In this paper, we present a new path-following interior-point algorithm for P*(k)-horizontal linear complementarity problems (HLCPs). The algorithm uses only full-Newton steps which has the advantage that no line searchs are needed. Moreover, we obtain the currently best known iteration bound for the algorithm with small-update method, namely, which is as good as the O (Ön+k)log n/e) linear analogue.

In this work‎, ‎we explore the entanglement entropy equipped with the $\kappa$-algebra‎. ‎This entanglement entropy is computed through the geometric setup as performed by Hartman-Maldacena‎, ‎which‎, ‎in their prescription‎, ‎finds that the entropy grows linearly in time‎. ‎In our case‎, ‎we show that the $\kappa$-algebra embedding provides a richer scenario where the third-order corrections in time added from $\kappa$-algebra to entanglement entropy imply that the growth of quantum correlations between subsystems is more intricate than a simple linear increase into the dynamics of black hole thermalization and quantum information flow‎. ‎In the context of holography‎, ‎such corrections suggest that the thermalization process is not instantaneous but involves higher-order interactions between subsystems‎.

Background and Objective: Identifying a milk-clotting enzyme (MCE) with high κ-casein specificity and heat sensitivity remains a challenge in cheese production. Current microbial, plant, and recombinant MCEs often exhibit low clotting activity, poor κ-casein specificity, and high thermostability, compromising cheese quality and increasing production costs. In this study, to address this, we developed a computational pipeline combining structural analysis, machine learning, and molecular dynamics simulation to design approximately 160, 000 peptides from the Rhizomucor miehei protease–Pepstatin A complex (PDB ID: 2RMP). Material and Methods: Single-site mutagenesis, ML-driven affinity re-prediction, and physicochemical filtering yielded 84 peptides. Their specificity as aspartic proteases were validated via predicted Pepstatin A binding and further screened for cross-reactivity with αs1-, αs2-, and β-caseins. Results and Conclusion: Two candidates, Pep1 and Pep2, demonstrated superior κ-casein binding affinities (ΔG =-50. 20 and-39. 07 kcal/mol at 40 °C, respectively), lower melting indices (-4. 05 and-3. 09), and significantly enhanced specificity scores (-10. 85) compared to Rhizomucor miehei protease (ΔG =-33. 9 kcal/mol at 45 °C,melting index = 0. 17,specificity score = 0. 85). These peptides represent promising vegan-and halal-friendly alternatives to chymosins, pending experimental validation. Keywords: Milk-clotting enzymes, Computational peptide design, κ-casein specificity, Thermolabile peptides, Sustainable cheese production, Molecular dynamics simulations, Machine learning, Vegan cheese production, Halal cheese production, Aspartic protease

Kappa casein plays an essential role in the case of micelle stabilization and their size and the specific biological function. Hence, the purpose of this study was to investigate polymorphism in the exon 4 gene of CSN3 using the PCR-RFLP technique. For this purpose, blood samples were taken from 150 Kermani sheep, and genomic DNA was extracted. The polymerase chain reaction (PCR) was performed a pair of specific primer. PCR productions were separated using agarose gel. The amplified fragment was digested with HaeIII enzyme and determining the genotype was performed. The results of this study led to the identification of two genotypes that allele frequencies were estimated by Popgene software. Allele frequency of A and B alleles for CSN3 gene was respectively 70% and 30% for the Kermani sheep population. Chi-square test showed that studied population is not in Hardy-Weinberg equilibrium (P≤ 0. 05). Number of observed allele, number of effective allele, observed heterozygosity, expected heterozygosity, Nei’ s index, mean of heterozygosity and Shanon’ s index were obtained 2, 1. 72, 0. 60, 0. 43, 0. 42, 0. 42 and 0. 61 respectively. In conclusion, it can be concluded that studied Kermani sheep population has a high degree of genetic variability. Therefore, next studies on these animals, especially on native animals should aim to determine crucial relationship between kappa casein genotypes and maternal characteristics, as selection could be enhanced by the inclusion of genetic markers in breeding decisions.

