生質燃料在不久的將來會成為重要的能量來源。如何以更有效率的方法取得此生質能源是個永不落幕的挑戰。過去，許多生化工程師著眼於基因體的重組以改善生質能源的產率。然而，隨機的系統結構變動、時變的生化反應延遲、內外在的分子噪音擾動以及不確定的系統初始條件等因素都會干擾生質能源的合成。於此，我們引用了馬可夫隨機程序(Markovian Jumping process or Markov chain)於系統的動態參數來擬合實驗中的生質能源合成代謝路徑。藉此，為求生質能源的最大產量，我們於本文提出一個以模糊化賽局理論為基礎的‘強健性生質能源代謝路徑設計’進而抵抗生化反應延遲、內在分子擾動與外在環境噪音等影響。
考量由外在噪音與系統不確定性對設計誤差所引起的負面影響，並將賽局設定成一個有生化反應延遲與內在分子擾動的隨機馬可夫動態系統。我們可以將外在噪音與系統不確定性視為賽局理論的其中一名玩家：此玩家的任務就是最大化對設計誤差的‘最壞情況’。相對的，系統中可合理調整的動態參數，將被視為另一名賽局玩家：從已知的啟動子列表(promoter library)與蛋白質資料庫(protein datasheet)中，利用基因遺傳演算法(Genetic Algorithm)搜尋適當的對應參數來最小化前一名玩家對設計誤差的‘最壞情況’。為了避免解決由高度非線性生化系統所引起的 Hamilton-Jacobi 不等式 (HJI) 條件，我們引用了T-S 模糊化方法(T-S fuzzy method)與 Lyapunov-Krasovskii functional 定理 (LKF theory) 將其轉變成一組等效的線性矩陣不等式(Linear Matrix Inequality, LMI)。因此，這個以模糊化賽局理論及強健性組合生物學之觀點設計的生質能源代謝路徑將可被有效且輕易的達成。
本文提出的設計理念除了可應用於生質能源外，也可應用在藥物分子，如：胰島素、抗生素，等量產設計。

Biofuel is a powerful energy source in the near future. How to produce biofuel efficiently is a sustaining challenge. In conventional studies, many engineers focused on the recombination of genes from different organisms to design the biofuel productivity and yield. However, the stochastic behaviors from random systemic switching, time-varying process delay, intrinsic molecular fluctuations, extrinsic noises and uncertain initial conditions are all affect the metabolic pathway. In this situation, a biofuel metabolic pathway in vivo can be modeled as a nonlinear Markovian jumping process. In this study, we proposed a fuzzy-based stochastic game theory approach method with GA-based design algorithm to engineer a metabolic pathway to achieve a desired yield despite stochastic behaviors. Here, the external noises and uncertainties of initial conditions are considered to be a player to maximize the deterioration as a worst-case effect on the regulation performance, while the design parameters via existing promoter libraries and datasheets are considered to be the other player to improve the regulation performance by minimizing the worst-case effect under random jumps of kinetic parameters, intrinsic fluctuations and process delays in a Markovian jumping system. Avoiding to solving the Hamilton-Jacobi inequality for the nonlinear stochastic game design problem, we solved an equivalent Linear Matrix Inequalities (LMIs)-constrained optimization problem via the help of T-S fuzzy interpolation method and Lyapunov-Krasovskii functional theory. Therefore, the robust metabolic engineering design could be easily and efficiently achieved. Our method could be applied to the progress of other metabolic engineerings like the mass production of medicinal metabolites e.g. insulin and so on.

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