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Purpose The purpose of this study is to develop an algorithm for approximate solutions of nonlinear hyperbolic partial differential equations. Design/methodology/approach In this paper, an algorithm based on the Haar wavelets operational matrix for computational modelling of nonlinear hyperbolic type wave equations has been developed. These types of equations describe a variety of physical models in nonlinear optics, relativistic quantum mechanics, solitons and condensed matter physics, interaction of solitons in collision-less plasma and solid-state physics, etc. The algorithm reduces the equations into a system of algebraic equations and then the system is solved by the Gauss-elimination procedure. Some well-known hyperbolic-type wave problems are considered as numerical problems to check the accuracy and efficiency of the proposed algorithm. The numerical results are shown in figures and Linf, RMS and L2 error forms. Findings The developed algorithm is used to find the computational modelling of nonlinear hyperbolic-type wave equations. The algorithm is well suited for some well-known wave equations. Originality/value This paper extends the idea of one dimensional Haar wavelets algorithms (Jiwari, 2015, 2012; Pandit et al., 2015; Kumar and Pandit, 2014, 2015) for two-dimensional hyperbolic problems and the idea of this algorithm is quite different from the idea for elliptic problems (Lepik, 2011; Shi et al., 2012). Second, the algorithm and error analysis are new for two-dimensional hyperbolic-type problems.

The Wnt/β-catenin pathway regulates expression of the SOX9 gene, which encodes sex-determining region Y-box (SOX) transcription factor 9, a differentiation factor and potential β-catenin regulator. Because APC tumor suppressor defects in approximately 80% of colorectal cancers (CRCs) activate the Wnt/β-catenin pathway, we studied SOX9 inactivation in CRC biology. Compared with effects of Apc inactivation in mouse colon tumors, combined Apc and Sox9 inactivation instigated more invasive tumors with epithelial-mesenchymal transition (EMT) and SOX2 stem cell factor upregulation. In an independent mouse CRC model with combined Apc, Kras, and Trp53 defects, Sox9 inactivation promoted SOX2 induction and distant metastases. About 20% of 171 human CRCs showed loss of SOX9 protein expression, which correlated with higher tumor grade. In an independent group of 376 patients with CRC, low SOX9 gene expression was linked to poor survival, earlier age at diagnosis, and increased lymph node involvement. SOX9 expression reductions in human CRC were linked to promoter methylation. EMT pathway gene expression changes were prominent in human CRCs with low SOX9 expression and in a mouse cancer model with high SOX2 expression. Our results indicate SOX9 has tumor suppressor function in CRC; its loss may promote progression, invasion, and poor prognosis by enhancing EMT and stem cell phenotypes.

Background/Objectives: Tubo-ovarian high-grade serous carcinoma (HGSC) is a highly lethal malignancy, usually diagnosed at an advanced stage due to the lack of early symptoms and biomarkers. Contraceptive hormone use is associated with a reduced risk of HGSC, but the relative contributions of natural versus synthetic progestins, and their interaction with estrogens, are poorly understood. Methods: We evaluated the chemo-preventive efficacy of a synthetic progestin medroxyprogesterone acetate (MPA), progesterone (P4), and combined 17β-estradiol-progesterone (E2 + P4) in a well-characterized genetically engineered mouse model (GEMM) of oviductal HGSC based on the conditional inactivation of one or both alleles of the Brca1, Trp53, Rb1, and Nf1 tumor suppressor genes (BPRN-het and BPRN-homo mice, respectively). Mice received hormones or placebo via slow-release pellets implanted subcutaneously. After induction of tumor formation, the mice were monitored for tumor development, progression, and survival. Tumor incidence was assessed histologically, and hormone effects were further explored via RNA-seq analysis of oviductal tissues. Results: MPA significantly reduced HGSC incidence and delayed tumor progression compared to the placebo, P4, and P4 + E2 in both BPRN-homo and BPRN-het mice, with up to 78% tumor-free survival in the MPA-treated BPRN-het cohort. P4 monotherapy did not provide significant protection vs. the placebo, but the effects of P4 could have been impacted by a failure to achieve sustained release of the hormone beyond 4–8 weeks. The E2 + P4 combination accelerated tumorigenesis and reduced survival (p < 0.0001 in BPRN-homo and p = 0.0004 in BPRN-het mice). MPA did not affect tumorigenesis in a colon cancer GEMM, or the growth of mouse HGSC-derived cells in vivo, suggesting the role of MPA in the early stages of HGSC development. Gene expression analyses showed that P4 and MPA downregulated cholesterol homeostasis, early and late estrogen response, and epithelial–mesenchymal transition pathways, though only MPA afforded tumor protection. Conclusions: These findings demonstrate that a synthetic progestin, specifically MPA, confers robust protection against HGSC development, while a combination including E2 (E2 + P4) increases risk. This work also illustrates how HGSC GEMMs can be used to compare the chemo-preventive effects of various synthetic progestins on HGSC development in order to prioritize the most effective ones for use in preventing HGSC in both general and high-risk populations.

