Definition of Flat Poset and Existence Theorems for Recursive Call

This text includes the definition and basic notions of product of posets, chain-complete and flat posets, flattening operation, and the existence theorems of recursive call using the flattening operator. First part of the article, devoted to product and flat posets has a purely mathematical quality. Definition 3 allows to construct a flat poset from arbitrary non-empty set [12] in order to provide formal apparatus which eanbles to work with recursive calls within the Mizar langauge. To achieve this we extensively use technical Mizar functors like BaseFunc or RecFunc. The remaining part builds the background for information engineering approach for lists, namely recursive call for posets [21].We formalized some facts from Chapter 8 of this book as an introduction to the next two sections where we concentrate on binary product of posets rather than on a more general case.Ishida Kazuhisa - Neyagawa-shi Osaka, JapanShidama Yasunari - Shinshu University Nagano, JapanGrabowski Adam - Institute of Informatics University of Białystok Akademicka 2, 15-267 Białystok PolandGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. Complete lattices. Formalized Mathematics, 2(5):719-725, 1991.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek. Bounds in posets and relational substructures. Formalized Mathematics, 6(1):81-91, 1997.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Bylinski. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990.Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.B.A. Davey and H.A. Priestley. Introduction to Lattices and Order. Cambridge University Press, 2002.Marek Dudzicz. Representation theorem for finite distributive lattices. Formalized Mathematics, 9(2):261-264, 2001.Adam Grabowski. On the category of posets. Formalized Mathematics, 5(4):501-505, 1996. http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000258624500003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=b7bc2757938ac7a7a821505f8243d9f3Kazuhisa Ishida and Yasunari Shidama. Fixpoint theorem for continuous functions on chain-complete posets. Formalized Mathematics, 18(1):47-51, 2010. doi:10.2478/v10037-010-0006-x.Artur Korniłowicz. Cartesian products of relations and relational structures. Formalized Mathematics, 6(1):145-152, 1997.Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1): 115-122, 1990.Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. Formalized Mathematics, 1(2):387-393, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Glynn Winskel. The Formal Semantics of Programming Languages. The MIT Press, 1993.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Mariusz Zynel and Czesław Bylinski. Properties of relational structures, posets, lattices and maps. Formalized Mathematics, 6(1):123-130, 1997

Molecular basis underlying the ciliary defects caused by IFT52 variations found in skeletal ciliopathies

Bidirectional protein trafficking within cilia is mediated by the intraflagellar transport (IFT) machinery, which contains the IFT-A and IFT-B complexes powered by the kinesin-2 and dynein-2 motors. Mutations in genes encoding subunits of the IFT-A and dynein-2 complexes cause skeletal ciliopathies. Some subunits of the IFT-B complex, including IFT52, IFT80, and IFT172, are also mutated in skeletal ciliopathies. We here show that IFT52 variants found in individuals with short-rib polydactyly syndrome (SRPS) are compromised in terms of formation of the IFT-B holocomplex from two subcomplexes, and its interaction with heterotrimeric kinesin-II. IFT52-knockout (KO) cells expressing IFT52 variants that mimic the cellular conditions of individuals with SRPS demonstrated mild ciliogenesis defects and a decrease in ciliary IFT-B level. Furthermore, in IFT52-KO cells expressing an SRPS variant of IFT52, ciliary tip localization of ICK/CILK1 and KIF17, both of which are likely to be transported to the tip via binding to the IFT-B complex, were significantly impaired. These results altogether indicate that impaired anterograde trafficking caused by a decrease in the ciliary level of IFT-B or in its binding to kinesin-II underlies the ciliary defects found in skeletal ciliopathies caused by IFT52 variations

Cooperation of the IFT-A complex with the IFT-B complex is required for ciliary retrograde protein trafficking and GPCR import

