The electronic structure of turnip cytochrome f has been investigated by CNDO method. The crystallographic coordinates were obtained from the Protein Data Bank at Brookhaven National Laboratory. The protein chain was truncated to separate the entity Cyt-f that retains the essential structural features of cytochrome f. Thus Cyt-f consists of the basic heme unit, one water molecule hydrogen bonded to a carboxylic acid substituent of the heme unit, and one tyrosine residue and one histidine residue along the axial positions on top and below the iron atom, respectively. The central metal atom's orbital angular momenta are found to be fully quenched. The HOMOs and the first few LUMOs are basically the π orbitals of the porphyrin macrocycle. Since the latter orbitals are quasi-degenerate, the Fe complex always has a high-spin ground state. Both heme and Cyt-f have pentet (2S + 1 = 5) ground states. The CNDO calculations indicate that the quartet (2S + 1 = 4) state is slightly more stable than the hextet (2S + 1 = 6) state for the oxidized forms of heme and Cyt-f; but the relative stability is so small that even the inclusion of only the monatomic exchange integrals would lead the spin hextets to clearly emerge as the ground states of respective cations. Hence the redox potentials were calculated with the pentet states of the reduced forms and the hextet states of the oxidized species. The reduction potential calculated for Cyt-f + in an aqueous solution at pH 7 is 0.295 V at 25 °C. This is in excellent agreement with the experimentally determined midpoint potential 0.365 V for the reduction of cytochrome f cation. The calculated potential for the species in the condensed phase of thylakoid is 0.398 V which agrees with the placement of cytochrome f in Z-scheme. Significant deviations in calculated potentials can be observed in the absence of histidine and tyrosine residues, which indicates the importance of these axial ligands in the evolution of the redox properties of cytochrome f.

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We present a method for dimensionality reduction of an affine variational inequality (AVI) defined over a compact feasible region. Centered around the Johnson Lindenstrauss lemma [16], our method is a randomized algorithm that produces with high probability an approximate solution for the given AVI by solving a lower-dimensional AVI. The algorithm allows the lower dimension to be chosen based on the quality of approximation desired. The algorithm can also be used as a subroutine in an exact algorithm for generating an initial point close to the solution. The lower-dimensional AVI is obtained by appropriately projecting the original AVI on a randomly chosen subspace. The lower-dimensional AVI is solved using standard solvers and from this solution an approximate solution to the original AVI is recovered through an inexpensive process. Our numerical experiments corroborate the theoretical results and validate that the algorithm provides a good approximation at low dimensions and substantial savings in time for an exact solution.