| 1. |
- Bajo, Esme, et al.
(författare)
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Weighted Ehrhart theory: Extending Stanley's nonnegativity theorem
- 2024
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Ingår i: Advances in Mathematics. - : Elsevier BV. - 0001-8708 .- 1090-2082. ; 444
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Tidskriftsartikel (refereegranskat)abstract
- We generalize R. P. Stanley's celebrated theorem that the h⁎-polynomial of the Ehrhart series of a rational polytope has nonnegative coefficients and is monotone under containment of polytopes. We show that these results continue to hold for weighted Ehrhart series where lattice points are counted with polynomial weights, as long as the weights are homogeneous polynomials decomposable as sums of products of linear forms that are nonnegative on the polytope. We also show nonnegativity of the h⁎-polynomial as a real-valued function for a larger family of weights. We explore the case when the weight function is the square of a single (arbitrary) linear form. We show stronger results for two-dimensional convex lattice polygons and give concrete examples showing tightness of the hypotheses. As an application, we construct a counterexample to a conjecture by Berg, Jochemko, and Silverstein on Ehrhart tensor polynomials.
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| 2. |
- Woestenenk, Esmeralda A., et al.
(författare)
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The solution structure of ribosomal protein L18 from Thermus thermophilus reveals a conserved RNA-binding fold
- 2002
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Ingår i: Biochemical Journal. - 0264-6021 .- 1470-8728. ; 363:3, s. 553-561
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Tidskriftsartikel (refereegranskat)abstract
- We have determined the solution structure of ribosomal protein L18 from Thermus thermophilus. L18 is a 12.5 kDa protein of the large subunit of the ribosome and binds to both 5 S and 23 S rRNA. In the uncomplexed state L18 folds to a mixed α/β globular structure with a long disordered N-terminal region. We compared our high-resolution structure with RNA-complexed L 18 from Haloarcula marismortui and T. thermophilus to examine RNA-induced as well as species-dependent structural differences. We also identified T. thermophilus S11 as a structural homologue and found that the structures of the RNA-recognition sites are conserved. Important features, for instance a bulge in the RNA-contacting β-sheet, are conserved in both proteins. We suggest that the L18 fold recognizes a specific RNA motif and that the resulting RNA-protein-recognition module is tolerant to variations in sequence.
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| 3. |
- Öhman, Anders, et al.
(författare)
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NMR structure of the ribosomal protein L23 from Thermus thermophilus.
- 2003
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Ingår i: Journal of Biomolecular NMR. - 0925-2738 .- 1573-5001. ; 26:2
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Tidskriftsartikel (refereegranskat)abstract
- The ribosomal protein L23 is a component of the large ribosomal subunit in which it is located close to the peptide exit tunnel. In this position L23 plays a central role both for protein secretion and folding. We have determined the solution structure of L23 from Thermus thermophilus. Uncomplexed L23 consists of a well-ordered part, with four anti-parallel beta-strands and three alpha-helices connected as beta-alpha-beta-alpha-beta-beta-alpha, and a large and flexible loop inserted between the third and fourth beta-strand. The observed topology is distantly related to previously known structures, primarily within the area of RNA biochemistry. A comparison with RNA-complexed crystal structures of L23 from T. thermophilus, Deinococcus radiodurans and Haloarcula marismourtui, shows that the conformation of the well-ordered part is very similar in the uncomplexed and complexed states. However, the flexible loop found in the uncomplexed solution structure forms a rigid extended structure in the complexed crystal structures as it interacts with rRNA and becomes part of the exit tunnel wall. Structural characteristics of importance for the interaction with rRNA and with the ribosomal protein L29, as well as the functional role of L23, are discussed.
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