The Signed Roman Domatic Number of a Digraph

Let $D$ be a finite and simple digraph with vertex set $V(D)$.A {\em signed Roman dominating function} on the digraph $D$ isa function $f:V (D)\longrightarrow \{-1, 1, 2\}$ such that$\sum_{u\in N^-[v]}f(u)\ge 1$ for every $v\in V(D)$, where $N^-[v]$ consists of $v$ andall inner neighbors of $v$, and every vertex $u\in V(D)$ for which $f(u)=-1$ has an innerneighbor $v$ for which $f(v)=2$. A set $\{f_1,f_2,\ldots,f_d\}$ of distinct signedRoman dominating functions on $D$ with the property that $\sum_{i=1}^df_i(v)\le 1$ for each$v\in V(D)$, is called a {\em signed Roman dominating family} (of functions) on $D$. The maximumnumber of functions in a signed Roman dominating family on $D$ is the {\em signed Roman domaticnumber} of $D$, denoted by $d_{sR}(D)$. In this paper we initiate the study of signed Romandomatic number in digraphs and we present some sharp bounds for $d_{sR}(D)$. In addition, wedetermine the signed Roman domatic number of some digraphs. Some of our results are extensionsof well-known properties of the signed Roman domatic number of graphs

On the Signed 22-independence Number of Graphs

In this paper, we study the signed 2-independence number in graphs and give new sharp upper and lower bounds on the signed 2-independence number of a graph by a simple uniform approach. In this way, we can improve and generalize some known results in this area

Control of ϕC31 integrase-mediated site-specific recombination by protein trans-splicing.

Serine integrases are emerging as core tools in synthetic biology and have applications in biotechnology and genome engineering. We have designed a split-intein serine integrase-based system with potential for regulation of site-specific recombination events at the protein level in vivo. The ϕC31 integrase was split into two extein domains, and intein sequences (Npu DnaEN and Ssp DnaEC) were attached to the two termini to be fused. Expression of these two components followed by post-translational protein trans-splicing in Escherichia coli generated a fully functional ϕC31 integrase. We showed that protein splicing is necessary for recombination activity; deletion of intein domains or mutation of key intein residues inactivated recombination. We used an invertible promoter reporter system to demonstrate a potential application of the split intein-regulated site-specific recombination system in building reversible genetic switches. We used the same split inteins to control the reconstitution of a split Integrase-Recombination Directionality Factor fusion (Integrase-RDF) that efficiently catalysed the reverse attR x attL recombination. This demonstrates the potential for split-intein regulation of the forward and reverse reactions using the integrase and the integrase-RDF fusion, respectively. The split-intein integrase is a potentially versatile, regulatable component for building synthetic genetic circuits and devices