MYC overexpression is a well-established cancer vulnerability, yet direct therapeutic targeting of Myc remains a challenge. Here, we identify DL78 as a potent antimitotic agent with selective anticancer activity through its regulation of Myc. DL78 demonstrated broad efficacy by inhibiting growth across nine cancer types and significantly reducing tumor burden in an in vivo model of platinum-resistant high-grade serous ovarian cancer, with no overt toxicity. DL78 preferentially targets chromosomally unstable, MYC -overexpressing cancer cells, a hallmark of high-grade serous ovarian cancer. Mechanistically, DL78 exploits Myc’s role in mitotic entry by disrupting its interaction with α-tubulin, leading to sustained mitotic arrest, mitotic catastrophe, and apoptosis while sparing nonmalignant cells. This study establishes a novel paradigm for Myc-targeted therapy by introducing DL78, which induces cancer-selective mitotic catastrophe by disrupting Myc’s interaction with α-tubulin rather than its transcriptional activity.

Lineage plasticity is recognized as a critical determinant of lethality and resistance to AR pathway inhibitors in prostate cancer. Lineage plasticity is a continuum, ranging from AR activity-low tumors, AR-null tumors that do not express a neuroendocrine prostate cancer (NEPC) program (i.e., double-negative prostate cancer [DNPC]), and AR-null NEPC tumors. Factors upregulated early in lineage plasticity are not well-characterized. The clarification of such factors is essential to identify tumors undergoing lineage plasticity or at risk of this occurring. Our integrative analysis of metastatic prostate cancer patient tumors, patient-derived xenografts, and cell models determined that PROX1 is upregulated early in the lineage plasticity continuum and progressively increases as tumors lose AR activity. We determined DNA methylation is a key regulator of PROX1 expression. PROX1 suppression in DNPC and NEPC reduces cell survival and impacts apoptosis and differentiation, demonstrating PROX1's functional importance. PROX1 is not directly targetable with standard drug development approaches. However, affinity immunopurification demonstrated histone deacetylases (HDACs) are among the top PROX1-interacting proteins; HDAC inhibition depletes PROX1 and recapitulates PROX1 suppression in DNPC and NEPC. Altogether, our results suggest PROX1 promotes the emergence of lineage plasticity, and HDAC inhibition is a promising approach to treat tumors across the lineage plasticity continuum.

Steady-state gene expression is a coordination of synthesis and decay of RNA through epigenetic regulation, transcription factors, micro RNAs (miRNAs), and RNA-binding proteins. Here, we present bromouride labeling and sequencing (Bru-Seq) and bromouridine pulse-chase and sequencing (BruChase-Seq) to assess genome-wide changes to RNA synthesis and stability in human fibroblasts at homeostasis and after exposure to the proinflammatory tumor necrosis factor (TNF). The inflammatory response in human cells involves rapid and dramatic changes in gene expression, and the Bru-Seq and BruChase-Seq techniques revealed a coordinated and complex regulation of gene expression both at the transcriptional and posttranscriptional levels. The combinatory analysis of both RNA synthesis and stability using Bru-Seq and BruChase-Seq allows for a much deeper understanding of mechanisms of gene regulation than afforded by the analysis of steady-state total RNA and should be useful in many biological settings.

