Pathogenicity of Salmonella: SopE-mediated membrane ruffling is independent of inositol phosphate signals

Studies [Zhou, D. Chen, L.-M. Hernandez, L. Shears, S.B. and Galán, J.E. (2001) A Salmonella inositol polyphosphatase acts in conjunction with other bacterial effectors to promote host-cell actin cytoskeleton rearrangements and bacterial internalization. Mol. Microbiol. 39, 248-259] with engineered Salmonella mutants showed that deletion of SopE attenuated the pathogen's ability to deplete host-cell InsP5 and remodel the cytoskeleton. We pursued these observations: In SopE-transfected host-cells, membrane ruffling was induced, but SopE did not dephosphorylate InsP5, nor did it recruit PTEN (a cytosolic InsP5 phosphatase) for this task. However, PTEN strengthened SopE-mediated membrane ruffling. We conclude SopE promotes host-cell InsP5 hydrolysis only with the assistance of other Salmonella proteins. Our demonstration that Salmonella-mediated cytoskeletal modifications are independent of inositolphosphates will focus future studies on elucidating alternate pathogenic consequences of InsP5 metabolism, including ion channel conductance and apoptosis.

Extended formulations, nonnegative factorizations, and randomized communication protocols

An extended formulation of a polyhedron P is a linear description of a polyhedron Q together with a linear map π such that π(Q)=P. These objects are of fundamental importance in polyhedral combinatorics and optimization theory, and the subject of a number of studies. Yannakakis’ factorization theorem (Yannakakis in J Comput Syst Sci 43(3):441–466, 1991) provides a surprising connection between extended formulations and communication complexity, showing that the smallest size of an extended formulation of $$P$$P equals the nonnegative rank of its slack matrix S. Moreover, Yannakakis also shows that the nonnegative rank of S is at most 2^c, where c is the complexity of any deterministic protocol computing S. In this paper, we show that the latter result can be strengthened when we allow protocols to be randomized. In particular, we prove that the base-2 logarithm of the nonnegative rank of any nonnegative matrix equals the minimum complexity of a randomized communication protocol computing the matrix in expectation. Using Yannakakis’ factorization theorem, this implies that the base-2 logarithm of the smallest size of an extended formulation of a polytope P equals the minimum complexity of a randomized communication protocol computing the slack matrix of P in expectation. We show that allowing randomization in the protocol can be crucial for obtaining small extended formulations. Specifically, we prove that for the spanning tree and perfect matching polytopes, small variance in the protocol forces large size in the extended formulation.