Networks Available at: http://arxiv.org/abs/1105.4705 [Accessed June 16, 2013].
51. Latora, V., and Marchiori, M. (2001). Efficient Behavior of Small-World Networks. Phys. Rev. Lett. 87, 198701.
52. Holland, P. W., and Leinhardt, S. (1971). Transitivity in Structural Models of Small Groups. Small Group Res. 2, 107–124.
53. Newman, M. E. J. (2004). Fast algorithm for detecting community structure in networks. Phys. Rev. E 69, 066133.
54. Humphries, M. D., and Gurney, K. (2008). Network “Small-World-Ness”: A Quantitative Method for Determining Canonical Network Equivalence. Plos One 3, e0002051.
55. Varshney, L. R., Chen, B. L., Paniagua, E., Hall, D. H., and Chklovskii, D. B. (2011). Structural Properties of the Caenorhabditis elegans Neuronal Network. Plos Comput Biol 7, e1001066.
56. Johnston, D. S., and Nüsslein-Volhard, C. (1992). The origin of pattern and polarity in the Drosophila embryo. Cell 68, 201–219.
57. Weir, P. T., and Dickinson, M. H. (2012). Flying Drosophila Orient to Sky Polarization. Curr. Biol. 22, 21–27.
58. Pan, Y., Zhou, Y., Guo, C., Gong, H., Gong, Z., and Liu, L. (2009). Differential roles of the fan-shaped body and the ellipsoid body in Drosophila visual pattern memory. Learn. Mem. 16, 289–295.