A O Ivanov

PABP enhances release factor recruitment and stop codon recognition during translation termination

Poly(A)-binding protein (PABP) is a major component of the messenger RNA–protein complex. PABP is able to bind the poly(A) tail of mRNA, as well as translation initiation factor 4G and eukaryotic release factor 3a (eRF3a). PABP has been found to stimulate translation initiation and to inhibit nonsense-mediated mRNA decay. Using a reconstituted mammalian in vitro translation system, we show that PABP directly stimulates translation termination. PABP increases the efficiency of translation termination by recruitment of eRF3a and eRF1 to the ribosome. PABPs function in translation termination depends on its C-terminal domain and its interaction with the N-terminus of eRF3a. Interestingly, we discover that full-length eRF3a exerts a different mode of function compared to its truncated form eRF3c, which lacks the N-terminal domain. Pre-association of eRF3a, but not of eRF3c, with pre-termination complexes (preTCs) significantly increases the efficiency of peptidyl–tRNA hydrolysis by eRF1. This implicates new, additional interactions of full-length eRF3a with the ribosomal preTC. Based on our findings, we suggest that PABP enhances the productive binding of the eRF1–eRF3 complex to the ribosome, via interactions with the N-terminal domain of eRF3a which itself has an active role in translation termination.

The Gromov–Hausdorff metric on the space of compact metric spaces is strictly intrinsic

It is proved that the Gromov-Hausdorff metric on the space of compact metric spaces considered up to an isometry is strictly intrinsic, i.e., the corresponding metric space is geodesic. In other words, each two points of this space (each two compact metric spaces) can be connected by a geodesic. For finite metric spaces a geodesic is constructed explicitly.

Steiner Ratio for Manifolds

The Steiner ratio characterizes the greatest possible deviation of the length of a minimal spanning tree from the length of the minimal Steiner tree. In this paper, estimates of the Steiner ratio on Riemannian manifolds are obtained. As a corollary, the Steiner ratio for flat tori, flat Klein bottles, and projective plane of constant positive curvature are computed.

Stabilization of Locally Minimal Trees

It is proved that any locally minimal tree on Euclidean space can be “stabilized” (i.e., rendered shortest) by adding boundary vertices without changing the initial tree as a set in space. This result is useful for constructing examples of shortest trees.

One-dimensional minimal fillings with negative edge weights

A.O. Ivanov and A.A. Tuzhilin proposed a particular case of Gromov’s minimal fillings problem generalized to the case of stratified manifolds using weighted graphs with a nonnegative weight function as minimal fillings of finite metric spaces. In this paper we introduce generalized minimal fillings, i.e., the minimal fillings where the weight function is not necessarily nonnegative. We prove that for any finite metric space its minimal filling has the minimum weight in the class of its generalized fillings.

The structure of minimal Steiner trees in the neighborhoods of the lunes of their edges

We give a complete description of small neighborhoods of the closures of lunes of the edges of Steiner minimal trees (Theorem 1.1); to this end, we prove a generalization of a stabilization theorem for embedded locally minimal trees [1]; the case of two such disjoint trees is considered (Theorem 2.2).

Planar Manhattan Local Minimal and Critical Networks

One-dimensional branching extremals of Lagrangian-type functionals are considered. Such extremals appear as solutions to the classical Steiner problem on a shortest network, i.e., a connected system of paths that has the smallest total length among all the networks spanning a given finite set of terminal points in the plane. In the present paper, the Manhattan-length functional is investigated, with Lagrangian equal to the sum of the absolute values of projections of the velocity vector onto the coordinate axes. Such functionals are useful in problems arising in electronics, robotics, chip design, etc. In this case, in contrast to the case of the Steiner problem, local minimality does not imply extremality (however, each extreme network is locally minimal). A criterion of extremality is presented, which shows that the extremality with respect to the Manhattan-length functional is a global topological property of networks. Bibliography: 95 titles.

Geometry and topology of local minimal 2-trees

The aim of this paper is to get an effective restriction on the topologies of minimal 2-trees in terms of twisting numbers of the trees and the convexity levels number of the trees boundaries.

SOME PROBLEMS CONCERNING MINIMAL NETWORKS

In this paper we study the geometry of minimal networks on some Riemannian manifolds (each small part of such a network has the smallest possible length). We discuss a complete classification of planar minimal networks spanning convex boundary sets, some results concerning the investigation of minimal networks spanning the vertex set of a regular polygon. Also, to study the bifurcations of a minimal network under a deformation of the boundary of the network, we construct a bifurcation graph. The last section of the paper is devoted to the complete classification of closed (without boundary) minimal networks on a flat torus.

Local structure of Gromov–Hausdorff space around generic finite metric spaces

We investigate the local structure of the space M consisting of isometry classes of compact metric spaces, endowed with the Gromov–Hausdorff metric. We consider finite metric spaces of the same cardinality and suppose that these spaces are in general position, i.e., all nonzero distances in each of the spaces are distinct, and all triangle inequalities are strict. We show that sufficiently small balls in M centered at these spaces and having the same radii are isometric. As consequences, we prove that the cones over such spaces (with the vertices at the single-point space) are isometric; the isometry group of each sufficiently small ball centered at a general position n points space, n ≥ 3, contains a subgroup isomorphic to the symmetric group Sn.