We use pressure tuning of spectral holes to estimate the compressibility of protein molecules by optical means. We found that the compressibility of mesoporphyrin-substituted horseradish peroxidase increases by a factor of three when it incorporates small aromatic H-donor molecules that bind in the vicinity of its heme pocket. Such a dramatic softening of its packing density corresponds to a jump from a compressibility range characteristic for the solid state into that characteristic for liquids.