## 4 Discussion  
### Interaction of A\(\beta\) with Planar Membranes  
First, we addressed the interaction between monomeric A\(\beta\) and planar membranes in terms of electrostatic interactions. [PERSON] et al. reported that the net charge of monomeric A\(\beta\) under physiological conditions was slightly negative [30], which was based on calculations using the pKa values for His [13], His [14], Glu [22], and Asp [23] of A\(\beta\) with 40 amino acid residues and Glu [3], Glu [11], His [6], Asp [1], Asp [7], and Tyr [10] of A\(\beta\) with 28 amino acid residues [52; 53]. In the present study, the direct electrostatic attractive or repulsive forces between the aforementioned residues and membranes should be small, considering the chemical structure of zwitterionic phospholipids and nonionic polymers. Even in such a state, the electrostatic interaction between the local charge of planar membranes and the individual charges of charged amino acid residues should be considered. For example, PSf-, DOPC-, and PLLA-50k-based membranes showed higher A\(\beta\) accumulation than the other membranes (Figure 4C). These membranes were zwitterionic or nonionic, based on their chemical structures (see Figure 1). The choline group in phospholipids has two positive and negative charges. These charges behave individually in the interaction between the phospholipids and A\(\beta\). Thus, the interaction of A\(\beta\) with these membranes cannot be simply explained by electrostatic interactions.  
Alternatively, we discuss the non-electrostatic contribution to the A\(\beta\)-membrane interaction. A\(\beta\) has ten hydrophobic amino acid residues: six Val, two Ile, and two Leu. It is possible that these residues behave individually in hydrophobic interactions. PSf contains a hydrophobic benzene group. Therefore, the hydrophobic interaction between the benzene group in PSf and the hydrophobic transmembrane region of A\(\beta\) (Gly29-Val40) with six hydrophobic residues might contribute to the increased accumulation of A\(\beta\). In contrast, PVP, PEG-PE, iso-PMME, and syn-PMMA showed low A\(\beta\) accumulation. PVP, which is widely used as a powerful hydrophillizing agent, is often blended with a PSf-based membrane owing to its improved hydrophilicity [15]. This hydrophilic property of PVP might be related to its weak A\(\beta\) accumulation behavior. In the case of PMMA, a study using sum frequency generation (SFG) vibrational spectroscopy demonstrated the following three aspects [54]: the PMMA surface was dominated by the ester methyl groups; the alpha methyl groups tended to lie down on the PMMA surface; and the methylene groups were not detected on the PMMA surface. In comparison, the surface of the PMMA-based membranes was likely to be hydrophilic. Alternatively, PLLA has a chemical structure similar to PMMA in terms of the inclusion of oxygen in the polymer segment. However, the PLLA-50k-based membrane showed higher A\(\beta\) accumulation than PMMA-based membranes (Figure 4C). Considering PLLA-5k- and PLLA-10k-based membranes, it is possible that A\(\beta\) formed a complex capable of detachment from the surface of the PLLA-based membranes (Figure 4B). Thus, it is likely that these membranes interact strongly with A\(\beta\). Alternatively, in the case of DOPC and DPPC, both have an identical headgroup, called the phosphocholine group, at the interface of lipid membranes. However, DOPC-based membranes, rather than DPPC-based membranes, showed higher A\(\beta\) accumulation (Figure 4C).  
From the aforementioned discussion, it may be inferred that only the argument concerning the chemical structure at the interface of polymer and phospholipid membranes provides an insufficient scenario for the interaction of A\(\beta\) with the membranes.