Discrete Painlevé equations from Y-systems

We consider T-systems and Y-systems arising from cluster mutations applied to quivers that have the property of being periodic under a sequence of mutations. The corresponding nonlinear recurrences for cluster variables (coefficient-free T-systems) were described in the work of Fordy and Marsh, who completely classified all such quivers in the case of period 1, and characterized them in terms of the skew-symmetric exchange matrix B that defines the quiver. A broader notion of periodicity in general cluster algebras was introduced by Nakanishi, who also described the corresponding Y-systems, and T-systems with coefficients. A result of Fomin and Zelevinsky says that the coefficient-free T-system provides a solution of the Y-system. In this paper, we show that in general there is a discrepancy between these two systems, in the sense that the solution of the former does not correspond to the general solution of the latter. This discrepancy is removed by introducing additional non-autonomous coefficients into the T-system. In particular, we focus on the period 1 case and show that, when the exchange matrix B is degenerate, discrete Painlev\'e equations can arise from this construction

Spina bifida-predisposing heterozygous mutations in Planar Cell Polarity genes and Zic2 reduce bone mass in young mice

Fractures are a common comorbidity in children with the neural tube defect (NTD) spina bifida. Mutations in the Wnt/planar cell polarity (PCP) pathway contribute to NTDs in humans and mice, but whether this pathway independently determines bone mass is poorly understood. Here, we first confirmed that core Wnt/PCP components are expressed in osteoblasts and osteoclasts in vitro. In vivo, we performed detailed µCT comparisons of bone structure in tibiae from young male mice heterozygous for NTD-associated mutations versus WT littermates. PCP signalling disruption caused by Vangl2 (Vangl2Lp/+) or Celsr1 (Celsr1Crsh/+) mutations significantly reduced trabecular bone mass and distal tibial cortical thickness. NTD-associated mutations in non-PCP transcription factors were also investigated. Pax3 mutation (Pax3Sp2H/+) had minimal effects on bone mass. Zic2 mutation (Zic2Ku/+) significantly altered the position of the tibia/fibula junction and diminished cortical bone in the proximal tibia. Beyond these genes, we bioinformatically documented the known extent of shared genetic networks between NTDs and bone properties. 46 genes involved in neural tube closure are annotated with bone-related ontologies. These findings document shared genetic networks between spina bifida risk and bone structure, including PCP components and Zic2. Genetic variants which predispose to spina bifida may therefore independently diminish bone mass

A Dutch guideline for the treatment of scoliosis in neuromuscular disorders

<p>Abstract</p> <p>Background</p> <p>Children with neuromuscular disorders with a progressive muscle weakness such as Duchenne Muscular Dystrophy and Spinal Muscular Atrophy frequently develop a progressive scoliosis. A severe scoliosis compromises respiratory function and makes sitting more difficult. Spinal surgery is considered the primary treatment option for correcting severe scoliosis in neuromuscular disorders. Surgery in this population requires a multidisciplinary approach, careful planning, dedicated surgical procedures, and specialized after care.</p> <p>Methods</p> <p>The guideline is based on scientific evidence and expert opinions. A multidisciplinary working group representing experts from all relevant specialties performed the research. A literature search was conducted to collect scientific evidence in answer to specific questions posed by the working group. Literature was classified according to the level of evidence.</p> <p>Results</p> <p>For most aspects of the treatment scientific evidence is scarce and only low level cohort studies were found. Nevertheless, a high degree of consensus was reached about the management of patients with scoliosis in neuromuscular disorders. This was translated into a set of recommendations, which are now officially accepted as a general guideline in the Netherlands.</p> <p>Conclusion</p> <p>In order to optimize the treatment for scoliosis in neuromuscular disorders a Dutch guideline has been composed. This evidence-based, multidisciplinary guideline addresses conservative treatment, the preoperative, perioperative, and postoperative care of scoliosis in neuromuscular disorders.</p

Determination of Stromal Signatures in Breast Carcinoma

Many soft tissue tumors recapitulate features of normal connective tissue. We hypothesize that different types of fibroblastic tumors are representative of different populations of fibroblastic cells or different activation states of these cells. We examined two tumors with fibroblastic features, solitary fibrous tumor (SFT) and desmoid-type fibromatosis (DTF), by DNA microarray analysis and found that they have very different expression profiles, including significant differences in their patterns of expression of extracellular matrix genes and growth factors. Using immunohistochemistry and in situ hybridization on a tissue microarray, we found that genes specific for these two tumors have mutually specific expression in the stroma of nonneoplastic tissues. We defined a set of 786 gene spots whose pattern of expression distinguishes SFT from DTF. In an analysis of DNA microarray gene expression data from 295 previously published breast carcinomas, we found that expression of this gene set defined two groups of breast carcinomas with significant differences in overall survival. One of the groups had a favorable outcome and was defined by the expression of DTF genes. The other group of tumors had a poor prognosis and showed variable expression of genes enriched for SFT type. Our findings suggest that the host stromal response varies significantly among carcinomas and that gene expression patterns characteristic of soft tissue tumors can be used to discover new markers for normal connective tissue cells

