The best possible lower bound for the Perron root using traces

AbstractLet A be an n×n matrix with real eigenvalues. Wolkowicz and Styan presented bounds for the eigenvalues, using only n, trA, and trA2. We show that their lower bound for the largest eigenvalue works also as a lower bound for the Perron root of A if A is nonnegative and its eigenvalues are not necessarily real. We also show that this bound is optimal under certain conditions. Finally, we solve completely the problem to find the optimal lower bound for the Perron root using only n, trA, and trA2

Additional file 1: Figure S1. of Erv1 of Arabidopsis thaliana can directly oxidize mitochondrial intermembrane space proteins in the absence of redox-active Mia40

Related to Fig. 1. Alignment of members of the Erv1 family. The sequences were compared using Clustal Omega with standard settings of the program. (DOCX 1001 kb

Additional file 3: Figure S3. of Erv1 of Arabidopsis thaliana can directly oxidize mitochondrial intermembrane space proteins in the absence of redox-active Mia40

Related to Fig. 2. The AtErv1-expressing Δerv1 mutant shows increased sensitivity to DTT. A, B For the experiment shown in panel A, 10 μL of 3 M DTT was added to the filter paper placed in the middle of the plates. For the experiment shown in panel B, the following solutions were used: water, 1 M diamide, 1 M DTT or 3 M DTT (10 µL each) or 30% H2O2 (5 μL) as indicated. Cells were grown at 30 °C for 3 days. C Wild-type and Δerv1 cells expressing yeast Erv1or AtErv1 were incubated on glucose plates in the presence (blue color of the indicator strip) or absence (white color of the indicator strip) of oxygen for 5 days at 30 °C. (EPS 142732 kb

Additional file 5: Figure S5. of Erv1 of Arabidopsis thaliana can directly oxidize mitochondrial intermembrane space proteins in the absence of redox-active Mia40

Related to Fig. 5 CCMH appears not to interact with Mia40 during import into AtErv1 mitochondria. A The experiment was performed as described for Fig. 5a, with the exception that Mia40-specific antibodies were used here. Radiolabeled A. thaliana CCMH was incubated for 2 min with isolated mitochondria from the AtErv1-expressing Δerv1 mutant. Mitochondria were treated with 400 μM cleavable cross-linker dithiobis succinimidyl propionate for 5 min at 25 °C and lysed with 1% SDS. The extract was used for immunoprecipitation with a combination of Mia40-specific antibodies or with pre-immune serum. The crosslinker was cleaved with DTT when indicated. Radiolabeled protein was visualized by autoradiography. Total samples contain 10% of the material used per immunoprecipitation reaction. Note that no CCMH was immunoprecipitated here, in contrast to the significant amounts that were pulled down with AtErv1 (Fig. 5a). (EPS 2090 kb

Additional file 6: Figure S6. of Erv1 of Arabidopsis thaliana can directly oxidize mitochondrial intermembrane space proteins in the absence of redox-active Mia40

Related to Fig. 5 Plant Erv1 facilitates import and oxidative folding of proteins in temperature-sensitive mia40 mutants. A Wild-type cells and the temperature-sensitive mia40-3 and mia40-4 mutants harboring either an empty vector or an AtErv1-expressing plasmid were serially dropped on glucose-, galactose-, or glycerol-containing medium. Plates were incubated for 5 days at the indicated temperatures. The expression of plant Erv1 partially restored the growth defect of mia40 strains at restrictive temperature. B The levels of the intermembrane space (IMS) proteins Mia40 and Cmc1 and of the matrix protein Mrpl40 were analyzed by western blotting in the indicated strains. Cells were cultured at permissive (22 °C) or at restrictive (34 °C) conditions before preparation of the protein extract. C Model of the Mia40 reaction cycle in the IMS of Arabidopsis. As described in this study, AtErv1 can directly interact with IMS proteins in order to oxidize them independently of Mia40. AtMia40, which is present in plants though non-essential, might improve the import reaction of certain substrates. (EPS 50673 kb

Development of the Mitochondrial Intermembrane Space Disulfide Relay Represents a Critical Step in Eukaryotic Evolution

The mitochondrial intermembrane space evolved from the bacterial periplasm. Presumably as a consequence of their common origin, most proteins of these compartments are stabilized by structural disulfide bonds. The molecular machineries that mediate oxidative protein folding in bacteria and mitochondria, however, appear to share no common ancestry. Here we tested whether the enzymes Erv1 and Mia40 of the yeast mitochondrial disulfide relay could be functionally replaced by corresponding components of other compartments. We found that the sulfhydryl oxidase Erv1 could be replaced by the Ero1 oxidase or the protein disulfide isomerase from the endoplasmic reticulum, however at the cost of respiration deficiency. In contrast to Erv1, the mitochondrial oxidoreductase Mia40 proved to be indispensable and could not be replaced by thioredoxin-like enzymes, including the cytoplasmic reductase thioredoxin, the periplasmic dithiol oxidase DsbA, and Pdi1. From our studies we conclude that the profound inertness against glutathione, its slow oxidation kinetics and its high affinity to substrates renders Mia40 a unique and essential component of mitochondrial biogenesis. Evidently, the development of a specific mitochondrial disulfide relay system represented a crucial step in the evolution of the eukaryotic cell.ISSN:0737-4038ISSN:1537-171