A note on scalable frames

We study the problem of determining whether a given frame is scalable, and when it is, understanding the set of all possible scalings. We show that for most frames this is a relatively simple task in that the frame is either not scalable or is scalable in a unique way, and to find this scaling we just have to solve a linear system. We also provide some insight into the set of all scalings when there is not a unique scaling. In particular, we show that this set is a convex polytope whose vertices correspond to minimal scalings

Verification of DNA motifs in Arabidopsis using CRISPR/Cas9-mediated mutagenesis.

Transcription factors (TFs) and chromatin-modifying factors (CMFs) access chromatin by recognizing specific DNA motifs in their target genes. Chromatin immunoprecipitation followed by next-generation sequencing (ChIP-seq) has been widely used to discover the potential DNA-binding motifs for both TFs and CMFs. Yet, an in vivo method for verifying DNA motifs captured by ChIP-seq is lacking in plants. Here, we describe the use of clustered regularly interspaced short palindromic repeat (CRISPR)/CRISPR-associated 9 (Cas9) to verify DNA motifs in their native genomic context in Arabidopsis. Using a single-guide RNA (sgRNA) targeting the DNA motif bound by REF6, a DNA sequence-specific H3K27 demethylase in plants, we generated stable transgenic plants where the motif was disrupted in a REF6 target gene. We also deleted a cluster of multiple motifs from another REF6 target gene using a pair of sgRNAs, targeting upstream and downstream regions of the cluster, respectively. We demonstrated that endogenous genes with motifs disrupted and/or deleted become inaccessible to REF6. This strategy should be widely applicable for in vivo verification of DNA motifs identified by ChIP-seq in plants