- 學位論文
偽結狀高分子結構熱力性質探討
Thermodynamics of a pseudoknot polymer formation
摘要
本論文應用蒙地卡羅法做分子模擬，研究偽結狀高分子結構的動態性質。在分子鏈中間我們設定了兩對會相互作用的反應基，其鍵結 能量各為-ε1與-ε2(ε1 < ε2)。首先，我們等比例放大分子鏈的長度，發現由狀態0 變化至狀態2或狀態5的速率常數與分子鏈長度有著2.48次方的指數關係，即τ∼N2.48；由狀態2 或狀態5 變化至狀態0的速率常數則與反應基的鍵結能量呈現e-ε/kT 的比例關係，而與分子鏈的長度無關。由實驗結果發現狀態2 發生的機率會隨著分子鏈長度的增加而降低，倘若分子鏈長度無限長時，狀態2 發生的機率也會趨近於0，此時系統將從四相模式變成三相模式。此外我們在熱容量與溫度的關係圖中，發現圖形有兩個高峰位置(peak)，得知系統處在狀態0到狀態5 及狀態5 到狀態7 的變化。之後我們固定總粒子及兩端粒子數目為40 及3，發現隨著鍵結能量大的反應基之間距離越長、鍵結能量小的反應基之間距離越短，狀態2 發生的機率會提高、狀態5 發生的機率會降低。這個結果顯示我們可以藉由調整分子鏈反應基間的距離以控制分子鏈的結構，使其呈現不同的皺褶現象。
並列摘要
The kinetics of conformational fluctuations of a pseudoknot polymer is studied by Monte Carlo simulation. The polymer chain is modeled as having two pair of binding sites at interior with binding energies of -ε1 and -ε2 (ε1 < ε2). Firstly, the length of each section divided by the binding sites are increased proportionally. We find that the rate constants form state 0 to state 2 or 5 scale as N2.48 and the rate constants form state 2 or 5 to state 0 is independent of chain length but proportional to e-ε/kT. The probability of state 2 decreases with increasing chain length and may be zero as N→∞. The four-state system will become a three-state system. In the figure of heat capacity plotted against temperature, two peaks are observed representing the transitions between state 0 and 5, and between 5 and 7. In the second part of the work, the total polymer chain length is fixed as 40 and the length of both end sections is set to be 3. By increasing the distance between pair of binding energy -ε1 and at the same time decreasing the distance between pair of binding energy -ε2,the probability of state 2 increases and the probability of state 5 decreases. This result indicates that we can control the folded forms of a pseudoknot by adjusting the length of each section divided by binding sites on the chain.