Cilia sense and transduce extracellular signals via specific receptors. The intraflagellar transport (IFT) machinery mediates not only bidirectional protein trafficking within cilia but also the import/export of ciliary proteins across the ciliary gate. The IFT machinery is known to comprise two multisubunit complexes, namely, IFT-A and IFT-B; however, little is known about how the two complexes cooperate to mediate ciliary protein trafficking. We here show that IFT144-IFT122 from IFT-A and IFT88-IFT52 from IFT-B make major contributions to the interface between the two complexes. Exogenous expression of the IFT88(Δα) mutant, which has decreased binding to IFT-A, partially restores the ciliogenesis defect of IFT88-knockout (KO) cells. However, IFT88(Δα)-expressing IFT88-KO cells demonstrate a defect in IFT-A entry into cilia, aberrant accumulation of IFT-B proteins at the bulged ciliary tips, and impaired import of ciliary GPCRs. Furthermore, overaccumulated IFT proteins at the bulged tips appeared to be released as extracellular vesicles. These phenotypes of IFT88(Δα)-expressing IFT88-KO cells resembled those of IFT144-KO cells. These observations together indicate that the IFT-A complex cooperates with the IFT-B complex to mediate the ciliary entry of GPCRs as well as retrograde trafficking of the IFT machinery from the ciliary tip. [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text]

Cancer Stem Cells and Aldehyde Dehydrogenase 1 in Liver Cancers

The cancer stem cell (CSC) theory posits that a small population of cells with stem cell-like features is responsible for tumor growth, resistance, and recurrence in many malignancies. This theory could be a useful paradigm for designing innovative targeted drug therapies. Liver cancer is the fifth most common cancer worldwide, with hepatocellular carcinoma (HCC) and cholangiocarcinoma (CCA) as the predominant forms. Hepatic stem/progenitor cells are believed to be the origin of HCCs and CCAs; however, this remains a controversial topic. Aldehyde dehydrogenase (ALDH) is the main enzymatic system responsible for the clearance of acetaldehyde from the hepatocytes in the liver tissue. Therefore, ALDH1 has been suggested to be a potential, biological and CSC marker in liver cancers. We here provide an overview of the current state of knowledge of CSCs in liver and the role of ALDH1 in the development and progression of liver cancers and discuss its potential value as a prognostic and diagnostic biomarker

Formation and Cycloreversion of 2-Silacyclobuta[2.3]cyclophanes via Photoinduced Electron Transfer

Irradiation of an acetonitrile solution containing dimethylbis(4-vinylphenylmethyl)silane 1a in the presence of 9,10-dicyanoanthracene leads to formation of the intramolecular photocycloadduct, 2-sila-cyclobuta[2.3]cyclophane (2a). In contrast, prolonged irradiation gave insoluble polymeric material. The photocycloreversion of 2a occurs efficiently (quantum yields exceeds unity) by use of redox-type photosensitization in the presence of magnesium perchlorate. The transient absorption spectra generated by pulse radiolysis and gamma-radiolysis show that the radical cation species generated from 1a is different from that arising from 2a

Fixpoint Theorem for Continuous Functions on Chain-Complete Posets

This text includes the definition of chain-complete poset, fix-point theorem on it, and the definition of the function space of continuous functions on chain-complete posets [10].Ishida Kazuhisa - Neyagawa-shi, Osaka, JapanShidama Yasunari - Shinshu University, Nagano, JapanGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. Bounds in posets and relational substructures. Formalized Mathematics, 6(1):81-91, 1997.Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Adam Grabowski. On the category of posets. Formalized Mathematics, 5(4):501-505, 1996. http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=000258624500003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=b7bc2757938ac7a7a821505f8243d9f3Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. Formalized Mathematics, 1(2):387-393, 1990.Glynn Winskel. The Formal Semantics of Programming Languages. The MIT Press, 1993.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 1990.Mariusz Żynel and Czesław Byliński. Properties of relational structures, posets, lattices and maps. Formalized Mathematics, 6(1):123-130, 1997

Isogenic pairs of induced-pluripotent stem-derived endothelial cells identify DYRK1A/PPARG/EGR1 pathway is responsible for Down syndrome-associated pulmonary hypertension

