Gaugement of the inner space of the apomyoglobin's heme binding site by a single free diffusing proton. I. Proton in the cavity.

Time resolved fluorimetry was employed to monitor the geminate recombination between proton and excited pyranine anion locked, together with less than 30 water molecules, inside the heme binding site of Apomyoglobin (sperm whale). The results were analyzed by a numerical reconstruction of the differential rate equation for time-dependent diffusion controlled reaction with radiating boundaries using N. Agmon's procedure (Huppert, Pines, and Agmon, 1990, J. Opt. Soc. Am. B., 7:1541-1550). The analysis of the curve provided the effective dielectric constant of the proton permeable space in the cavity and the diffusion coefficient of the proton. The electrostatic potential within the cavity was investigated by the equations given by Gilson et al. (1985, J. Mol. Biol., 183:503-516). According to this analysis the dielectric constant of the protein surrounding the site is epsilon prot < or = 6.5. The diffusion coefficient of the proton in the heme binding site of Apomyoglobin-pyranine complex is D = 4 x 10(-5) cm2/s. This value is approximately 50% of the diffusion coefficient of proton in water. The lower value indicates enhanced ordering of water in the cavity, a finding which is corroborated by a large negative enthropy of binding delta S0 = -46.6 cal.mole-1 deg-1. The capacity of a small cavity in a protein to retain a proton had been investigated through the mathematical reconstruction of the dynamics. It has been demonstrated that Coulombic attraction, as large as delta psi of energy coupling membrane, is insufficient to delay a free proton for a time frame comparable to the turnover time of protogenic sites.