Oxygen equilibrium curves of the purified hemoglobin component I from the Atlantic bluefin tuna (Thunnus thynnus) have been determined between pH 6.5 and 8.75 at 25 degrees C, and for five temperatures between 10 and 30 degrees C at pH 7.0 and 7.5. From the equilibrium data oxygen equilibrium constants for four oxygenation steps, Ki (i = 1 to 4) were estimated. The number of the Bohr protons released on the ith oxygenation (delta Hi+), and the enthalpy and entropy changes at each oxygenation step (delta Hi and delta Si) were calculated. The Hill plot for oxygenation below neutral pH is biphasic; the top asymptote lies to the right of the bottom one and the linking limb between them exhibits a slope less than unity, exhibiting apparent negative co-operativity. The values of K1 and K2 exhibit little pH dependence, while those of K3 and K4 increase by two orders of magnitudes as the pH is changed from 6.5 to 8.75. In consequence, oxygen equilibrium above neutral pH exhibits a normal positive co-operativity. The oxygen equilibrium at lower temperature is biphasic as is that below neutral pH. The shape of the Hill plot is temperature-dependent. The affinity at low saturation decreases, and that at high saturation increases upon raising the temperature from 10 to 30 degrees C, resulting in crossing of the middle portion of the equilibrium curves at different temperatures. The delta H1 and delta H2 values are negative as are those of most other hemoglobins, but the delta H3 and delta H4 values are positive. Consideration of these results in a framework of the allosteric model extended to take account of differences between subunits has indicated that the deoxy quaternary structure is stabilized at low pH or low temperature, and that subunit heterogeneity gives rise to the biphasic oxygen equilibrium curve. An analysis of delta Hi+ suggests that the large number of the Bohr groups is responsible for the biased allosteric equilibrium towards the deoxy quaternary structure. The positive delta H3 and delta H4 values are also considered to arise from the large endothermic contribution of the Bohr protons released at the third and fourth steps of oxygenation.