Some physical properties of hydrated biomolecules, e.g., the occurrence of a boson peak, have been recognized to resemble those of glassy states. The present work shows that quantum fluctuations play a fundamental role in describing the glassy state of biomolecules, particularly at lower hydration levels. There is a linear relationship between the quantumness and the slope of the temperature dependence of the boson peak frequency, which is used to classify the extent of quantum contributions to the glassy state of glasses in general. Lastly, we demonstrate that the boson peak two-band spectral structure that is observed in some cases can be directly linked to the anisotropy of the elastic properties of the material. The amino acid L-cysteine is studied in detail. The findings are compared with previously reported data for other macromolecules.