以布朗動態法研究表面正電荷密度及溶液離子強度對DNA在脂雙層上擴散行為之影響

Abstract

目前已經有許多實驗觀察到當DNA吸附於帶有正電荷脂雙層表面時，會使脂雙層局部組成比例改變，並且DNA的運動遵守Rouse model，並受到脂雙層的電荷密度以及溶液離子強度的影響。本實驗室在低正電荷密度脂雙層，高離子強度溶液中所測得吸附態DNA的擴散係數與環動半徑（radius of gyration）與理論模型趨勢十分吻合；但在高正電荷密度脂雙層，低溶液離子強度溶液中所測得吸附態DNA的擴散係數與環動半徑則與理論模型預測有大幅偏差。我們推測此現象與DNA吸附後因為靜電交互作用力造成脂雙層局部組成比例改變有關，故運用模擬方法加以解析。 本研究運用布朗動態法（Brownian dynamics, BD）模擬DNA吸附於帶正電荷的脂雙層之行為，使用鏈球模型（bead-spring model）作為DNA的模型，首先設置一電荷密度均勻的xy平面作為對照組，接著分別以局部非勻相脂雙層模型（local heterogeneous model）和由兩種電荷密度不同且只在xy平面運動的小球所組成的可流動脂雙層模型來加以檢驗。在勻相脂雙層模型下，DNA行為為正規擴散，但沒有實驗中所觀察到的次級擴散（sub-diffusion）。在局部非勻相脂雙層模型下，吸附態DNA運動出現許多黏滯點（sticky points），有觀察到次級擴散（sub-diffusion）但沒有正規擴散（normal diffusion）。 我們推測吸附態DNA的正規擴散行為是來自脂雙層的運動，因此我們利用在xy平面運動並有著不同電荷密度的兩種小球來模擬二維脂雙層的運動，同時此模型能因與DNA的靜電交互作用力而自然形成局部非勻相。在可流動脂雙層模型中，我們分別以脂雙層電荷密度和溶液離子強度為變因。首先在固定溶液離子強度下，隨著脂雙層電荷密度增加，DNA從部分吸附轉變為完全吸附於脂雙層表面，其擴散係數有顯著的下降，環動半徑也隨之增加，但當電荷密度增加到足以將DNA完全吸附於脂雙層表面後，繼續增加脂雙層電荷密度對DNA擴散係數卻沒有太大影響；環動半徑則些微增大。接著，通過改變德拜長度（Debye length）得以實現改變模擬系統中的溶液離子強度，隨著德拜長度增加，相當於降低溶液離子強度，DNA從部分吸附轉變為完全吸附於脂雙層表面，然而當DNA完全吸附於脂雙層表面後，再增加德拜長度（降低溶液離子強度）對DNA擴散係數一樣沒有太大的影響；環動半徑則小幅度增大。模擬結果與實驗中所觀察到的結果大相逕庭，並且未出現實驗中所觀察到的次級擴散行為。 通過模擬得知，（１）吸附態DNA的正規擴散行為來自脂雙層的運動（２）脂雙層局部非勻相並不會對侷限DNA而造成次級擴散行為。結合上述模擬的分析並配合實驗中觀察到的現象，我們推測造成DNA次級擴散行為來自基材表面缺陷而形成的局部位能井，故我們於可運動的二維脂雙層模型中加入數個位置固定，不具體積的點電荷來模擬位能井。通過改變井的電荷密度，使得吸附態DNA出現不同程度的次級擴散行為，並且發現在高電荷密度以及低溶液離子強度，DNA初始吸附後確實會因位能井之侷限而無法延展，與我們實驗中所觀察到的現象一致，也就是模擬結果支持基材表面存在位能井的假設。

It is observed in the experiments that when DNA is adsorbed on a positive charged lipid bilayer, its behavior follows Rouse model in two dimension. Moreover, the charge density of the lipid bilayer and the ionic strength of the solution have a significant influence on the behavior of adsorbed DNA. In our experimental observations, the diffusivity and the radius of gyration of the adsorbed DNA with low charge density of lipid bilayers and high ionic strength solution are in good agreement with the theoretical prediction. However, DNA behavior greatly deviates from the theoretical prediction when the measurement is taken at the lipid bilayer with high positive charge density or in the solution with low ionic strength. We supposed that this deviation is related to the change of the local composition of the lipid bilayer due to electrostatic interaction after DNA is adsorbed. Therefore, we intend to parse it with the help of simulation. We used Brownian dynamics (BD) with bead-spring model to simulate the behavior of DNA adsorbed on positively charged lipid bilayers. We first set up a fixed lipid bilayer model with a uniform charge density and a local heterogeneous model. In the local heterogeneous lipid bilayer model, there existed many sticky points and sub-diffusion is also observed. However, normal diffusion DNA was not observed. We speculated that the normal diffusion of adsorbed DNA comes from the movement of the lipids. Therefore, we used beads with different charges to simulate the lipids in two-dimensional bilayer. This model, called mobile lipid bilayer model, also allows the interaction between DNA and lipids, and therefore local heterogeneity can naturally occur. Under a constant ionic strength, the DNA conformation changes from partial adsorption to complete adsorption on the surface of the lipid bilayer as the charge density of the lipid bilayer increases. Furthermore, DNA radius of gyration increases but DNA diffusivity decreases. However, after the surface charge density is high enough to completely adsorb the DNA, increasing the charge density of the lipid bilayer does not have much effect on the DNA diffusivity and its radius of gyration. Under constant lipid charge density, we found that decreasing ionic strength has similar effects as increasing lipid charge density in our simulations. These results were quite different from those observed in our experiments, and the sub-diffusion observed in the experiment did not occur in this model. From the simulation results, we have deduced that (1) the normal diffusion behavior of the adsorbed DNA comes from the movement of the lipids and (2) the local heterogeneity in system with mobile lipids does not restrict DNA motion and not cause the sub-diffusion. (3) Fixed charges can form sticky points and induce sub-diffusion. Combining above simulation analysis with the phenomenon observed in the experiments, we suspected that the surface defects might form several local energy wells which confine DNA motion. To simulate the effect of these energy wells, we added several fixed charge points without volume to the mobile lipid bilayer model to mimic the local energy well. By changing the charges of the energy well, the adsorbed DNA exhibits different degrees of sub-diffusion behavior. Moreover, we found that DNA is confined between fixed charges and cannot reach its equilibrium conformation at low ionic strength condition, consistent with our observation in experiments. Therefore, the simulation results support our postulation that there are potential wells existing on the lipid bilayers.