Argonaute with stepwise endonuclease activity promotes specific and multiplex nucleic acid detection

Argonaute proteins (Agos) from thermophiles function as endonucleases via guide-target base-pairing cleavage for host defense. Since guides play a key role in regulating the catalytic specificity of Agos, elucidating its underlying molecular mechanisms would promote the application of Agos in the medical sciences. Here, we reveal that an Ago from Pyrococcus furiosus (PfAgo) showed a stepwise endonuclease activity, which was demonstrated through a double-stranded DNA cleavage directed by a single guide DNA (gDNA) rather than a canonical pair of gDNAs. We validated that the cleavage products with 5'-phosphorylated ends can be used as a new guide to induce a new round of cleavage. Based on the reprogrammable capacity of Ago’s stepwise activity, we established a rapid and specific platform for unambiguous multiplex gene detection, termed Renewed-gDNA Assisted DNA cleavage by Argonaute (RADAR). Combined with a pre-amplification step, RADAR achieved sensitivity at the femtomolar level and specificity with at least a di-nucleotide resolution. Furthermore, RADAR simultaneously discriminated among multiple target sequences simply by corresponding multiple guides. We successfully distinguished four human papillomavirus serotypes from patient samples in a single reaction. Our technique, based on the unique properties of Ago, provides a versatile and sensitive method for molecular diagnosis.

The Dual Complex of a Semi-log Canonical Surface

Semi-log canonical varieties are a higher-dimensional analogue of stable curves. They are the varieties appearing as the boundary $\Delta $ of a log canonical pair $(X,\Delta )$ and also appear as limits of canonically polarized varieties in moduli theory. For certain three-fold pairs $(X,\Delta ),$ we show how to compute the PL homeomorphism type of the dual complex of a dlt minimal model directly from the normalization data of $\Delta $.

On the log canonical ring with Kodaira dimension two

We prove that the log canonical ring of a projective log canonical pair with Kodaira dimension two is finitely generated.

Cis-regulatory basis of sister cell type divergence in the vertebrate retina

Multicellular organisms evolved via repeated functional divergence of transcriptionally related sister cell types, but the mechanisms underlying sister cell type divergence are not well understood. Here, we study a canonical pair of sister cell types, retinal photoreceptors and bipolar cells, to identify the key cis-regulatory features that distinguish them. By comparing open chromatin maps and transcriptomic profiles, we found that while photoreceptor and bipolar cells have divergent transcriptomes, they share remarkably similar cis-regulatory grammars, marked by enrichment of K50 homeodomain binding sites. However, cell class-specific enhancers are distinguished by enrichment of E-box motifs in bipolar cells, and Q50 homeodomain motifs in photoreceptors. We show that converting K50 motifs to Q50 motifs represses reporter expression in bipolar cells, while photoreceptor expression is maintained. These findings suggest that partitioning of Q50 motifs within cell type-specific cis-regulatory elements was a critical step in the evolutionary divergence of the bipolar transcriptome from that of photoreceptors.

Cis-regulatory basis of sister cell type divergence in the vertebrate retina

Multicellular organisms evolved via repeated functional divergence of transcriptionally related sister cell types, but the mechanisms underlying sister cell type divergence are not well understood. Here, we study a canonical pair of sister cell types, retinal photoreceptors and bipolar cells, to identify the key cis-regulatory features that distinguish them. By comparing open chromatin maps and transcriptomic profiles, we found that while photoreceptor and bipolar cells have divergent transcriptomes, they share remarkably similar cis-regulatory grammars, marked by enrichment of K50 homeodomain binding sites. However, cell class-specific enhancers are distinguished by enrichment of E-box motifs in bipolar cells, and Q50 homeodomain motifs in photoreceptors. We show that converting K50 motifs to Q50 motifs represses reporter expression in bipolar cells, while photoreceptor expression is maintained. These findings suggest that partitioning of Q50 motifs within cell type-specific cis-regulatory elements was a critical step in the divergence of the bipolar transcriptome from that of photoreceptors.

Perturbation analysis of a matrix differential equation ẋ = ABx

Two complex matrix pairs (A, B) and (A′, B′) are contragrediently equivalent if there are nonsingular S and R such that (A′, B′) = (S−1AR, R−1BS). M.I. García-Planas and V.V. Sergeichuk (1999) constructed a miniversal deformation of a canonical pair (A, B) for contragredient equivalence; that is, a simple normal form to which all matrix pairs (A + A͠, B + B͠) close to (A, B) can be reduced by contragredient equivalence transformations that smoothly depend on the entries of A͠ and B͠. Each perturbation (A͠, B͠) of (A, B) defines the first order induced perturbation AB͠ + A͠B of the matrix AB, which is the first order summand in the product (A + A͠)(B + B͠) = AB + AB͠ + A͠B + A͠B͠. We find all canonical matrix pairs (A, B), for which the first order induced perturbations AB͠ + A͠B are nonzero for all nonzero perturbations in the normal form of García-Planas and Sergeichuk. This problem arises in the theory of matrix differential equations ẋ = Cx, whose product of two matrices: C = AB; using the substitution x = Sy, one can reduce C by similarity transformations S−1CS and (A, B) by contragredient equivalence transformations (S−1AR, R−1BS).

Semiample perturbations for log canonical varieties over an F-finite field containing an infinite perfect field

Let [Formula: see text] be an [Formula: see text]-finite field containing an infinite perfect field of positive characteristic. Let [Formula: see text] be a projective log canonical pair over [Formula: see text]. In this note, we show that, for a semi-ample divisor [Formula: see text] on [Formula: see text], there exists an effective [Formula: see text]-divisor [Formula: see text] such that [Formula: see text] is log canonical if there exists a log resolution of [Formula: see text].

Polarized pairs, log minimal models, and Zariski decompositions

We continue our study of the relation between log minimal models and various types of Zariski decompositions. Let (X,B) be a projective log canonical pair. We will show that (X,B) has a log minimal model if either KX + B birationally has a Nakayama–Zariski decomposition with nef positive part, or if KX +B is big and birationally has a Fujita–Zariski or Cutkosky–Kawamata–Moriwaki–Zariski decomposition. Along the way we introduce polarized pairs (X,B +P), where (X,B) is a usual projective pair and where P is nef, and we study the birational geometry of such pairs.

Polarized pairs, log minimal models, and Zariski decompositions

We continue our study of the relation between log minimal models and various types of Zariski decompositions. Let (X,B) be a projective log canonical pair. We will show that (X,B) has a log minimal model if eitherKX+Bbirationally has a Nakayama–Zariski decomposition with nef positive part, or ifKX+Bis big and birationally has a Fujita–Zariski or Cutkosky–Kawamata–Moriwaki–Zariski decomposition. Along the way we introduce polarized pairs (X,B+P), where (X,B) is a usual projective pair and wherePis nef, and we study the birational geometry of such pairs.