The general question by what mechanism an "effector" molecule and the hemes of hemoglobin interact over widely separated intramolecular distances to change the oxygen affinity has been extensively investigated, and still has remained of central interest. In the present work we were interested in clarifying the general role of the protein matrix and its dynamics in the regulation of human adult hemoglobin (HbA). We used a spectroscopy approach that yields the compressibility (κ) of the protein matrix around the hemes of the subunits in HbA and studied how the binding of heterotropic allosteric effectors modify this parameter. κ is directly related to the variance of volume fluctuation, therefore it characterizes the molecular dynamics of the protein structure. For the experiments the heme groups either in the α or in the β subunits of HbA were replaced by fluorescent Zn-protoporphyrinIX, and series of fluorescence line narrowed spectra were measured at varied pressures. The evaluation of the spectra yielded the compressibility that showed significant dynamic asymmetry between the subunits: κ of the α subunit was 0.17±0.05/GPa, while for the β subunit it was much higher, 0.36±0.07/GPa. The heterotropic effectors, chloride ions, inositol hexaphosphate and bezafibrate did not cause significant changes in κ of the α subunits, while in the β subunits the effectors lead to a significant reduction down to 0.15±0.04/GPa. We relate our results to structural data, to results of recent functional studies and to those of molecular dynamics simulations, and find good agreements. The observed asymmetry in the flexibility suggests a distinct role of the subunits in the regulation of Hb that results in the observed changes of the oxygen binding capability.