A fourth algebraic order explicit trigonometrically- fitted modified Runge-Kutta method for the numerical solution of periodic IVPs

This study has constructed an explicit Trigonometrically-Fitted Modified Runge-Kutta (TFMRK) method for solving first-order differential equations with periodic solutions. The newly developed method was made according to the method of Runge-Kutta Dorm and to fourth algebraic order. Numerical results for the new method were compared with the existing method, showing the potential of the new method over other existing methods

A phase-fitted and amplification-fitted modified Runge-Kutta method of fourth order for periodic initial value problems

A new Runge-Kutta method, with phase-fitted and amplification-fitted is constructed for solving first-order ordinary differential equations with periodic solutions. This new method is based on the Runge-Kutta 3/8 Rule with fourth algebraic order. In the numerical results the new method is compared with the existing method; which show that the new method is more efficient

Explicit Runge-Kutta method with trigonometrically-fitted for solving first order ODEs

In this note, an explicit trigonometrically-fitted (RK) method is developed to determine the approximate solution of the first-order IVPs with oscillatory solution. The proposed method solves first order ODEs by first converting the second order ODEs to an equivalent first order; which is based on the RK method of order four. The numerical experiment performed shows the efficacy of our newly developed method

Targeting nuclear transporters in cancer: Diagnostic, prognostic and therapeutic potential

The Karyopherin superfamily is a major class of soluble transport receptors consisting of both import and export proteins. The trafficking of proteins involved in transcription, cell signalling and cell cycle regulation among other functions across the nuclear membrane is essential for normal cellular functioning. However, in cancer cells, the altered expression or localization of nuclear transporters as well as the disruption of endogenous nuclear transport inhibitors are some ways in which the Karyopherin proteins are dysregulated. The value of nuclear transporters in the diagnosis, prognosis and treatment of cancer is currently being elucidated with recent studies highlighting their potential as biomarkers and therapeutic targets