Philadelphia chromosome can be founding 95% of patients with chronic myeloid leukemia (CML) by cytogenetic studies. The fused bcr/abl is transcribed in two types of chimeric mRNA. RT-PCR amplification of these two transcripts have been designed to give two different size products. This assay can detect one positive bcr/abl expressing cell in a back ground of 106 negative bcr/abl cells. The power of this assay is the detection of minimal residual disease (MRD) between 6-12 months following bone marrow transplantation (BMT) is an independent and significant factor that predicts the relapse in future. The aim of optimization was to detect β2 microglobulin (β 2M) mRNA. Detection of β2 mRNA and absence of bcr/abl indicates that the patient is negative for MRD and as a result, there is molecular remission in addition to clinical remission. To monitor MRD we tested a patient's blood sample who had tolerated allogenic BMT 7 years ago. bcr/abl wasn't detected in this patient and only β2 M was observed. This result confirmed the absence of MRD in this case. To effectively monitor minimal leukemic activity after BMT, we used a competitive RT- PCR to quantify expression of the characteristic bcr/abl fusion gene mRNA in patients with CML.    

The genetic polymorphism of goat caseins has raised a considerable research interest due to its relationship with milk composition and technological characteristics important for cheese making. The goat milk also is important in human nutrition because of its quite different composition from bovine milk. In this study, the blood samples of 80 goats were collected from a herd kept in Sanandaj research station. After extraction of genomic DNA, two separate fragments of 407 and 279bp of goat kappa-casein gene located on exon four were amplified using specific primers and analyzed using PCR-SSCP and PCR-RFLP techniques, respectively. The 279-bp fragment had polymorphic restriction sites for Hae III and Taq I endonucleases for alleles E and K, respectively but these alleles were not seen in this population. In the SSCP, 13 different alleles such as A, G, C', J, M, C, H, B'', D/I/L and B'/B were identified. The allele A and B with frequencies of 0.401 and 0.018 were the most frequent and the lowest frequency respectively. The results of this research showed that combination of these two techniques can determine polymorphism presented in the studied population.

The quantification of protein in four mammals’s milk including cow, buffalo, sheep and goat using lowry method based on the measurement of the color intensity formed during reaction between phenolic amino acids and folin-phenol reagent by spectrophotometer at 750 nm, showed highest amount of protein in sheep and lowest in goat’s milk. The results of quantification of different fractions of caseins in above milk samples using Agarose Gel Electrophoresis (AGE) technique showed maximum amount of α-casein in cow’s milk with corresponding minimum β-casein fraction. The highest amount of β-casein was found in goat’s milk with corresponding minimum α-casein. No significant differences were observed in κ-casein fractions in four different kinds of milks.

Kappa-casein, as a major protein component in mammalian milk, plays an essential role in formation and stabilization milk micelles and preventing them from aggregating and therefore, helping to keep calcium phosphate in solution and transfer of calcium and phosphors from animal milk to consumers. Therefore, the objective of the current study was to investigate genetic and phylogenetic analysis of exon 4 of k-casein (CSN3) gene in Iranian camels using 10 blood samples from Dromedary camels and 5 blood samples from Bacterian camels. After DNA extraction, partial DNA fragment (713 bp) of the k-casein gene was amplified and sequenced using specific primers by PCR reaction. Obtained sequences were edited and subsequently were compared with other k-casein gene sequences which were submitted in NCBI data base. The results showed that there were no significant variations among analyzed sequences. Furthermore, the Neighbor-Joining phylogenetic analysis showed that according to k-casein gene sequence, Iranian Dromedary and Bacterian camels have the lowest genetic distance with Lama species.

Milk has long been considered as a complete food supply and supplying part of the daily nutritional needs of humans. Kappa casein has the most important role in stability of casein micelles, size and their specific function among the milk proteins. Also it has an important role in the quality of the produced cheese and speed cottage and the process of changing milk to cheese. Hence, the purpose of this study was to investigate polymorphism in the exon 4 gene of CSN3 using the PCR-RFLP technique. For this purpose, blood samples were taken from 75 goats (Sannan, Raini and wild breeds), and genomic DNA was extracted. The polymerase chain reaction (PCR) was performed for amplification of exon 4 on CSN3 gene with a length of 645bp using a pair of specific primer. PCR productions were separated using agarose gel and it was found that the intended fragment was amplified well. The amplified fragment was digested with HaeIII enzyme and determining the genotype was performed on the 2% agarose. The result of studies carried out on the goat breeds indicated that the population was monomorphic for the kappa casein gene. Lack of the polymorphism, can be because of no mating with others goat breeds, the closed breeding place and small sample size probably, therefore, next studies on more number of these animals should aim to determine crucial relationship between kappa casein genotypes and maternal characteristics, as selection could be enhanced by the inclusion of genetic markers in breeding decisions.