Down syndrome (DS) is the most prevalent chromosomal disorder associated with a higher incidence of pulmonary arterial hypertension (PAH). The dysfunction of vascular endothelial cells (ECs) is known to cause pulmonary arterial remodeling in PAH, although the physiological characteristics of ECs harboring trisomy 21 (T21) are still unknown. In this study, we analyzed the human vascular ECs by utilizing the isogenic pairs of T21-induced pluripotent stem cells (iPSCs) and corrected disomy 21 (cDi21)-iPSCs. In T21-iPSC-derived ECs, apoptosis and mitochondrial reactive oxygen species (mROS) were significantly increased, and angiogenesis and oxygen consumption rate (OCR) were significantly impaired as compared with cDi21-iPSC-derived ECs. The RNA-sequencing identified that EGR1 on chromosome 5 was significantly upregulated in T21-ECs. Both EGR1 suppression by siRNA and pharmacological inhibitor could recover the apoptosis, mROS, angiogenesis, and OCR in T21-ECs. Alternately, the study also revealed that DYRK1A was responsible to increase EGR1 expression via PPARG suppression, and that chemical inhibition of DYRK1A could restore the apoptosis, mROS, angiogenesis, and OCR in T21-ECs. Finally, we demonstrated that EGR1 was significantly upregulated in the pulmonary arterial ECs from lung specimens of a patient with DS and PAH. In conclusion, DYRK1A/PPARG/EGR1 pathway could play a central role for the pulmonary EC functions and thus be associated with the pathogenesis of PAH in DS.Suginobe Hidehiro, Ishida Hidekazu, Ishii Yoichiro, et al. Isogenic pairs of induced-pluripotent stem-derived endothelial cells identify DYRK1A/PPARG/EGR1 pathway is responsible for Down syndrome-associated pulmonary hypertension. Human Molecular Genetics 163, 1163 (2023); https://doi.org/10.1093/hmg/ddad162

A low-frequency IL4R locus variant in Japanese patients with intravenous immunoglobulin therapy-unresponsive Kawasaki disease

Background: Kawasaki disease (KD) is a systemic vasculitis which may be associated with coronary artery aneurysms. A notable risk factor for the development of coronary artery aneurysms is resistance to intravenous immunoglobulin (IVIG) therapy, which comprises standard treatment for the acute phase of KD. The cause of IVIG resistance in KD is largely unknown; however, the contribution of genetic factors, especially variants in immune-related genes, has been suspected. Methods: To explore genetic variants related to IVIG-unresponsiveness, we designated KD patients who did not respond to both first and second courses of IVIG therapy as IVIG-unresponsive patients. Using genomic DNA from 30 IVIG-unresponsive KD patients, we performed pooled genome sequencing targeting 39 immune-related cytokine receptor genes. Results: The single nucleotide variant (SNV), rs563535954 (located in the IL4R locus), was concentrated in IVIG-unresponsive KD patients. Individual genotyping showed that the minor allele of rs563535954 was present in 4/33 patients with IVIG-unresponsive KD, compared with 20/1063 individuals in the Japanese genome variation database (odds ratio = 7.19, 95% confidence interval 2.43-21.47). Furthermore, the minor allele of rs563535954 was absent in 42 KD patients who responded to IVIG treatment (P = 0.0337), indicating that a low-frequency variant, rs563535954, is associated with IVIG-unresponsiveness in KD patients. Although rs563535954 is located in the 3'-untranslated region of IL4R, there was no alternation in IL4R expression associated with the mior allele of rs563535954. However, IVIG-unresponsive patients that exhibited the minor allele of rs563535954 tended to be classified into the low-risk group (based on previously reported risk scores) for prediction of IVIG-resistance. Therefore, IVIG-unresponsiveness associated with the minor allele of rs563535954 might differ from IVIG-unresponsiveness associated with previous risk factors used to evaluate IVIG-unresponsiveness in KD. Conclusion: These findings suggest that the SNV rs563535954 could serve as a predictive indicator of IVIG-unresponsiveness, thereby improving the sensitivity of risk scoring systems, and may aid in prevention of coronary artery lesions in KD patients.ArticlePEDIATRIC RHEUMATOLOGY.17:34(2019)journal articl