Recruitment of the ParG Segregation Protein to Different Affinity DNA Sites

ABSTRACT The segrosome is the nucleoprotein complex that mediates accurate plasmid segregation. In addition to its multifunctional role in segrosome assembly, the ParG protein of multiresistance plasmid TP228 is a transcriptional repressor of the parFG partition genes. ParG is a homodimeric DNA binding protein, with C-terminal regions that interlock into a ribbon-helix-helix fold. Antiparallel β-strands in this fold are presumed to insert into the OF operator major groove to exert transcriptional control as established for other ribbon-helix-helix factors. The OF locus comprises eight degenerate tetramer boxes arranged in a combination of direct and inverted orientation. Each tetramer motif likely recruits one ParG dimer, implying that the fully bound operator is cooperatively coated by up to eight dimers. OF was subdivided experimentally into four overlapping 20-bp sites (A to D), each of which comprises two tetramer boxes separated by AT-rich spacers. Extensive interaction studies demonstrated that sites A to D individually are bound with different affinities by ParG (C > A ≈ B ≫ D). Moreover, comprehensive scanning mutagenesis revealed the contribution of each position in the site core and flanking sequences to ParG binding. Natural variations in the tetramer box motifs and in the interbox spacers, as well as in flanking sequences, each influence ParG binding. The OF operator apparently has evolved with sites that bind ParG dissimilarly to produce a nucleoprotein complex fine-tuned for optimal interaction with the transcription machinery. The association of other ribbon-helix-helix proteins with complex recognition sites similarly may be modulated by natural sequence variations between subsites.

On the Σ2-theory of the upper semilattice of Turing degrees

A first-order sentence Φ is Σ2 if there is a quantifier-free formula Θ such that Φ has the form . The Σ2-theory of a structure for a language ℒ is the set of Σ2-sentences of ℒ true in . It was shown independently by Lerman and Shore (see [Le, Theorem VII.4.4]) that the Σ2-theory of the structure = 〈D, ≤ 〉 is decidable, where D is the set of degrees of unsolvability and ≤ is the standard ordering of D. This result is optimal in the sense that the Σ3-theory of is undecidable, a result due to J. Schmerl. (For a proof, see [Le, Theorem VII.4.5]. As Lerman has pointed out, this proof should be corrected by defining θσ to be ∀xσ1(x) rather than ∀x(ψ(x)→ σ1(x)).) Nonetheless, in this paper we extend the decidability result of Lerman and Shore by showing that the Σ2-theory of is decidable, where ⋃ is the least upper bound operator and 0 is the least degree. Of course ⋃ is definable in , but many interesting degree-theoretic results are expressible as Σ2-sentences in the language of ∪ but not as Σ2-sentences in the language of . For instance, Simpson observed that the Posner-Robinson cupping theorem could be used to show that for any nonzero degrees a, b, there is a degree g such that b ≤ a ⋃ g, and b ⋠ g (see [PR, Corollary 6]). However, the Posner-Robinson technique does not seem to suffice to decide the Σ2-theory of ∪. We introduce instead a new method for coding a set into the join of two other sets and use it to decide this theory.