Assessment of DNA-damage repair in breast cancer

Background: Current evidence indicates that DNA damage response (DDR) is a highly complex process that involves various pathways working in an orchestrated and interwoven manner in response to different types of damage to DNA. Although specific defects of DDR remain to be deciphered in cancer as a general, there is certainly an undeniable relationship between a particular dysfunction of DDR and the phenotype of tumour [1, 2]. It has been demonstrated that familial forms of breast and ovarian cancer are characterised by defects in one of the main mechanisms of DDR homologous recombination (HR) as a result of germline loss-of-function mutations in one of HR modifying genes, such as BRCA1 and BRCA2 [1, 3, 4]. Defects of genes involved in other DDR pathways are also associated with specific types of cancers; for instance hereditary non polyposis colorectal cancer (HNPCC) is strongly associated with specific mutations in the DNA mismatch repair pathway. Several previous studies have demonstrated that impaired DDR play a fundamental role in the pathogenesis and behaviour of breast cancer (BC). However, characterisation of this complex process, the expression and co-expression of the key proteins involved in the various DDR pathways and their prognostic significance in BC remain to be defined. In BC, it is reported that genes involved in DNA double strand breaks (DSB) repair are the most important. Two main pathways are involved in the repair of DNA-DSB; HR and Non Homologous End Joining (NHEJ) [3]. The common characteristics of global DDR are multiple genes induction directly associated with sensing and repair of DNA, arrest of cell cycle, and cell division inhibition. As a result DDR process does not only include genes activation involved in damage sensing as well as repair but additionally genes involved in control of cell-cycle [5]. Despite the fact that DDR may possibly involve activation of several pathways (such as SUMOylation (SUMO)) [6, 7] and many genes are engaged in different overlapping mechanisms, each pathway is characterised by activation and expression of a unique set of genes. This could allow discovering the active or aberrant pathway in a given tumour [1, 4, 5]. This study explores the hypothesis that investigation of alterations in the different pathways of DNA-DSB, may contribute to the characteristics of BC. Therefore, the aim was to perform a comprehensive profiling of key proteins involved in the different DNA-DSB repair pathways in the different molecular classes of BC. This approach aims to address the inherent problems arising from the complexity of DDR mechanism in BC with the potential of discovering a key pathway that is active or inactive in specific forms of BC that can be helpful to identify DNA repair status in individual BC patients. Method: The study cohort comprises three BC groups: A) Large series of unselected primary sporadic operable invasive tumours (n=1904) in addition to B) 386 cases of oestrogen receptor (ER) negative tumours and C) a well-characterised series of BC from patients with known BRCA1 germline mutations (n=24). The proteins investigated in this study are known to participate in different DNA-DSB repair pathways including, DNA damage sensors (ATM and ATR), HR repair (BRCA1, BARD1, Rad51, γH2AX and SMC6L1), DNA damage checkpoint signalling protein (CHK1 and CHK2), NHEJ repair (KU70/KU80, and DNA-PK), and SUMO (PIAS1, PIAS4, and UBC9). Because subcellular localisation of DDR proteins may affect their function, two markers that have role in nuclear transport in the cell were examined (NPM and KPNA2). The expression of these proteins was assessed using the well-established immunohistochemical technique utilising tissue microarray technology. The expression of proteins was further evaluated in various cell lines; BRCA1 deficient HeLaSilenciX® cells, and control BRCA1 proficient HeLaSilenciX®, MDA-MB-436 (BRCA1 deficient), and MCF-7 (BRCA1 proficient and ER+) using Reverse Phase Protein Microarray (RPPA). Results: Both cytoplasmic and nuclear expression was observed for expression of Rad51, SMC6L1, BRCA1, BARD1; (HR markers), PIAS1, UBC9 (SUMO markers), γH2AX (DNA-DSB marker) and CHK1 (checkpoint signalling protein). In contrast, both NHEJ markers and most of the DNA damage sensors (ATM and ATR), CHK2 and PIAS4 were mainly expressed in the nucleus. Generally, tumours that showed positive cytoplasmic/negative nuclear expression such as CHK1, PIAS1, Rad51, and BRCA1, and positive nuclear NHEJ markers showed an association with a poor outcome and adverse prognostic characteristics including high histologic grade, high mitotic frequency, high nuclear pleomorphism and larger tumour size in addition to ER negativity, and triple negative breast cancer (TNBC). Conversely, nuclear+/cytoplasmic- expression showed an association the better outcome. Interestingly, ATM protein expression showed no association with the expression of the two NHEJ markers, whereas ATR showed an association with cytoplasmic expression of BRCA1 and BARD1 and was positively associated with NHEJ markers. In non-TNBC, tumours showing BRCA1-/KU70/KU80- phenotype had worse breast cancer specific survival (BCSS) than positive expression (P<0.0001), whereas in the TN cohort,complex of KU70/KU80-&DNA-PK+ had the worst BCSS (P=0.001), and both are independent prognostic markers for BC. KPNA2, but not NPM was highly associated with poor BCSS (P<0.0001). At least one of nucleocytoplasmic transport markers (NPM or KPNA2) was significantly associated with the subcellular localisation of the most of the markers that showed cytoplasmic expression including SMC6L1, γH2AX, BRCA1, BARD1, UBC9, PIAS1 ,Rad51 and CHK1. RPPA was used to investigate the protein expression in different cell lines, although the correlation between RPPA and IHC was not significant, the results of RPPA were consistent with that demonstrated by IHC further supporting the finding of the current study. Conclusion: This study highlight the complexity of DDR related proteins and the overlap between different pathways involved in DDR. The finding of this study may help in the classification of BC and therefore, targeting active pathways in the development of drugs would enhance better patients’ outcomes. Major prognostic and predictive variables can be very important in choosing suitable treatment plans, identifying the risk of recurrence and classifying patients for clinical trials. Our results show that the HR- repair marker Rad51, complex of HR and NHEJ repair markers (BRCA1&KU70/KU80) in non-TNBC, and a complex of NHEJ markers (KU70/KU80&DNA-PK) are all independent prognostic markers for BC. In addition to expression, subcellular localisation of DDR proteins appeared to be a major factor in their role. Particularly, HR repair markers (but not NHEJ) showed worse features of cytoplasmic location of expression, whereas nuclear expression was associated with more favourable features. Finally, the results of this study provide further evidence to support combined use of IHC with the parallel analytic capability of protein microarray RPPA to investigate protein alterations in human tumours

Clinical and biological significance of RAD51 expression in breast cancer: a key DNA damage response protein

