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.

第1章 背景介紹
1.1. 中央複合體的結構與功能
1.2. 網路分析與生物神經網路特性
1.3. 研究內容概述
第2章 材料與方法
2.1. 數據處理
2.2. 神經細胞原始資料
2.3. 神經細胞端點分佈向量與產生器矩陣
2.4. 實測網路與模型網路
2.5. 連結矩陣與典型複雜網路分析
2.6. 資訊的輸入、輸出與傳遞階層
2.7. 路徑數目矩陣與處理複雜度
第 3章 結果
3.1. 神經細胞的端點分佈規則與數學模型
3.2. 各神經細胞群的實測細胞與模型細胞
3.3. 實測網路與模型網路的特性差異
3.4. 一對特殊神經細胞造成高度處理複雜度
第 4章 討論
4.1. 總結與展望
4.2. 神經結構的規律與不規律來源
4.3. 網路的資訊傳遞與生理功能
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附錄
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