Abstract:
Background and Methodology Toxoplasma gondii causes substantial morbidity, mortality, and costs for healthcare in the developed and developing world. Current medicines are not well tolerated and cause hypersensitivity reactions. The dihydrotriazine JPC-2067-B (4, 6-diamino-1, 2-dihydro-2, 2-dimethyl-1-(3′(2-chloro-, 4-trifluoromethoxyphenoxy)propyloxy)-1, 3, 5-triazine), which inhibits dihydrofolate reductase (DHFR), is highly effective against Plasmodium falciparum, Plasmodium vivax, and apicomplexans related to T. gondii. JPC-2067-B is the primary metabolite of the orally active biguanide JPC-2056 1-(3′-(2-chloro-4-trifluoromethoxyphenyl？oxy)propyloxy)- 5-isopropylbiguanide, which is being advanced to clinical trials for malaria. Efficacy of the prodrug JPC-2056 and the active metabolite JPC-2067-B against T. gondii and T. gondii DHFR as well as toxicity toward mammalian cells were tested. Principal Findings and Conclusions Herein, we found that JPC-2067-B is highly effective against T. gondii. We demonstrate that JPC-2067-B inhibits T. gondii growth in culture (IC50 20 nM), inhibits the purified enzyme (IC50 6.5 nM), is more efficacious than pyrimethamine, and is cidal in vitro. JPC-2067-B administered parenterally and the orally administered pro-drug (JPC-2056) are also effective against T. gondii tachyzoites in vivo. A molecular model of T. gondii DHFR-TS complexed with JPC-2067-B was developed. We found that the three main parasite clonal types and isolates from South and Central America, the United States, Canada, China, and Sri Lanka have the same amino acid sequences preserving key binding sites for the triazine. Significance JPC-2056/JPC-2067-B have potential to be more effective and possibly less toxic treatments for toxoplasmosis than currently available medicines.

Abstract:
In this paper, we show that both 12312-avoiding partitions and 12321-avoiding partitions of the set $[n+1]$ are in one-to-one correspondence with Schr\"oder paths of semilength $n$ without peaks at even level. As a consequence, the refined enumeration of 12312-avoiding (resp. 12321-avoiding) partitions according to the number of blocks can be reduced to the enumeration of certain Schr\"oder paths according to the number of peaks. Furthermore, we get the enumeration of irreducible 12312-avoiding (resp. 12321-avoiding) partitions, which are closely related to skew Dyck paths.

Abstract:
This note provide bijective proofs of two combinatorial identities involving generalized Catalan number $C_{m,5}(n)={m\over 5n+m}{5n+m\choose n}$ recently proposed by Sun.

Abstract:
Recently, Kitaev and Remmel posed a conjecture concerning the generating function for the number of unlabeled $(2+2)$-free posets with respect to number of elements and number of minimal elements. In this paper, we present a combinatorial proof of this conjecture.

Abstract:
A sequence x=x_1 x_2...x_n $ is said to be an ascent sequence of length $n$ if it satisfies x_1=0 and $0\leq x_i\leq asc(x_1x_2...x_{i-1})+1$ for all $2\leq i\leq n$, where $asc(x_1x_2... x_{i-1})$ is the number of ascents in the sequence $x_1x_2... x_{i-1}$. Recently, Duncan and Steingr\'{\i}msson proposed the conjecture that 210-avoiding ascent sequences of length $n$ are equinumerous with 3-nonnesting set partitions of $\{1,2,..., n\}$. In this paper, we confirm this conjecture by showing that 210-avoiding ascent sequences of length $n$ are in bijection with 3-nonnesting set partitions of $\{1,2,..., n\}$ via an intermediate structure of growth diagrams for 01-fillings of Ferrers shapes.

Abstract:
Recently, Mansour and Shattuck related the total number of humps in all of the $(k, a)$-paths of order $n$ to the number of super $(k, a)$-paths, which generalized previous results concerning the cases when $k = 1$ and $a = 1$ or $a = \infty$. They also derived a relation on the total number of peaks in all of the $(k, a)$-paths of order $n$ and the number of super $(k, a)$-paths, and asked for bijective proofs. In this paper, we will give bijective proofs of these two relations.

Abstract:
Recently, Chen et al. derived the generating function for partitions avoiding right nestings and posed the problem of finding the generating function for partitions avoiding right crossings. In this paper, we derive the generating function for partitions avoiding right crossings via an intermediate structure of partial matchings avoiding 2-right crossings and right nestings. We show that there is a bijection between partial matchings avoiding 2-right crossing and right nestings and partitions avoiding right crossings.

Abstract:
Recently, Jel\'{i}nek derived that the number of self-dual interval orders of reduced size $n$ is twice the number of row-Fishburn matrices of size $n$ by using generating functions. In this paper, we present a bijective proof of this relation by establishing a bijection between two variations of upper-triangular matrices of nonnegative integers. Using the bijection, we provide a combinatorial proof of the refined relations between self-dual Fishburn matrices and row-Fishburn matrices in answer to a problem proposed by Jel\'{i}nek.

Abstract:
In this paper, we give bijections between the set of 4123-avoiding down-up alternating permutations of length $2n$ and the set of standard Young tableaux of shape $(n,n,n)$, and between the set of 4123-avoiding down-up alternating permutations of length $2n-1$ and the set of shifted standard Young tableaux of shape $(n+1, n, n-1)$ via an intermediate structure of Yamanouchi words. Moreover, we get the enumeration of 4123-avoiding up-down alternating permutations of even and odd length by presenting bijections between 4123-avoiding up-down alternating permutations and standard Young tableaux.

Abstract:
Here we present a novel assay for assessing the quality of directly labeled fluorescent cDNA prior to microarray hybridization utilizing the Agilent 2100 Bioanalyzer, which employs microfluidic technology for the analysis of nucleic acids and proteins. Using varying amounts of RNase to simulate RNA degradation, we show the strength of this un-advertised assay in determining the relative amounts of cDNA obtained from a direct labeling reaction.Utilization of this method in the lab will help to prevent the costly mistake of hybridizing poor quality direct labeled products to expensive arrays.The use of cDNA and oligonucleotide microarray technology has revolutionized the fields of molecular biology, biochemistry and genetics. The ability to simultaneously evaluate gene expression across tens of thousands of genes gives researchers opportunities not previously afforded to them.RNA extractions have proven to be of large concern for evaluating messenger RNA transcript levels by microarrays and other procedures such as RT-PCR, RNase protection assays and Northern blot analyses. Extraction procedures are still evolving and adapt to meet different needs, such as for pure cell populations [1]. Differences between two RNA extractions from the same source material have been shown to make a significant contribution to technical variance in microarray data [2].Microarray technology utilizes various protocols based in part on reverse transcription and PCR technologies [3,4]. Direct labeling protocols use modified deoxyribonucleotide phosphates (dNTPs) incorporated during a reverse transcription reaction, in which mRNA is copied into cDNA. One possible modification to the dNTPs is the addition of an amino-propagyl cyanine (Cy) fluorescent molecule at the 5-carbon of the pyrimidine base [5,6]. For cDNA and oligonucleotide microarrays, Cy3 and Cy5 are commonly used fluorescent dyes that are excited by different wavelengths of light. Therefore they can be used in combination, one lab