應用OKID於生物系統建模與強健性評估

Abstract

本研究係應用OKID(Observer / Kalman Filter Identification)於生物系統的建模上，藉由OKID求出的系統矩陣與觀測增益矩陣可以進行系統性地分析、探討擾動系統的穩定性與強健性。OKID屬於狀態空間模型的參數估計方法之ㄧ，本研究藉此描述代謝反應與強健性評估。OKID可有效地鑑別狀態空間模型參數，在少許資料量下即可估計參數、確定適當的模型階數、降低雜訊影響並接受各式資料輸入等特性。由於S-system模型目前被廣泛地應用於代謝網路的建模上，因此藉由輸入各種型式的資料，透過S-system產生輸出資料，利用這些輸出入資料以及OKID的鑑別方法，得出系統參數，並將OKID鑑別出來的模型與S-system比較，OKID鑑別之狀態空間系統矩陣更適於分析生物系統。針對7個生化反應路徑，經由OKID鑑別出來的模型資料與原始資料相比對，至少具有92.1%以上的相似度；並且可依據模型特徵值有效地評估系統強健性。

The purpose of this paper is to apply OKID (Observer/Kalman Filter Identification), which is an approach for state space model parameter estimation, to the modeling of bio-systems. With the identified system matrices and observer gain matrix obtained from OKID approach, we can systematically investigate and analyze the stability and robustness of a perturbed system. OKID can effectively and easily identify a state space model, which requires fewer data for estimation, determines appropriate model order, reduces disturbance effect and allows general data inputs. Since S-system has currently been widely used in the modeling of metabolism networks, we adopt S-system to generate output data with various inputs, and use the input-output data sets to identify parameters by OKID approach. Furthermore, compared with S-system model, the model identified by OKID is more suitable for analyzing a bio-system based on the system matrices of the model. Seven numerical examples for biological pathways are given to illustrate and validate the method developed in this study. Results suggest that the built models can fit original data with at least 92.1% similarity and easily evaluate the robustness of the system by eigenvalues of the model.