| 摘要: | 本研究主旨為發展新的統計與動態分析方法並應用在分子叢集(cluster)以及聚分子(polymer)的動靜態行為(例如相變、折疊)，我們將原本運用在蛋白質資料庫(PDB)比對形狀的方法(shape matching technique)轉移到分子動力學的分子軌跡分析，所使用的方法包含統計機率分佈以及時間序列動態分析，諸如time series segmentation、time series cross correlation等。利用上述方法，我們發現形狀辨識技術(shape recognition technique )非常適合運用在有限尺度系統(finite-size system)，因為任何有限系統的動態行為都與形狀的變化息息相關，本研究也是分子動力學文獻中少數以分子形狀變化作為分析的依據，是屬於具原創性的研究工作。
運用形狀辨識技術，我們獲得分子叢集相變(phase transition)的新觀點--利用形狀的機率分佈隨溫度的變化可以清楚解釋融化以及前置融化現象的機制，我們分析的對象為AgCu的合金，最大到45顆原子。而在聚分子方面，我們採用了TTR(105-115)這個素材，其與視網膜病變以及大腦疾病息息相關，因此研究他的折疊與沈澱機制是最近非常熱門的議題，利用形狀辨識所產生的形狀時間序列(定溫與定壓下)，並透過時間序列分析方法，我們了解了非常詳細的折疊機制，並呈現了一般蛋白質折疊分析(例如contact map)所無法得到的動態資訊。
最後，本論文的主要題目之一為擴散理論(Diffusion Theory)在TTR(105-115)的應用，我們產生了非常龐大資料的分子動力學軌跡(2μs)，模擬系統包含了數以千計的實體水分子，用以驗證Dr. A. Rapallo所發展的 Hybrid Basis Approach (HBA)，HBA為結合廣泛應用的 Maximum Correlation Approximation (MCA)還有 Long Time Sorting Procedure (LTSP) 所得到的新理論方法，已於2008年在合成的聚分子上取得極佳的結果，其主要目的是在考慮聚分子或蛋白質長時間記憶效應，也就是計算其時間相關函式(time correlation function)的同時，還能保有區域動態(local dynamics)行為的特徵，而本論文則是將此方法應用到生物體內的蛋白質片斷，其複雜度高於合成聚分子。在TTR(105-115)的擴散理論計算中，我們發現HBA的精確度勝於LTSP，且能得到非常貼近模擬實驗的結果，換而言之，HBA可以作為目前Diffusion Theory領域裡一個非常強大的理論。我們期望這個理論能夠更進一步成功地應用在各式蛋白質與聚分子的動態理論分析上。;Part I--An ultrafast shape-recognition technique was used to analyze the phase transition of finite-size clusters, which, according to our research, has not yet been accomplished. The shape of clusters is the unique property that distinguishes clusters from bulk systems, and is comprehensive and natural for structural analysis. In this study, an isothermal molecular dynamics simulation was performed to generate a structural database for shape recognition of Ag-Cu metallic clusters using empirical many-body potential. The probability contour of the shape similarity exhibits the characteristics of both the specific heat and Lindemann index (bond length fluctuation) of clusters. Moreover, our implementation of the substructure to the probability of shapes provides a detailed observation of the atom/shell-resolved analysis, and the behaviors of the clusters were reconstructed based on the statistical information. The method is efficient, flexible, and applicable in any type of finite-size system, including polymers and nanostructures.
Part II--Folded conformations of proteins in thermodynamically stable states have long lifetimes. Between such stable folded conformations the protein will generally stray from one random conformation to another leading thus to rapid fluctuations. Brief structural changes therefore occur before folding and unfolding events. These short-lived movements are easily overlooked in studies of folding/unfolding for they represent momentary excursions of the protein to explore conformations in the neighborhood of the stable conformation. The present study looks for precursory signatures of protein folding/unfolding within these rapid fluctuations through a combination of three techniques: (1) ultrafast shape recognition, (2) time series segmentation, and (3) time series clustering. The first procedure measures the differences between statistical distributions of atoms in different conformations by calculating shape similarity indices from molecular dynamics simulation trajectories. The second procedure is used to discover the times at which the protein makes transitions from one conformation to another. Finally, the third technique exploits spatial fingerprints of the stable conformations, since strongly correlated atoms in different conformations are different because the bond and steric constraints are different, to map out the sequences of changes preceding the actual folding and unfolding events. The aforementioned high-frequency fluctuations are therefore characterized by distinct correlational changes and structural changes associated with rate-limiting precursors translate into brief segments. Guided by these technical procedures, we identify not only the signatures of transitions between α helix and β hairpin for transthyretin fragment TTR(105-115) (the model system chosen in this work for illustration), but also the important role played by weaker correlations in such protein folding dynamics.
Part III--Improved basis sets for the study of polymer dynamics by means of the diffusion theory, and tests on a melt of cis-1,4-polyisoprene decamers, and a toluene solution of a 71-mer syndiotactic trans-1,2-polypentadiene were presented recently [R. Gaspari and A. Rapallo, J. Chem. Phys. 128, 244109 (2008)]. The proposed hybrid basis approach (HBA) combined two techniques, the long time sorting procedure and the maximum correlation approximation. The HBA takes advantage of the strength of these two techniques, and its basis sets proved to be very effective and computationally convenient in describing both local and global dynamics in cases of flexible synthetic polymers where the repeating unit is a unique type of monomer. The question then arises if the same efficacy continues when the HBA is applied to polymers of different monomers, variable local stiffness along the chain and with longer persistence length, which have different local and global dynamical properties against the above-mentioned systems. Important examples of this kind of molecular chains are the proteins, so that a fragment of the protein transthyretin is chosen as the system of the present study. This peptide corresponds to a sequence that is structured in β-sheets of the protein, and is located on the surface of the channel with thyroxin. The protein transthyretin forms amyloid fibrils in vivo, whereas the peptide fragment has been shown [C.P. Jaroniec, C.E. MacPhee, N.S. Astrof, C.M. Dobson, and R.G. Griffin, PNAS 99, 16748 (2002)] to form amyloid fibrils in vitro in extended β-sheet conformations. For these reasons the latter is given considerable attention in the literature, and studied also as an isolated fragment in water solution where both experimental and theoretical efforts have indicated the propensity of the system to form β turns or α-helices, but is otherwise predominantly unstructured. Differing from previous computational studies that employed implicit solvent, we performed in this work the classical molecular dynamics simulation on a realistic model solution with the peptide embedded in an explicit water environment, and calculated its dynamic properties both as an outcome of the simulations, and by the diffusion theory in reduced statistical-mechanical approach within HBA on the premise that the mode-coupling approach to the diffusion theory can give both the long-range and local dynamics starting from equilibrium averages which were obtained from detailed atomistic simulations. |
