Understanding molecular mechanisms governing interactions of glycosaminoglycans (such as heparin) with proteins remains challenging due to their enormous structural heterogeneity. Commonly accepted approaches seek to reduce the structural complexity by searching for "binding epitopes" within the limited subsets of short heparin oligomers produced either enzymatically or synthetically. A top-down approach presented in this work seeks to preserve the chemical diversity displayed by heparin by allowing the longer and structurally diverse chains to interact with the client protein. Enzymatic lysis of the protein-bound heparin chains followed by the product analysis using size exclusion chromatography with online mass spectrometry detection (SEC/MS) reveals the oligomers that are protected from lysis due to their tight association with the protein, and enables their characterization (both the oligomer length, and the number of incorporated sulfate and acetyl groups). When applied to a paradigmatic heparin/antithrombin system, the new method generates a series of oligomers with surprisingly distinct sulfation levels. The extent of sulfation of the minimal-length binder (hexamer) is relatively modest yet persistent, consistent with the notion of six sulfate groups being both essential and sufficient for antithrombin binding. However, the masses of longer surviving chains indicate complete sulfation of disaccharides beyond the hexasaccharide core. Molecular dynamics simulations confirm the existence of favorable electrostatic interactions between the high charge-density saccharide residues flanking the "canonical" antithrombin-binding hexasaccharide and the positive patch on the surface of the overall negatively charged protein. Furthermore, electrostatics may rescue the heparin/protein interaction in the absence of the canonical binding element.