Impaired DNA damage response (DDR) may play a fundamental role in the pathogenesis of breast cancer (BC). RAD51 is a key player in DNA double-strand break repair. In this study, we aimed to assess the biological and clinical significance of RAD51 expression with relevance to different molecular classes of BC and patients’ outcome. The expression of RAD51 was assessed immunohistochemically in a well-characterised annotated series (n = 1184) of early-stage invasive BC with long-term follow-up. A subset of cases of BC from patients with known BRCA1 germline mutations was included as a control group. The results were correlated with clinicopathological and molecular parameters and patients’ outcome. RAD51 protein expression level was also assayed in a panel of cell lines using reverse phase protein array (RPPA). RAD51 was expressed in the nuclei (N) and cytoplasm (C) of malignant cells. Subcellular colocalisation phenotypes of RAD51 were significantly associated with clinicopathological features and patient outcome. Cytoplasmic expression (RAD51C+) and lack of nuclear expression (RAD51 N-) were associated with features of aggressive behaviour, including larger tumour size, high grade, lymph nodal metastasis, basal-like, and triple-negative phenotypes, together with aberrant expression of key DDR biomarkers including BRCA1. All BRCA1-mutated tumours had RAD51C+/N- phenotype. RPPA confirmed IHC results and showed differential expression of RAD51 in cell lines based on ER expression and BRCA1 status. RAD51 N+ and RAD51C+ tumours were associated with longer and shorter breast cancer-specific survival (BCSS), respectively. The RAD51 N+ was an independent predictor of longer BCSS (P<0.0001). Lack of RAD51 nuclear expression is associated with poor prognostic parameters and shorter survival in invasive BC patients. The significant associations between RAD51 subcellular localisation and clinicopathological features, molecular subtype and patients’ outcome suggest that the trafficking of DDR proteins between the nucleus and cytoplasm might play a role in the development and progression of BC