Periodic cluster mutations and related integrable maps

One of the remarkable properties of cluster algebras is that any cluster, obtained from a sequence of mutations from an initial cluster, can be written as a Laurent polynomial in the initial cluster (known as the 'Laurent phenomenon'). There are many nonlinear recurrences which exhibit the Laurent phenomenon and thus unexpectedly generate integer sequences. The mutation of a typical quiver will not generate a recurrence, but rather an erratic sequence of exchange relations. How do we 'design' a quiver which gives rise to a given recurrence? A key role is played by the concept of 'periodic cluster mutation', introduced in 2009. Each recurrence corresponds to a finite dimensional map. In the context of cluster mutations, these are called 'cluster maps'. What properties do cluster maps have? Are they integrable in some standard sense? In this review I describe how integrable maps arise in the context of cluster mutations. I first explain the concept of 'periodic cluster mutation', giving some classification results. I then give a review of what is meant by an integrable map and apply this to cluster maps. Two classes of integrable maps are related to interesting monodromy problems, which generate interesting Poisson algebras of functions, used to prove complete integrability and a linearization. A connection to the Hirota–Miwa equation is explained

Invasion and MMP expression profile in desmoid tumours

Desmoid tumours are locally invasive soft tissue tumours in which beta-catenin mediated TCF-dependent transcription is activated. The role of soluble factors secreted by the myofibroblastic desmoid tumour, which could stimulate tumour invasiveness, was investigated. Using collagen gel invasion assays, the presence of factors stimulating invasion in desmoid conditioned media (CM) could be established. Since matrix metalloproteinases (MMPs) have been implicated in the process of tumoral invasion, the expression levels of the MMP family members were evaluated. Quantitative reverse transcription-PCR was used to determine the expression levels of MMP1, MMP2, MMP3, MMP7, MMP11, MMP12, MMP13, MMP14 and the inhibitors TIMP1, TIMP2 and TIMP3. Besides overexpression of MMP7, a known TCF-dependent target gene, a striking upregulation of the expression levels of MMP1, MMP3, MMP11, MMP12 and MMP13 in desmoid tumours, compared to unaffected fibroblasts from the same patients, was found. Treating the CM of desmoids with a synthetic and a physiologic MMP inhibitor reduced the invasion-stimulating capacity of the desmoid CM by approximately 50%. These results suggest the involvement of soluble factors, released by the desmoid cells, in stimulating invasion and implicate the MMPs as facilitators of invasion

Time Trends in the Incidence and Treatment of Extra-Abdominal and Abdominal Aggressive Fibromatosis: A Population-Based Study

BACKGROUND: Aggressive fibromatosis (AF) is a locally infiltrating soft-tissue tumor. In a population-based study in the Netherlands, we evaluated time trends for the incidence and treatment of AF. METHODS: In PALGA: Dutch Pathology Registry, all patients diagnosed between 1993 and 2013 as having extra-abdominal or abdominal wall aggressive fibromatosis were identified and available pathology data of the patients were evaluated. Epidemiological and treatment-related factors were analyzed with χ(2)and regression analysis. RESULTS: During the study period, 1134 patients were identified. The incidence increased from 2.10 to 5.36 per million people per year. Median age at the time of diagnosis increased annually by B 0.285 (P = 0.001). Female gender prevailed and increased over time [annual odds ratio (OR) 1.022; P = 0.058]. All anatomic localizations, but in particular truncal tumors, became more frequent. During the study period diagnostic histological biopsies were performed more often (annual OR 1.096; P < 0.001). The proportion of patients who underwent surgical treatment decreased (annual OR 0.928; P < 0.001). When resection was preceded by biopsy, 49.8 % of the patients had R0-resection versus 30.7 % in patients without biopsy (P < 0.001). CONCLUSIONS: In this population-based study, an increasing incidence of extra-abdominal and abdominal-wall aggressive fibromatosis was observed. The workup of patients improved and a trend towards a nonsurgical treatment policy was observed

Elevated levels of β-catenin and fibronectin in three-dimensional collagen cultures of Dupuytren's disease cells are regulated by tension in vitro

BACKGROUND: Dupuytren's contracture or disease (DD) is a fibro-proliferative disease of the hand that results in the development of scar-like, collagen-rich disease cords within specific palmar fascia bands. Although the molecular pathology of DD is unknown, recent evidence suggests that β-catenin may play a role. In this study, collagen matrix cultures of primary disease fibroblasts show enhanced contraction and isometric tension-dependent changes in β-catenin and fibronectin levels. METHODS: Western blots of β-catenin and fibronectin levels were determined for control and disease primary cell cultures grown within stressed- and attached-collagen matrices. Collagen contraction was quantified, and immunocytochemistry analysis of filamentous actin performed. RESULTS: Disease cells exhibited enhanced collagen contraction activity compared to control cells. Alterations in isometric tension of collagen matrices triggered dramatic changes in β-catenin and fibronectin levels, including a transient increase in β-catenin levels within disease cells, while fibronectin levels steadily decreased to levels below those seen in normal cell cultures. In contrast, both fibronectin and β-catenin levels increased in attached collagen-matrix cultures of disease cells, while control cultures showed only increases in fibronectin levels. Immunocytochemistry analysis also revealed extensive filamentous actin networks in disease cells, and enhanced attachment and spreading of disease cell in collagen matrices. CONCLUSION: Three-dimensional collagen matrix cultures of primary disease cell lines are more contractile and express a more extensive filamentous actin network than patient-matched control cultures. The elevated levels of β-catenin and Fn seen in collagen matrix cultures of disease fibroblasts can be regulated by changes in isometric tension