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Publication# Toxin:antitoxin ratio sensing autoregulation of the <i>Vibrio cholerae parDE2</i> module

Abstract

The parDE family of toxin-antitoxin (TA) operons is ubiquitous in bacterial genomes and, in Vibrio cholerae, is an essential component to maintain the presence of chromosome II. Here, we show that transcription of the V. cholerae parDE2 (VcparDE) operon is regulated in a toxin:antitoxin ratio-dependent manner using a molecular mechanism distinct from other type II TA systems. The repressor of the operon is identified as an assembly with a 6:2 stoichiometry with three interacting ParD2 dimers bridged by two ParE2 monomers. This assembly docks to a three-site operator containing 5 '- GGTA-3 ' motifs. Saturation of this TA complex with ParE2 toxin results in disruption of the interface between ParD2 dimers and the formation of a TA complex of 2:2 stoichiometry. The latter is operator binding-incompetent as it is incompatible with the required spacing of the ParD2 dimers on the operator.

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Unbounded operator

In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases. The term "unbounded operator" can be misleading, since "unbounded" should sometimes be understood as "not necessarily bounded"; "operator" should be understood as "linear operator" (as in the case of "bounded operator"); the domain of the operator is a linear subspace, not necessarily the whole space; this linear subspace is not necessarily closed; often (but not always) it is assumed to be dense; in the special case of a bounded operator, still, the domain is usually assumed to be the whole space.

Self-adjoint operator

In mathematics, a self-adjoint operator on an infinite-dimensional complex vector space V with inner product (equivalently, a Hermitian operator in the finite-dimensional case) is a linear map A (from V to itself) that is its own adjoint. If V is finite-dimensional with a given orthonormal basis, this is equivalent to the condition that the matrix of A is a Hermitian matrix, i.e., equal to its conjugate transpose A^∗. By the finite-dimensional spectral theorem, V has an orthonormal basis such that the matrix of A relative to this basis is a diagonal matrix with entries in the real numbers.

Compact operator

In functional analysis, a branch of mathematics, a compact operator is a linear operator , where are normed vector spaces, with the property that maps bounded subsets of to relatively compact subsets of (subsets with compact closure in ). Such an operator is necessarily a bounded operator, and so continuous. Some authors require that are Banach, but the definition can be extended to more general spaces. Any bounded operator that has finite rank is a compact operator; indeed, the class of compact operators is a natural generalization of the class of finite-rank operators in an infinite-dimensional setting.

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