第一部分
脂質奈米碟( lipid nanodisc )提供細菌視紫質( bacteriorhodopsin, bR )極佳的水相分散性、近似原生態的脂雙層( lipid bilayer )環境並能維持其光誘發質子幫浦能力。為研究細菌視紫質在不同脂質電性環境中的光迴圈動力學反應，吾人將單體細菌視紫質包裹入脂質奈米碟中，並建構以相異比例的陰電性( DMPG、DOPG )及雙性( DMPC、DOPC )脂質混合之脂雙層環境。所得樣品依據陰離子交換層析法與界面電位分析儀，證實奈米碟表面陰電性質確實隨脂質親水端PG比例提升而增強。而穩態可見光吸收光譜結果顯示，奈米碟細菌視紫質α譜帶並未有顯著改變，表示脂質電性並未使視蛋白三級結構發生嚴重變化。以可見光瞬態吸收光譜法偵測光迴圈中間態M、N、O與基態的動力學，顯示隨兩性脂質的比率增加而顯著減緩，尤其以M態之消逝速率變化最為明顯，並伴隨N、O態的瞬態布居分布大幅降低。而脂質的相轉變溫度、流動性及碳鏈長度亦有可能造成光迴圈動力學的差異。本論文中，吾人證實調整奈米碟中的脂質種類及電性，對於光合作用跨膜蛋白的質子幫浦影響甚大。
第二部分
時相關量子波包( time-dependent quantum wavepacket )能提供理論證據以解釋量子現象與化學動力學，而含時薛丁格方程式為主導波包傳播行為的波動方程式。利用有限差分法得變換含時薛丁格方程式中的微分項，建立以純數值運算波包隨時間發展的演算法，並應用吾人所設計之截斷格點法改良其演算模組，以減輕波函數中趨近零值之數據所造成的運算負擔。多種位能系統的演算試例中，顯示演算法在應用截斷格點法後有能力表現波包的擴展、位移與振盪行為，並且其運算精確度與原始演算法相當。此外，在虛數時間法的試例中，截斷格點法得獲取與解析解相符的基態波函數及其能量期望值，並顯示演算穩定度有所提升。吾人設計的截斷格點法能在保有運算準確度的前提下，得縮減運算負擔，並提供了比原始演算法更高的穩定度。

I. Monodisperse lipid nanodisc provides bacteriorhodopsin (bR), a light-driven proton pump membrane protein, excellent aqueous dispersibility and native-mimic lipid bilayer environment. To study the lipid-composition dependence of the photo-cycle kinetics of bR, the monomeric bR was embedded in nanodiscs composed of different ratios of negatively-charged lipids (DMPG, DOPG) to zwitterionic lipids (DMPC, DOPC). The steady-state absorption spectra of light-adapted monomeric bR in nanodiscs composed of different lipid ratios exhibited the conservation of the tertiary structure of embedded bR and the ion-exchange chromatography showed increment on negative surface charge as the content of DOPG or DMPG increased. By utilizing transient absorption spectroscopy to monitor the evolution of photocycle intermediates of bR in nanodisc, the photocycle kinetics of bR was significantly retarded and the transient populations of intermediates N and O were decreased as the content of DMPG or DOPG was reduced. In this work, we not only demonstrated the usefulness of nanodiscs as a membrane mimicking system, but also showed that the surrounding lipids play a crucial role in altering the biological functions, e.g., the ion translocation kinetics of the transmembrane proteins.
II. Time-dependent quantum wave packet obtained by solving the time-dependent Schrödinger equation (TDSE) provides theoretical information for quantum phenomena of physical systems. In conventional computational methods, the finite difference method is employed to obtain approximate solutions to the TDSE. In order to improve the numerical algorithm for the TDSE, we develop the truncated grid method to reduce the computational effort by eliminating grid points with extremely low probability densities. By applying the new method to several quantum systems, including the free Guassian wave packet and the coherent state of the harmonic oscillator, the propagation behavior of wavepacket were demonstrated. In addition, we employ the truncated grid method to solve the imaginary-time Schrödinger equation for the ground and first-excited states of the harmonic oscillator, the double well potential, and the Morse potential. Excellent computational results for these examples show that the truncated grid method significantly reduces the computational effort relative to the full-grid integration for the TDSE.

