From microorganisms to humans, ferritin plays a central role in the biological management of iron. The ferritins function as iron storage and detoxification proteins by oxidatively depositing iron as a hydrous ferric hydroxide mineral core within their shell-like structures. The mechanism by which the mineral core is formed has been the subject of intense investigation for many years. A diiron ferroxidase site located on the H-chain subunit of vertebrate ferritins catalyzes the oxidation of Fe(II) to Fe(III) by molecular oxygen. A previous stopped-flow kinetics study of a transient mu-peroxodiFe(III) intermediate formed at this site revealed very unusual kinetics curves, the shape of which depended markedly on the amount of iron presented to the protein. In the present work, a mathematical model for catalysis is developed that explains the observed kinetics. The model consists of two sequential mechanisms. In the first mechanism, turnover of iron at the ferroxidase site is rapid, resulting in steady-state production of the peroxo intermediate with continual formation of the mineral core until the available Fe(II) in solution is consumed. At this point, the second mechanism comes into play whereby the peroxo intermediate decays and the ferroxidase site is postulated to vacate its complement of iron. The kinetic data reveal for the first time that Fe(II) in excess of that required to saturate the ferroxidase site promotes rapid turnover of Fe(III) at this site and that the ferroxidase site plays a role in catalysis at all levels of iron loading of the protein (48-800 Fe/protein). The data also provide evidence for a second intermediate, a putative hydroperoxodiFe(III) complex, that is a decay product of the peroxo intermediate.

In a recent paper, Gregurick, Alexander, and Hartke ͓S. K. Gregurick, M. H. Alexander, and B. Hartke, J. Chem. Phys. 104, 2684 ͑1996͔͒ proposed a global geometry optimization technique using a modified Genetic Algorithm approach for clusters. They refer to their technique as a deterministic/ stochastic genetic algorithm ͑DS-GA͒. In this technique, the stochastic part is a traditional GA, with the manipulations being carried out on binary-coded internal coordinates ͑atom-atom distances͒. The deterministic aspect of their method is the inclusion of a coarse gradient descent calculation on each geometry. This step avoids spending a large amount of computer time searching parts of the configuration space which correspond to high-energy geometries. Their tests of the technique show it is vastly more efficient than searches without this local minimization. They report geometries for clusters of up to nϭ29 Ar atoms, and find that their computer time scales as O͑n 4.5 ͒. In this work, we have recast the genetic algorithm optimization in space-fixed Cartesian coordinates, which scale much more favorably than internal coordinates for large clusters. We introduce genetic operators suited for real ͑base-10͒ variables. We find convergence for clusters up to nϭ55. Furthermore, our algorithm scales as O͑n 3.3 ͒. It is concluded that genetic algorithm optimization in nonseparable real variables is not only viable, but numerically superior to that in internal candidates for atomic cluster calculations. Furthermore, no special choice of variable need be made for different cluster types; real Cartesian variables are readily portable, and can be used for atomic and molecular clusters with no extra effort.

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