Entropic Attraction: DNA Condensation and Expansion Induced by Nano-particles in Confinement

本論文旨在研究DNA 在奈米粒子溶液中的行為。熱力學系統處於平衡狀態時，在系統內能變化不大的情況下，自由能將趨向達到最低值，亦即熵趨近於最大值。DNA 於奈米粒子溶液中，隨著奈米粒子濃度增加，奈米粒子對系統總熵佔的比重更大，DNA片段間因而感受到更強大的空乏相吸力，使得DNA尺寸變小。當系統受到奈米侷限(nano-confinement)，邊界限制了DNA與奈米粒子運動方式，進而影響DNA形狀及尺寸隨奈米粒子濃度變化的趨勢。因此，DNA同時受到奈米粒子濃度及奈米侷限的因素控制，其行為比DNA處於自由溶液中複雜許多。 論文首先探討自由溶液中奈米粒子體積濃度百分比、奈米粒子尺寸及DNA高分子鏈長與DNA尺寸的關係，我們模擬的結果與實驗文獻的趨勢相同，DNA處於高濃度的奈米粒子溶液中會產生DNA凝縮現象。接下來我們探討在奈米狹縫(nano-slit)的限制下，狹縫寬、奈米粒子濃度、及邊界與奈米粒子之間的排斥力範圍如何影響DNA形狀與尺寸。最後探討使用奈米狹縫與奈米通道(nano-channel)的異同之處。在研究過程中，我們發現了實驗沒有發現的新奇現象：熵誘發吸引力使DNA緊貼邊界導致DNA自身延展。We investigate nanoparticle-induced DNA condensation in a confined suspension of dilute DNA molecules and ideal nano-particles (NP) using Langevin dynamics simulation. DNA condensation has been observed in a solution of dilute DNA molecules (persistence length Lp ~ 50 nm) and high concentration of electrostatically neutral nano-particles (diameter Sigma_NP ~ 5 to 35 nm) in recent experimental measurements. It is believed that nano-particles entropically induce an attraction between DNA segments. For nano-particles much smaller than Lp, a DNA molecule can be considered as a chain of connected rods, and the nanoparticle-induced depletion attraction between DNA segments can be regarded as rod-rod attraction. Thus, the strength of the depletion attraction is proportional to the number of persistence length in a DNA chain, Np = L/Lp, the depletion volume NpLp^2(Sigma_ NP + Sigma_ M), and the NP volume fraction Phi , where L is the DNA contour length. We performed Langevin dynamics simulation with coarse-grained DNA molecules and accounted for the most important factors: (1) excluded volume forces between a DNA segment and NP, (2) elasticity of the semi-flexible DNA molecule, (3) bending rigidity of the DNA segment, and (4) steric repulsion between DNA segments. In nano-slit confinement with ionic strength corresponding to intra-cellular environment, owing to the repulsion from the walls, the local density of nano-particles near two walls is lower than the central region, which indicates the strength of intra-DNA attraction is weaker near walls. Thus, as the density of nano-particles Phi increases, the DNA chain will be pushed toward one wall. DNA conformation changes are much different from in an unconfined environment. The height of the nano-slit H relative to the nanoparticle size Sigma_ NP strongly influences the DNA conformation. For H/Lp ~ 1, DNA size decreases monotonically as Phi increases. In contrast, the dependence on Phi is non-monotonic for H/Lp ~ 6, due to the competition between DNA-DNA, DNA-NP, DNA-wall and NP-wall interactions.口試委員會審定書 i 致謝 ii 中文摘要 iv Abstract v Contents vii List of Figures ix List of Tables xi 1 Introduction 1 2 Theory 8 2.1 Depletion force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1 Two large colloids immersed in a dilute suspension of short polymers . . . . . . . . . . . . . . . 8 2.1.2 Depletion force of two stiff polymers dissolved in nano-particle solution . . . . . . . . . . . . . . . . . 9 2.2 Statistical model of DNA . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.1 Ideal chain model . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Stiffness of a polymer . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.3 Excluded volume effect . . . . . . . . . . . . . . . . . . . . . . 14 2.2.4 Conformation of single DNA in a nano-channel and a nano-slit . . 15 3 Simulation Methods and System Description 17 3.1 Langevin dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Velocity Verlet and Langevin dynamics . . . . . . . . . . . . . . . . . . 18 3.3 Model of molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3.1 Bonded interaction . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.3.2 Non-bonded interaction . . . . . . . . . . . . . . . . . . . . . . 21 3.4 The unit conversion and the set-up details . . . . . . . . . . . . . . . . . 22 4 Result and Discussion 26 4.1 Nanoparticle-induced DNA condensation in a free solution . . . . . . . . 27 4.2 Conformation of DNA dissolved in nano-particle solution under nano-confinement . . . . . . . . . . . . . . 29 4.2.1 Interaction between confining walls and molecules . . . . . . . . 29 4.2.2 Nano-slit confinement with moderate ionic strength . . . . . . . . 31 4.2.3 Nano-slit confinement with low ionic strength . . . . . . . . . . . 35 4.2.4 Nano-channel confinement . . . . . . . . . . . . . . . . . . . . . 36 5 Summary 39 Bibliography 4