The marcus prediction for the normal free energy re

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The Marcus prediction (for the normal free-energy re- gion) amounts to a linear free-energy relation (LFER) for outer-sphere electron transfer. 1. Cross reactions of blue copper proteins Given the measured self-exchange rate constant for stellacyanin (k ll ~ 1.2 X 10 5 M -I S -I), the Marcus cross relation (Equation 6.26a) can be used to calculate the reaction rates for the reduction of eu II-stellacyanin by Fe(EDTA) 2 and the oxidation of Cul-stellacyanin by Co(phenh3+. EO(Cu 2 +/+) for stella- cyanin is 0.18 V vs. NHE, and the reduction potentials and self-exchange rate constants for the inorganic reagents are given in Table 6.3. 66 ,67 For relatively small ~Eo values, 112 is ~ 1; here a convenient form of the Marcus cross relation is log k 12 = 0.5[log k ll + log k 22 + 16.9~E12]' Calculations with k ll , k 22 , and ~E12 from experiments give k 12 values that accord quite closely with the mea- sured rate constants. Cu"S! + Fe(EDTA)2- ~ CUIS! + Fe(EDTA)- kdcalc.) = 2.9 x 10 5 M -I s-I kdobs.) = 4.3 x 105 M -1 s-I (~ET2 = 0.06 V) CUIS! + Co(phenh 3 + ~ Cu"S! + Co(phenh 2 + k 12 (calc.) kdobs.) 1.4 X lOsM- 1 S-l 1.8 x 105 M- 1 s-I (~ET2 = 0.19 V) The success of the Marcus cross relation with stellacyanin indicates that the copper site in the protein is accessible to inorganic reagents. The rate constants
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IV. LONG-RANGE ELECTRON TRANSFER IN PROTEINS 343 Table 6.3 Reduction potentials and self-exchange rate constants for inorganic reagents. Reagent Fe(EDTA) -!2~ Co(phenh 3 +!2+ 0.12 0.37 6.9 X 10 4 9.8 X 10 1 for the reactions of other blue copper proteins with inorganic redox agents show deviations from cross-relation predictions (Table 6.4).68 These deviations sug- gest the following order of surface accessibilities of blue copper sites: stellacy- anin > plastocyanin > azurin. Rate constants for protein-protein electron trans- fers also have been subjected to cross-relation analysis. 69 Table 6.4 Reactions of blue copper proteins with inorganic reagents. Protein Reagent k ,2 (obs.)" ~E~2' V kll(obs.)" kll(calc.)" Stellacyanin Fe(EDTA)2- 4.3 X 10 5 0.064 1.2 X 10 5 2.3 X 10 5 Co(phenh 3 + 1.8 X 10 5 0.186 1.2 X 10 5 1.6 X 10 5 Ru(NH 3 )s Py 3+ 1.94 X 10 5 0.069 1.2 X 10 5 3.3 X 10 5 Plastocyanin Fe(EDTA)2- 1.72 X 105 0.235 -10 3 _10 4 7.3 X 10 1 Co(phen)33 + 1.2 X 10 3 0.009 -10 3 _10 4 1.1 X 10 4 Ru(NH 3 ) spy 3 + 3.88 X 10 3 -0.100 -10 3 _10 4 4.9 X 10 4 Azurin Fe(EDTA)2- 1.39 X 10 3 0.184 2.4 X 10 6 2.8 X 10 -2 Co(phenh H 2.82 X 10 3 0.064 2.4 X 10 6 7.0 X 10 3 Ru(NH 3 )spy 3+ 1.36 X 10 3 0.058 2.4 X 10 6 l.1x 10 3 aM I S -I. IV. LONG-RANGE ELECTRON TRANSFER IN PROTEINS A. Electronic Coupling The electron-transfer reactions that occur within and between proteins typically involve prosthetic groups separated by distances that are often greater than 10 A. When we consider these distant electron transfers, an explicit expression for the electronic factor is required. In the nonadiabatic limit, the rate constant for re- action between a donor and acceptor held at fixed distance and orientation is: 70-73 (6.27) The electronic (or tunneling) matrix element H AB is a measure of the electronic coupling between the reactants and the products at the transition state. The mag-
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344 6 / ELECTRON TRANSFER nitude of R AB depends upon donor-acceptor separation, orientation, and the na- ture of the intervening medium. Various approaches have been used to test the
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