第一篇 奈米碟中脂質對細菌視紫質光迴圈動力學之調制
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 1
1.2.1 細菌視紫質之發現 1
1.2.2 光迴圈及質子幫浦 1
1.2.3 細菌視紫質與紫膜的結構 2
1.2.4 紫膜組成形式與脂質環境 2
1.3 研究動機與目的 3
第二章 細菌視紫質與奈米碟之特性 5
2.1 細菌視紫質相關性質 5
2.1.1 細菌視紫質結構及紫膜的組成 5
2.1.2 靜態紫外/可見光吸收光譜特性 6
2.1.3 圓二色可見光吸收光譜特性 7
2.2 細菌視紫質之光迴圈與瞬態吸收光譜性質 7
2.3 質子幫浦與脂質之關係 8
2.4 奈米碟之組成與特性 9
第三章 光譜技術原理、實驗系統與數據處理 17
3.1 光譜技術及實驗儀器原理 17
3.1.1 穩態紫外/可見光吸收光譜儀 17
3.1.2 圓二色光譜法 18
3.1.3 快速蛋白質液相層析儀 19
3.1.4 界面電位分析儀 20
3.1.5 可見光瞬態吸收光譜法 22
3.2 儀器架設 22
3.2.1 穩態紫外/可見光吸收光譜儀 22
3.2.2 單波長可見光瞬態吸收光譜法 23
3.3 樣品製備 24
3.3.1 嗜鹽古菌Halobacteria salinarum之培養 24
3.3.2 紫膜之純化 25
3.3.3 單體化細菌視紫質的製備 26
3.3.4 合成奈米碟選用之脂質種類 27
3.3.5 奈米碟環境的單體細菌視紫質( nbR )製備 28
3.3.6 實驗之樣品種類與溶液環境 29
3.4 實驗儀器之參數設定 30
3.4.1 穩態紫外/可見光吸收光譜儀 30
3.4.2 圓二色可見光吸收光譜儀 30
3.4.3 單波長可見光瞬態吸收光譜法 30
第四章 實驗結果與討論 46
4.1 奈米碟細菌視紫質之表面電性 46
4.2 奈米碟細菌視紫質之穩態吸收光譜 46
4.3 奈米碟細菌視紫質之圓二色光譜 47
4.4 奈米碟細菌視紫質之光迴圈動力學 47
4.4.1 雷射重覆頻率測試 47
4.4.2 差異吸收度與雷射強度之相依性 48
4.4.3 奈米碟細菌視紫質之基態差異吸收時間側寫 48
4.4.4 奈米碟細菌視紫質之瞬態差異吸收光譜 48
第五章 結論與未來展望 60
5.1 結論 60
5.2 未來展望 61
第六章 文獻參考 62

第二篇 截斷格點法對於量子波包動力學之應用
第一章 緒論 69
1.1 緒論 69
1.2 理論方法 69
第二章 理論介紹與計算原理 71
2.1 量子波包 71
2.2 含時薛丁格方程式 71
2.3 自由粒子波包模型 72
2.4 高斯波包 73
2.5 虛時薛丁格方程式 73
2.6 有限差分法 74
第三章 演算系統與程式設計 77
3.1 波包演繹之演算法 77
3.2 截斷格點法 79
3.3 演算法之程式主要架構 80
3.4 運算試例 81
3.4.1 自由粒子之靜止與傳播形式 81
3.4.2 簡諧位能波包傳播 83
3.4.3 虛數時間法於簡諧位能之應用 83
3.4.4 虛數時間法於雙井位能之應用 84
3.4.5 虛數時間法於摩斯位能( Morse potential)之應用 85
第四章 結論與研究方向 98
4.1 結論 98
4.2 研究方向 98
第五章 文獻參考 101

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第二篇
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