<p>An arc search interior-point algorithm for monotone symmetric cone linear complementarity problem is presented. The algorithm estimates the central path by an ellipse and follows an ellipsoidal approximation of the central path to reach an <em>ε</em>-approximate solution of the problem in a wide neighborhood of the central path. The convergence analysis of the algorithm is derived. Furthermore, we prove that the algorithm has the complexity bound <em>O (√rL)</em> using Nesterov-Todd search direction and <em>O (√rL)</em> by the <em>xs</em> and <em>sx</em> search directions. The obtained iteration complexities coincide with the best-known ones obtained by any proposed interior-point algorithm for this class of mathematical problems.</p>
<div>Abstract<p>We discovered that 90.3% of patients with angiomyolipomas, lymphangioleiomyomatosis (LAM), and tuberous sclerosis complex (TSC) carry the arginine variant of codon 72 (R72) of <i>TP53</i> and that R72 increases the risk for angiomyolipoma. R72 transactivates <i>NOTCH1</i> and <i>NODAL</i> better than the proline variant of codon 72 (P72); therefore, the expression of <i>NOTCH1</i> and <i>NODAL</i> is increased in angiomyolipoma cells that carry R72. The loss of <i>Tp53</i> and <i>Tsc1</i> within nestin-expressing cells in mice resulted in the development of renal cell carcinomas (RCC) with high <i>Notch1</i> and <i>Nodal</i> expression, suggesting that similar downstream mechanisms contribute to tumorigenesis as a result of p53 loss in mice and p53 polymorphism in humans. The loss of murine <i>Tp53</i> or expression of human R72 contributes to tumorigenesis via enhancing epithelial-to-mesenchymal transition and motility of tumor cells through the Notch and Nodal pathways.</p>Implications:<p>This work revealed unexpected contributions of the p53 polymorphism to the pathogenesis of TSC and established signaling alterations caused by this polymorphism as a target for therapy. We found that the codon 72 TP53 polymorphism contributes to TSC-associated tumorigenesis via Notch and Nodal signaling.</p></div>
<p>S1. Expression of hamartin and p53 in mice. S2. CRISPR-Cas9 mediated editing of TP53 codon 72 in angiomyolipoma cells and the impact of R72 on Notch/Nodal axis. S3. Overexpression of Nodal in LAM. S4. Overexpression of Nodal in TSC-associated renal tumors. S5. R72 increases migration of angiomyolipoma cells. Supplementary Table S1. The frequency of TP53 codon 72 germline polymorphism in TSC and LAM patients. Supplementary Table S2. The frequency of TP53 R72 codon polymorphism in TSC and sporadic angiomyolipoma and TSC-associated RCC. Supplementary Table S3. The number of experimental mice used in study.</p>
<p>S1. Expression of hamartin and p53 in mice. S2. CRISPR-Cas9 mediated editing of TP53 codon 72 in angiomyolipoma cells and the impact of R72 on Notch/Nodal axis. S3. Overexpression of Nodal in LAM. S4. Overexpression of Nodal in TSC-associated renal tumors. S5. R72 increases migration of angiomyolipoma cells. Supplementary Table S1. The frequency of TP53 codon 72 germline polymorphism in TSC and LAM patients. Supplementary Table S2. The frequency of TP53 R72 codon polymorphism in TSC and sporadic angiomyolipoma and TSC-associated RCC. Supplementary Table S3. The number of experimental mice used in study.</p>
<p>An arc search interior-point algorithm for monotone symmetric cone linear complementarity problem is presented. The algorithm estimates the central path by an ellipse and follows an ellipsoidal approximation of the central path to reach an <em>ε</em>-approximate solution of the problem in a wide neighborhood of the central path. The convergence analysis of the algorithm is derived. Furthermore, we prove that the algorithm has the complexity bound <em>O (√rL)</em> using Nesterov-Todd search direction and <em>O (√rL)</em> by the <em>xs</em> and <em>sx</em> search directions. The obtained iteration complexities coincide with the best-known ones obtained by any proposed interior-point algorithm for this class of mathematical problems.</p>
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