Assessment of DNA-damage repair in breast cancer

Background: Current evidence indicates that DNA damage response (DDR) is a highly complex process that involves various pathways working in an orchestrated and interwoven manner in response to different types of damage to DNA. Although specific defects of DDR remain to be deciphered in cancer as a general, there is certainly an undeniable relationship between a particular dysfunction of DDR and the phenotype of tumour [1, 2]. It has been demonstrated that familial forms of breast and ovarian cancer are characterised by defects in one of the main mechanisms of DDR homologous recombination (HR) as a result of germline loss-of-function mutations in one of HR modifying genes, such as BRCA1 and BRCA2 [1, 3, 4]. Defects of genes involved in other DDR pathways are also associated with specific types of cancers; for instance hereditary non polyposis colorectal cancer (HNPCC) is strongly associated with specific mutations in the DNA mismatch repair pathway. Several previous studies have demonstrated that impaired DDR play a fundamental role in the pathogenesis and behaviour of breast cancer (BC). However, characterisation of this complex process, the expression and co-expression of the key proteins involved in the various DDR pathways and their prognostic significance in BC remain to be defined. In BC, it is reported that genes involved in DNA double strand breaks (DSB) repair are the most important. Two main pathways are involved in the repair of DNA-DSB; HR and Non Homologous End Joining (NHEJ) [3]. The common characteristics of global DDR are multiple genes induction directly associated with sensing and repair of DNA, arrest of cell cycle, and cell division inhibition. As a result DDR process does not only include genes activation involved in damage sensing as well as repair but additionally genes involved in control of cell-cycle [5]. Despite the fact that DDR may possibly involve activation of several pathways (such as SUMOylation (SUMO)) [6, 7] and many genes are engaged in different overlapping mechanisms, each pathway is characterised by activation and expression of a unique set of genes. This could allow discovering the active or aberrant pathway in a given tumour [1, 4, 5]. This study explores the hypothesis that investigation of alterations in the different pathways of DNA-DSB, may contribute to the characteristics of BC. Therefore, the aim was to perform a comprehensive profiling of key proteins involved in the different DNA-DSB repair pathways in the different molecular classes of BC. This approach aims to address the inherent problems arising from the complexity of DDR mechanism in BC with the potential of discovering a key pathway that is active or inactive in specific forms of BC that can be helpful to identify DNA repair status in individual BC patients. Method: The study cohort comprises three BC groups: A) Large series of unselected primary sporadic operable invasive tumours (n=1904) in addition to B) 386 cases of oestrogen receptor (ER) negative tumours and C) a well-characterised series of BC from patients with known BRCA1 germline mutations (n=24). The proteins investigated in this study are known to participate in different DNA-DSB repair pathways including, DNA damage sensors (ATM and ATR), HR repair (BRCA1, BARD1, Rad51, γH2AX and SMC6L1), DNA damage checkpoint signalling protein (CHK1 and CHK2), NHEJ repair (KU70/KU80, and DNA-PK), and SUMO (PIAS1, PIAS4, and UBC9). Because subcellular localisation of DDR proteins may affect their function, two markers that have role in nuclear transport in the cell were examined (NPM and KPNA2). The expression of these proteins was assessed using the well-established immunohistochemical technique utilising tissue microarray technology. The expression of proteins was further evaluated in various cell lines; BRCA1 deficient HeLaSilenciX® cells, and control BRCA1 proficient HeLaSilenciX®, MDA-MB-436 (BRCA1 deficient), and MCF-7 (BRCA1 proficient and ER+) using Reverse Phase Protein Microarray (RPPA). Results: Both cytoplasmic and nuclear expression was observed for expression of Rad51, SMC6L1, BRCA1, BARD1; (HR markers), PIAS1, UBC9 (SUMO markers), γH2AX (DNA-DSB marker) and CHK1 (checkpoint signalling protein). In contrast, both NHEJ markers and most of the DNA damage sensors (ATM and ATR), CHK2 and PIAS4 were mainly expressed in the nucleus. Generally, tumours that showed positive cytoplasmic/negative nuclear expression such as CHK1, PIAS1, Rad51, and BRCA1, and positive nuclear NHEJ markers showed an association with a poor outcome and adverse prognostic characteristics including high histologic grade, high mitotic frequency, high nuclear pleomorphism and larger tumour size in addition to ER negativity, and triple negative breast cancer (TNBC). Conversely, nuclear+/cytoplasmic- expression showed an association the better outcome. Interestingly, ATM protein expression showed no association with the expression of the two NHEJ markers, whereas ATR showed an association with cytoplasmic expression of BRCA1 and BARD1 and was positively associated with NHEJ markers. In non-TNBC, tumours showing BRCA1-/KU70/KU80- phenotype had worse breast cancer specific survival (BCSS) than positive expression (P<0.0001), whereas in the TN cohort,complex of KU70/KU80-&DNA-PK+ had the worst BCSS (P=0.001), and both are independent prognostic markers for BC. KPNA2, but not NPM was highly associated with poor BCSS (P<0.0001). At least one of nucleocytoplasmic transport markers (NPM or KPNA2) was significantly associated with the subcellular localisation of the most of the markers that showed cytoplasmic expression including SMC6L1, γH2AX, BRCA1, BARD1, UBC9, PIAS1 ,Rad51 and CHK1. RPPA was used to investigate the protein expression in different cell lines, although the correlation between RPPA and IHC was not significant, the results of RPPA were consistent with that demonstrated by IHC further supporting the finding of the current study. Conclusion: This study highlight the complexity of DDR related proteins and the overlap between different pathways involved in DDR. The finding of this study may help in the classification of BC and therefore, targeting active pathways in the development of drugs would enhance better patients’ outcomes. Major prognostic and predictive variables can be very important in choosing suitable treatment plans, identifying the risk of recurrence and classifying patients for clinical trials. Our results show that the HR- repair marker Rad51, complex of HR and NHEJ repair markers (BRCA1&KU70/KU80) in non-TNBC, and a complex of NHEJ markers (KU70/KU80&DNA-PK) are all independent prognostic markers for BC. In addition to expression, subcellular localisation of DDR proteins appeared to be a major factor in their role. Particularly, HR repair markers (but not NHEJ) showed worse features of cytoplasmic location of expression, whereas nuclear expression was associated with more favourable features. Finally, the results of this study provide further evidence to support combined use of IHC with the parallel analytic capability of protein microarray RPPA to investigate protein alterations in human tumours

Transcriptomic and Protein Expression Analysis Reveals Clinicopathological Significance of Bloom Syndrome Helicase (BLM) in Breast Cancer

