An important component of modern biomedicine is the development and use of hybrid bioactive nanomaterials with a hierarchical structure. The unique physical and chemical properties of low-dimensional aluminum oxyhydroxide nanomaterials with an irregular structure make it a promising base for the creation of hierarchical nanoagents with biological activity. Therefore, it is of fundamental and applied importance to study the interaction of organic molecules and ions of a biological medium with irregular fragments of folded (crumpled) two-dimensional aluminum oxyhydroxide nanostructures. This paper uses all-atom molecular dynamics models to investigate numerically the interaction of AlOOH fragments with a biomolecule and the formation of a hybrid nanocomplex in the zone of a nanosheet defect. The free energy of hybrid complex formation in the region with an irregular structure of AlOOH is estimated using steered molecular dynamics. It is shown by the example of a defect observed as nanosheet folding with a kink that the irregular regions of low-dimensional nanomaterial can play a major role in the adsorption of ions of a biological medium and the formation of hierarchical organo-inorganic complexes with bioactive molecules.