Amyloid fibrils are formed by denatured proteins when the supersaturation of denatured proteins is broken by agitation, such as ultrasonication, or by seeding, although the detailed mechanism of how solubility and supersaturation regulate amyloid formation remains unclear. To further understand the mechanism of amyloid formation, we examined α-synuclein (α-syn) amyloid formation at varying concentrations of SDS, LPA, heparin or NaCl at pH 7.5. Amyloid fibrils were formed below or around the critical micelle concentrations (CMCs) of SDS (2.75 mM) and LPA (0.24 mM), although no fibrils were formed above CMCs. On the other hand, amyloid fibrils were formed with 0.01-2.5 mg/ml of heparin and 0.5-1.0 M NaCl, and amyloid formation was gradually suppressed at higher concentrations of heparin and NaCl. To reproduce these concentration-dependent effects of additives, we constructed two models, (i) the ligand binding-dependent solubility-modulation model and (ii) the cosolute-dependent direct solubility-modulation model, both of which were used by Tanford and colleagues to analyze the additive-dependent conformational transitions of proteins. The solubility of α-syn was assumed to vary depending on the concentration of additives either by the decreased solubility of the additive-α-syn complex (model i) or by the direct regulation of α-syn solubility (model ii). Both models well reproduced additive-dependent bell-shaped profiles of acceleration and inhibition observed for SDS and LPS. As for heparin and NaCl, participation of amorphous aggregates at high concentrations of additives was suggested. The models confirmed that solubility and supersaturation play major roles in driving amyloid formation in vitro, furthering our understanding of the pathogenesis of amyloidosis in vivo.