樹狀體高分子具有可以被質子化的氨基，且在生理學上及酸性的環境中對於基因治療會和DNA產生具有靜電錯合力的巨陽離子，稱為”dendriplex”。在使用小角度X-ray散射和小角度中子散射的過程中，我們利用DNA和第四代的PAMAM dendrimer 在電荷密度與N/P的比例關係上建構相圖。當在固定nominal N/P比例的狀態下隨著dendrimer電荷密度增加，結構的轉變會從四面柱狀堆積轉變成DNA會以超螺旋形式存在的六角堆積，而最後在變成beads-on-string 結構。從相的轉變中，可以去了解到在DNA的結合自由能和決定於從釋放反離子中得到的熵的charge matching 中的自由能彼此之間的平衡關係。在固定dendrimer 電荷密度下，減少nominal N/P的比例會發現，效應會和增加dendrimer的電荷密度有一樣的效果 ; 也就是說當，在錯合體在處於較低的dendrimer 電荷密度下，有較高的DNA 彎曲率形成會頃向在較低的nominal N/P 比例。N/P比例的影響是歸因於系統頃向增加釋放反離子到水溶液中所得到的熵，藉由降低在水溶液中的free DNA 和dendrimer。實驗結果顯示，反離子的熵在DNA-dendrimer錯合物中扮演決定性的角色，而且此熵的貢獻來自於dendrimer的電荷密度，nominal N/P 比例，以及藉由在製備錯合物中，由DNA濃度和dendrimer的使用。進一步的了解反離子的熵是主要的角色並藉由質子化的酸來影響錯合物，在這邊使用的酸類包含多價酸類H2SO4和H3PO4。

Polyamidoamine (PAMAM) dednrimer bearing well-defined number of amine groups can be protonated under physiological or acidic condition to generate the macrocations capable of forming electrostatic complex (called “dendriplex”) with DNA for gene delivery. Using small angle X-ray scattering (SAXS) and small angle neutron scattering (SANS), here we constructed the morphological map of the complex of DNA with PAMAM dendrimer of generation four (G4) in terms of the dendrimer charge density and the nominal N/P ratio given by the feed molar ratio of dendrimer amine group to DNA phosphate group. With the increase of dendrimer charge density under a given nominal N/P ratio, the structure was found to transform from square columnar phase (in which the DNA chains packed in square lattice were locally straightened) to hexagonally-packed DNA superhelices (in which the DNA chains organizing in a hexagonal lattice twisted moderately into superhelices) and finally to beads-on-string structure (in which DNA wrapped around the dendrimer to form nuclesome-like array). The phase transition sequence was understood from the balance between the bending energy of DNA and the free energy of charge matching governed by the entropic gain from counterion release. Decreasing nominal N/P ratio under fixed dendrimer charge density was found to exert the same effect as increasing dendrimer charge density; that is, the structure with higher DNA curvature tended to form at lower nominal N/P ratio, in particular for the dendriplex with low dendrimer charge density. The effect of N/P ratio was attributed to the tendency of the system to increase the translational entropy of the counterions released to the bulk solution by reducing the concentration of free DNA or dendrimer remained in the solution. The experimental results presented here thus demonstrated the crucial role of counterion entropy in the structural formation of DNA-dendrimer complexes, and this entropic contribution was governed by the dendrimer charge density, the nominal N/P ratio, and the initial concentrations of DNA and dendrimer used for complex preparation. The dominant role of counterion entropy was further verified by examining the effect of protonic acid on the nanostructure of the dendriplex, where the dendrimer was also protonated by multivalent acids, including H2SO4 and H3PO4.

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