本研究以有限單元法為基礎，建立一叢集原子-連體理論，用以計算奈米尺寸結構之力學行為。於該理論中，吾人首先將特定之原子團利用叢集單元代表之，而原子團間之化學鍵能即可利用原子-連體理論表現之。經由叢集原子-連體理論，即可將奈米尺度結構之物理特性以數值模型表現。並且，吾人可利用暫態有限單元方法分析奈米結構之力學行為，亦可更詳細地獲得於外負載下奈米結構中之化學鍵能的變化。若與一般之分子動力學計算比較，本研究中所提出的叢集原子-連體理論計算可以同時模擬數百萬個原子的行為。另外，因為本研究所提出之理論可將計算累進時間間隔擴充至百萬分一秒，但分子動力學之時間間隔則為百億分之一秒，故本研究之計算理論較分子動力學理論有更長的模擬時間。同時，由於本研之理論乃以有限單元法為計算基礎，故可以在計算的同時考慮多種化學鍵能之共同作用。
另外，本研究利用前述之叢集原子-連體計算理論研究雙股螺旋之去氧核醣核酸(double strand deoxyribonucleic acid, dsDNA)之力學行為，並建立dsDNA之數值模型。利用本研究之計算理論進行dsDNA之數值模擬，吾人可以得到dsDNA分子於受外負載作用下之暫態力學行為。此外，為驗證dsDNA數值模型之真確性，吾人將該數值模型於受特定外負載下之分析結果，與受類似外負載下單分子操作之實驗數據比對。而該比對結果顯示，數值模型除數值方面與實驗數據相當符合外，並可賦予實驗結果合理之物理現象解釋。同時，利用前述之數值模型，吾人可更進一步地研究dsDNA分子，在受外負載下之堆垛作用勢與氫鍵能量之變化，以及相關結構變化之力學行為。
然於奈米等級結構分析中，吾人需要同時考慮微觀力學與巨觀力學之綜合作用。因此，奈米尺寸之模擬需要考量尺寸效應、古典力學與量子力學之兩像性與實驗導向模擬等物理概念。而本研究之叢集原子-連體理論，實源於有限單元法之局域廣域(Micro-macro)模擬技術，並且適當地於邊界上考慮原子級能量關係。實言之，本研究之叢集原子-連體理論包含叢集原子理論以及原子-連體理論二部分。叢集原子理論主要將特定之叢集原子團，利用有限單元法中之適當單元予以描述。而原子-連體理論則處理叢集原子團間之原子級能量關係，並將該能量關係轉換為前述叢集單元間之作用力(矩)與位移(轉角)關係。因此，本研究將利用叢集原子-連體理論建立自由旋動邊界條件下之dsDNA分子數值模型，並且於外負載下之該數值模型則可經由暫態有限單元法軟體求解。吾人將前述之數值模擬與實驗量測模擬結果比對，可獲得相當的一致性，並且可以賦予dsDNA分子於拉申負載下結構變形之力學解釋。
另外一方面，吾人將驗證以本研究提出之叢集原子-連體理論所見建立之dsDNA 數值模型的預測能力，故將該數值模型施予不同之外負載條件與邊界條件，並與單分子實驗結果比對。首先，吾人將研究雙股兩端固定之dsDNA於外負載下之力學行為，並將其分析結果與實驗比對。此外，吾人亦研究具實際生物序列雙股dsDNA打開(unzipping the dsDNA)之力學行為，並與實際之生物物理現象比較(如複製或轉錄起使序列)，以期獲得該生物現象之力學解釋。

A novel clustered atomistic-continuum mechanics (CACM) method, based on the finite element theory, has been proposed to simulate the mechanical characteristics of the nano-scaled structures. To accomplish the nano-scaled mechanical numerical simulation via CACM, the specific atomic groups are modeled as the clustered elements and the chemical bonding energies between the said clustered groups are described. Hence, the mechanical characteristics of the nano-scaled structure could be represented by the numerical model of CACM. The transient mechanical response of the nano-scaled molecules and the interested chemical bonds could be analyzed by the proposed method. Comparing the proposed method with the conventional molecule dynamic (MD) method, the CACM could efficiently extend total atom numbers from thousands atoms to million atoms, the total simulated time from nano seconds to seconds and the time step from femto second to micron second. Moreover, the CACM could simulate the structure with several different kinds of the chemical binding energies.
The dsDNA molecule is treated as the test vehicle of the proposed CACM method. Through dsDNA CACM model, the mechanics of dsDNA could be represented visually. Moreover, the numerical simulations exhibit good agreements with the experimental results which are obtained by the single molecule manipulation technique. Additionally, the response of the chemical bonds in dsDNA while applying the external loading would be then elucidated, including the stacking energy bonds and hydrogen bonds. Moreover, the mechanical characteristic of the dsDNA with different sequence would be then understood.
Since the analyzed domain of the dsDNA related problem is the nano-scale, both the micro-scaled mechanics (quantum mechanics) and the macro-scaled mechanics (continuum mechanics) should be considered. Therefore, the nano-scaled modeling should consider the size effect, the complementary of the classical and quantum mechanics and the experimental oriented modeling method. In order to implement the said modeling theory, the proposed CACM is based on the continuum mechanics, and it is deduced form the micro-macro numerical analysis technique of the finite element method. Moreover, the CACM comprises both the clustered atomistic and atomistic-continuum methods. The clustered atomistic method treats the covalent bond atom groups as clustered elements with effective characteristic properties. The atomistic-continuum method transfers from the stacking energy and hydrogen bond energy into the different types of virtual elements. Therefore, the freely-untwisting dsDNA model could be numerically represented by the CACM, and the simulation result could be obtained by the transient finite element solver. Good agreement was achieved between the numerical simulation and single molecular experimental results, with the mechanical behavior of stretching dsDNA being revealed.
Furthermore, the predictive capability of the dsDNA model based on the CACM would be then investigated. The numerical models of the stretching both-strand-fixed dsDNA and that of the unzipping the dsDNA were established, respectively. Good agreements between these two models and experimental results were achieved. Moreover, the simulation results of the both-strand-fixed dsDNA under tensile loading clarified the mechanical behavior of dsDNA stretching. Additionally, the sequence-dependent mechanical response of the unzipping dsDNA would be reveal by the simulation results of the dsDNA CACM, and the molecular biological phenomenon, such as the replication and transcription, could be then understood.

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