In response to ionizing radiation (IR), cells activate a DNA damage response (DDR) pathway to re-program gene expression. Previous studies using total cellular RNA analyses have shown that the stress kinase ATM and the transcription factor p53 are integral components required for induction of IR-induced gene expression. These studies did not distinguish between changes in RNA synthesis and RNA turnover and did not address the role of enhancer elements in DDR-mediated transcriptional regulation. To determine the contribution of synthesis and degradation of RNA and monitor the activity of enhancer elements following exposure to IR, we used the recently developed Bru-seq, BruChase-seq and BruUV-seq techniques. Our results show that ATM and p53 regulate both RNA synthesis and stability as well as enhancer element activity following exposure to IR. Importantly, many genes in the p53-signaling pathway were coordinately up-regulated by both increased synthesis and RNA stability while down-regulated genes were suppressed either by reduced synthesis or stability. Our study is the first of its kind that independently assessed the effects of ionizing radiation on transcription and post-transcriptional regulation in normal human cells.

Lysine-specific demethylase 1 (LSD1) is a histone demethylase that promotes stemness and cell survival in cancers such as prostate cancer. Most prostate malignancies are adenocarcinomas with luminal differentiation. However, some tumors undergo cellular reprogramming to a more lethal subset termed neuroendocrine prostate cancer (NEPC) with neuronal differentiation. The frequency of NEPC is increasing since the widespread use of potent androgen receptor signaling inhibitors. Currently, there are no effective treatments for NEPC. We previously determined that LSD1 promotes survival of prostate adenocarcinoma tumors. However, the role of LSD1 in NEPC is unknown. Here, we determined that LSD1 is highly upregulated in NEPC versus adenocarcinoma patient tumors. LSD1 suppression with RNAi or allosteric LSD1 inhibitors - but not catalytic inhibitors - reduced NEPC cell survival. RNA-Seq analysis revealed that LSD1 represses pathways linked to luminal differentiation, and TP53 was the top reactivated pathway. We confirmed that LSD1 suppressed the TP53 pathway by reducing TP53 occupancy at target genes while LSD1's catalytic function was dispensable for this effect. Mechanistically, LSD1 inhibition disrupted LSD1-HDAC interactions, increasing histone acetylation at TP53 targets. Finally, LSD1 inhibition suppressed NEPC tumor growth in vivo. These findings suggest that blocking LSD1's noncatalytic function may be a promising treatment strategy for NEPC.

The anti-cancer drug camptothecin inhibits replication and transcription by trapping DNA topoisomerase I (Top1) covalently to DNA in a \"cleavable complex\". To examine the effects of camptothecin on RNA synthesis genome-wide we used Bru-Seq and show that camptothecin treatment primarily affected transcription elongation. We also observed that camptothecin increased RNA reads past transcription termination sites as well as at enhancer elements. Following removal of camptothecin, transcription spread as a wave from the 5'-end of genes with no recovery of transcription apparent from RNA polymerases stalled in the body of genes. As a result, camptothecin preferentially inhibited the expression of large genes such as proto-oncogenes, and anti-apoptotic genes while smaller ribosomal protein genes, pro-apoptotic genes and p53 target genes showed relative higher expression. Cockayne syndrome group B fibroblasts (CS-B), which are defective in transcription-coupled repair (TCR), showed an RNA synthesis recovery profile similar to normal fibroblasts suggesting that TCR is not involved in the repair of or RNA synthesis recovery from transcription-blocking Top1 lesions. These findings of the effects of camptothecin on transcription have important implications for its anti-cancer activities and may aid in the design of improved combinatorial treatments involving Top1 poisons.

Dynamic regulation of gene expression via signal transduction pathways is of fundamental importance during many biological processes such as cell state transitioning, cell cycle progression and stress responses. In this study we used serum stimulation as a cell response paradigm to apply the nascent RNA Bru-seq technique in order to capture early dynamic changes in the nascent transcriptome. Our data provides an unprecedented view of the dynamics of genome-wide transcription during the first two hours of serum stimulation in human fibroblasts. While some genes showed sustained induction or repression, other genes showed transient or delayed responses. Surprisingly, the dynamic patterns of induction and suppression of response genes showed a high degree of similarity, suggesting that these opposite outcomes are triggered by a common set of signals. As expected, early response genes such as those encoding components of the AP-1 transcription factor and those involved in the circadian clock were immediately but transiently induced. Surprisingly, transcription of important DNA damage response genes and histone genes were rapidly repressed. We also show that RNA polymerase II accelerates as it transcribes large genes and this was independent of whether the gene was induced or not. These results provide a unique genome-wide depiction of dynamic patterns of transcription of serum response genes and demonstrate the utility of Bru-seq to comprehensively capture rapid and dynamic changes of the nascent transcriptome.