We investigate the structural response of a dense peptide metal-organic framework using in situ powder and single-crystal X-ray diffraction under high-pressures. Crystals of Zn(GlyTyr)2 show a reversible compression by 13% in volume at 4 GPa that is facilitated by the ability of the peptidic linker to act as a flexible string for a cooperative response of the structure to strain. This structural transformation is controlled by changes to the conformation of the peptide, which enables a bond rearrangement in the coordination sphere of the metal and changes to the strength and directionality of the supramolecular interactions specific to the side chain groups in the dipeptide sequence. Compared to other structural transformations in Zn(II) peptide MOFs, this behaviour is not affected by host/guest interactions and relies exclusively on the conformational flexibility of the peptide and its side chain chemistry.