Amyloid fibrils are known to be responsible for several neurological disorders, like Alzheimer's disease (AD), Parkinson's disease (PD), etc. For decades, mostly proteins and peptide-based amyloid fibrils have been focused on, and the topic has acknowledged the rise, development, understanding of, and controversy, as well. However, the single amino acid based amyloid fibrils, responsible for several disorders, such as phenylketonuria, tyrosenimia type II, hypermethioninemia, etc., have gotten scientific attention lately. To understand the molecular level pathogenesis of such disorders originated due to the accumulation of single amino acid-based amyloid fibrils, interaction of these fibrils with phospholipid vesicle membranes is found to be an excellent cell-free in vitro setup. Based on such an in vitro setup, these fibrils show a generic mechanism of membrane insertion driven by electrostatic and hydrophobic effects inside the membrane that reduces the integral rigidity of the membrane. Alteration of such fundamental properties of the membrane, therefore, might be referred to as one of the prime pathological factors for the development of these neurological disorders. Hence, such interactions must be investigated in cellular and intracellular compartments to design suitable therapeutic modulators against fibrils.