BLM has key roles in homologous recombination repair, telomere maintenance and DNA replication. Germ-line mutation in the BLM gene causes Bloom’s syndrome, a rare disorder characterised by premature aging and predisposition to multiple cancers including breast cancer. The clinicopathological significance of BLM in sporadic breast cancers is unknown. We investigated BLM mRNA expression in the Molecular Taxonomy of Breast Cancer International Consortium cohort (n=1950) and validated in an external dataset of 2413 tumours. BLM protein level was evaluated in the Nottingham Tenovus series comprising 1650 breast tumours. High BLM mRNA expression was highly significantly associated with high histological grade, larger tumour size, ER negative, PgR negative and triple negative phenotypes (ps<0.0001). High BLM mRNA expression was also linked to aggressive molecular phenotypes including PAM50.Her2 (p<0.0001), PAM50.Bas al (p<0.0001) and PAM50.LumB (p<0.0001) and Genufu subtype (ER+/Her2-/High proliferation) (p<0.0001). PAM50.LumA tumours and Genufu subtype (ER+/Her2-/low proliferation) were more likely to express low levels of BLM mRNA (ps<0.0001). Integrative molecular clusters (intClust) intClust.1 (p<0.0001), intClust.5 (p<0.0001), intClust.9 (p<0.0 001) and intClust.10 (p<0.0001) were also more likely in tumours with high BLM mRNA expression. High BLM mRNA expression was associated with poor breast cancer specific survival (BCSS) (ps<0.000001). At the protein level, altered sub-cellular localisation with high cytoplasmic BLM and low nuclear BLM was linked to aggressive phenotypes. In multivariate analysis, BLM mRNA and BLM protein levels independently influenced BCSS ( p=0.03). This is the first and the largest study to provide evidence that BLM is a promising biomarker in breast cancer

Nuclear rupture at sites of high curvature compromises retention of DNA repair factors.

The nucleus is physically linked to the cytoskeleton, adhesions, and extracellular matrix-all of which sustain forces, but their relationships to DNA damage are obscure. We show that nuclear rupture with cytoplasmic mislocalization of multiple DNA repair factors correlates with high nuclear curvature imposed by an external probe or by cell attachment to either aligned collagen fibers or stiff matrix. Mislocalization is greatly enhanced by lamin A depletion, requires hours for nuclear reentry, and correlates with an increase in pan-nucleoplasmic foci of the DNA damage marker γH2AX. Excess DNA damage is rescued in ruptured nuclei by cooverexpression of multiple DNA repair factors as well as by soft matrix or inhibition of actomyosin tension. Increased contractility has the opposite effect, and stiff tumors with low lamin A indeed exhibit increased nuclear curvature, more frequent nuclear rupture, and excess DNA damage. Additional stresses likely play a role, but the data suggest high curvature promotes nuclear rupture, which compromises retention of DNA repair factors and favors sustained damage

Hidden regulators: the emerging roles of lncRNAs in brain development and disease

Long non-coding RNAs (lncRNAs) have emerged as critical players in brain development and disease. These non-coding transcripts, which once considered as “transcriptional junk,” are now known for their regulatory roles in gene expression. In brain development, lncRNAs participate in many processes, including neurogenesis, neuronal differentiation, and synaptogenesis. They employ their effect through a wide variety of transcriptional and post-transcriptional regulatory mechanisms through interactions with chromatin modifiers, transcription factors, and other regulatory molecules. Dysregulation of lncRNAs has been associated with certain brain diseases, including Alzheimer’s disease, Parkinson’s disease, cancer, and neurodevelopmental disorders. Altered expression and function of specific lncRNAs have been implicated with disrupted neuronal connectivity, impaired synaptic plasticity, and aberrant gene expression pattern, highlighting the functional importance of this subclass of brain-enriched RNAs. Moreover, lncRNAs have been identified as potential biomarkers and therapeutic targets for neurological diseases. Here, we give a comprehensive review of the existing knowledge of lncRNAs. Our aim is to provide a better understanding of the diversity of lncRNA structure and functions in brain development and disease. This holds promise for unravelling the complexity of neurodevelopmental and neurodegenerative disorders, paving the way for the development of novel biomarkers and therapeutic targets for improved diagnosis and treatment