高分子系統非平衡群集弛釋過程的統計力學與其拓展之研究

Abstract

蛋 白質群集(aggregation) 現象與各種神經退化性疾病如阿茲海默症（Alzheimer`s disease），巴金森症（Parkinson`s disease），杭丁頓舞蹈症(Huntington`s disease) 乃至具傳染性的庫賈氏症 (Creutzfeldt-Jakob disease)…等的關係是現今科學界一項跨領域研究的重要題材。本計畫將以相圖（phase diagram）上的氣-液共存區(coexistence region)中發生的非平衡弛釋過程看待高分子聚合物的群集現象；把引起阿茲海默症的蛋白質牲肽片斷Aβ40/Aβ42的結構與作用參數，依不同層次、逐一加入我們的模型分子。檢視共存區範圍以及群集速率的改變，以釐清各層次的因素所扮演的角色，獲得可與實驗作定性或定量比較的數據。我們的先期分子動力模擬研究發現:模型分子鍊上的韌度(rigidity)性質以及彎曲角(bending angle) 和雙面角(torsion angle)的作用力參數，除了會影響群集發生的動力過程，也會改變系統的統計動力性質，造成出現具有Generalized Maxwell-Boltzmann速度分佈的狀態，此現象涉及統計力學的若干基本議題。我們將有系統地持續追蹤高分子模型動態曲度性質與系統統計動力性質的關聯性，並探討此類統計與結構間之關係在各類複雜系統研究的可能應用。

The study of aggregations of peptides or proteins and their roles in the occurrence of neurodegenerative diseases, such as Alzheimer`s disease, Parkinson`s disease, Huntington`s disease and the transmissible Creutzfeldt-Jakob disease, has become an important cross- discipline issue for scientists. We propose to adopt the aspect that the aggregation process of polymer is the relaxation of a non-equilibrium state located within the liquid-vapor coexistence region in its phase diagram, to study the aggregation of Aβ40/Aβ42 peptide segments. The latter process has been suspected to be responsible for Alzheimer`s disease. We will examine, in a step-by-step manner, the changes in the extent of coexistence region and in the aggregation rate as the results of putting various factors in conformation and interactions into the model polymer chains. So that, the effects at different levels can be distinguished systematically and compared with the outcome of experiments qualitatively or quantitatively. Our previous molecular dynamics simulation studies show that the chain rigidity, the bending angle and torsion angle interaction strengths affect not only the process of aggregation, they also render the emergence of states, the statistical properties of which are dominated by the generalized Maxwell-Boltzmann velocity distributions. There involve a few fundamental issues of statistical mechanics. We will continue to find the relationship between the curvatures of the floating chains and the nature of the statistical dynamic properties. Such knowledge may be potentially useful in the studies of various complex systems.