The mechanism of proton uptakes by the secondary ubiquinone (Q(B)) in the reaction center of the photosynthetic bacteria Rhodobacter sphaeroides is investigated theoretically. Two protons are transferred to the secondary ubiquinone (Q(B)) upon two electron transfers to it. The pathways of the proton transfers are explored through molecular dynamics and free-energy calculations by a molecular mechanical method and potential energy surface calculations by a hybrid ab initio quantum mechanical/molecular method. Initial locations of donor protons are identified at Glu-L212 and at Asp-L210. It is shown that the first proton transfer takes place from Glu-L212 to Q(B) through their direct hydrogen bond only when the second electron is transferred to Q(B). The second proton transfer from Asp-L210 to Q(B) proceeds through long-range hydrogen-bond network bridges connecting them. The hydrogen-bond network bridges are occasionally formed with several water molecules in the water molecular structural fluctuation dynamics of the "proton channel". The activation energy barrier along the second proton-transfer path thus formed is consistent with the experimental rate. It is also found that there exist very strong interactions among water molecules and a protonated carboxyl group of Asp-L210, suggesting formation of a hydronium ion in the surroundings of negatively charged acidic groups in the proton channel.