Emerging nanotechnology has rapidly broadened interfacial prospects of biological molecules with carbon nanomaterials (CNs). A prerequisite for effectively harnessing such hybrid materials is a multi-faceted understanding of their complex interfacial interactions as functions of the physico-chemical characteristics and the surface topography of the individual components. In this article, we address the origins of the curvature dependence of polypeptide adsorption on CN surfaces (CNSs), a phenomenon bearing an acute influence upon the behavior and activity of CN-protein conjugates. Our benchmark molecular dynamics (MD) simulations with the amphiphilic full-length amyloid beta (Aβ) peptide demonstrate that protein adsorption is strongest on the concave (inner) CN surface, weakest on the convex (outer) surface, and intermediary on the planar surface, in agreement with recent experimental reports. The curvature effects, however, are found to manifest non-uniformly between the amino acid subtypes. To understand the underlying interplay of the chemical nature of the amino acids and surface topography of the CNs, we performed high-level quantum chemical (QM) calculations with amino acid analogs (AAA) representing their five prominent classes, and convex, concave and planar CN fragments. Molecular electrostatic potential maps reveal pronounced curvature dependence in the mixing of electron densities, and a resulting variance in the stabilization of the non-covalently bound molecular complexes. Interestingly, our study revealed that the interaction trends of the high-level QM calculations were captured well by the empirical force field. The findings in this study have important bearing upon the design of carbon based bio-nanomaterials, and additionally, provide valuable insights into the accuracy of various computational techniques for probing non-bonded interfacial interactions.