The cu c distance would be 25 a if the unpaired

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The Cu-C distance would be 2.5 A if the unpaired electron were completely on the copper ion, as estimated by using Equation (2.1) and a value of 'T c 2.1 x 10 -9 S independently obtained from water IH NMRD. 83 This dis- tance is much too short for a coordinated bicarbonate; however, electron delo- calization on the bicarbonate ligand may account for such a short calculated distance; the possibility of a bidentate type of ligation cannot be discarded. The dissociation rate, which is very low, by itself accounts for the lack of activity of the derivative. For CO 2 , a carbon-copper distance could be calculated if the affinity con- stants of the substrate for the protein were known. When the binding site, if any, starts being saturated, fast exchange with excess ligand (in this case, CO 2 ) decreases the observed paramagnetic effect. From this behavior, the affinity constant may be estimated. For CO 2 the paramagnetic effect remained constant up to I M CO 2 ; i.e., the affinity constant is smaller than I M -I. This means that practically there is no affinity for copper; yet the paramagnetic effect is paradoxically high. 88 Another picture comes by analyzing the NMR data in terms of a pure dif- fusive model. 88 Here Hubbard's equation 91 has been used: (2.16) where IS f (w, 'TD) = "2 1 (u); u = [W'TD] l/2; I(u) = U -5{U 2 - 2 + e U[(u 2 - 2) sin u + (u 2 + 4u + 2) cos un; d is the distance of closest approach, D N and D M are the diffusion coefficients of the molecules containing the nucleus under investigation, and 'TD = 2d 2 j (D N + D M ). The experimental paramagnetic effect can be reproduced with a CO 2 concentration inside the cavity much larger than the one in the bulk solu- tion. This result indicates that substrate does not bind to a specific site, but probably binds in the hydrophobic region. Note that CO 2 is more soluble in organic solvents than in water. The effect of the cavity is to attract CO 2 by interaction either with the metal ion or with a hydrophobic part of the cavity itself. But the affinity constant is in any case lower than expected from the Michaelis constant (see Section IV.B) measured under steady-state conditions, indicating that the latter does not rep- resent the dissociation constant of the enzyme-C0 2 system. In summary, the main information concerning the catalytic cycle obtained from the copper derivative is the structural and kinetic characterization of both
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72 2/ THE REACTION PATHWAYS OF ZINC ENZYMES AND RELATED BIOLOGICAL CATALYSTS CO 2 and HC0 3 - species when they are not interconverting but present within the cavity. In this way we have further proof that HC0 3 - is bound to the metal and that CO 2 is attracted inside the cavity either by hydrophobic interactions or by the metal ion or both. The data obtained on the geometry around copper are consistent with those obtained on cobalt.
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