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https://www.selleckchem.com/products/nvp-cgm097.html In 2004, Pachter and Speyer introduced the higher dissimilarity maps for phylogenetic trees and asked two important questions about their relation to the tropical Grassmannian. Multiple authors, using independent methods, answered affirmatively the first of these questions, showing that dissimilarity vectors lie on the tropical Grassmannian, but the second question, whether the set of dissimilarity vectors forms a tropical subvariety, remained opened. We resolve this question by showing that the tropical balancing condition fails. However, by replacing the definition of the dissimilarity map with a weighted variant, we show that weighted dissimilarity vectors form a tropical subvariety of the tropical Grassmannian in exactly the way that Pachter and Speyer envisioned. Moreover, we provide a geometric interpretation in terms of configurations of points on rational normal curves and construct a finite tropical basis that yields an explicit characterization of weighted dissimilarity vectors.Metal ions are vital to metabolism, as they can act as cofactors on enzymes and thus modulate individual enzymatic reactions. Although many enzymes have been reported to interact with metal ions, the quantitative relationships between metal ions and metabolism are lacking. Here, we reconstructed a genome-scale metabolic model of the yeast Saccharomyces cerevisiae to account for proteome constraints and enzyme cofactors such as metal ions, named CofactorYeast. The model is able to estimate abundances of metal ions binding on enzymes in cells under various conditions, which are comparable to measured metal ion contents in biomass. In addition, the model predicts distinct metabolic flux distributions in response to reduced levels of various metal ions in the medium. Specifically, the model reproduces changes upon iron deficiency in metabolic and gene expression levels, which could be interpreted by optimization principles (i.e., yeas

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