Angles of Arc-Polygons and Lombardi Drawings of Cacti

We characterize the triples of interior angles that are possible in non-self-crossing triangles with circular-arc sides, and we prove that a given cyclic sequence of angles can be realized by a non-self-crossing polygon with circular-arc sides whenever all angles are at most pi. As a consequence of these results, we prove that every cactus has a planar Lombardi drawing (a drawing with edges depicted as circular arcs, meeting at equal angles at each vertex) for its natural embedding in which every cycle of the cactus is a face of the drawing. However, there exist planar embeddings of cacti that do not have planar Lombardi drawings.Comment: 12 pages, 8 figures. To be published in Proc. 33rd Canadian Conference on Computational Geometry, 202

ARHGDIA mutations cause nephrotic syndrome via defective RHO GTPase signaling

Nephrotic syndrome (NS) is divided into steroid-sensitive (SSNS) and -resistant (SRNS) variants. SRNS causes end-stage kidney disease, which cannot be cured. While the disease mechanisms of NS are not well understood, genetic mapping studies suggest a multitude of unknown single-gene causes. We combined homozygosity mapping with whole-exome resequencing and identified an ARHGDIA mutation that causes SRNS. We demonstrated that ARHGDIA is in a complex with RHO GTPases and is prominently expressed in podocytes of rat glomeruli. ARHGDIA mutations (R120X and G173V) from individuals with SRNS abrogated interaction with RHO GTPases and increased active GTP-bound RAC1 and CDC42, but not RHOA, indicating that RAC1 and CDC42 are more relevant to the pathogenesis of this SRNS variant than RHOA. Moreover, the mutations enhanced migration of cultured human podocytes; however, enhanced migration was reversed by treatment with RAC1 inhibitors. The nephrotic phenotype was recapitulated in arhgdia-deficient zebrafish. RAC1 inhibitors were partially effective in ameliorating arhgdia-associated defects. These findings identify a single-gene cause of NS and reveal that RHO GTPase signaling is a pathogenic mediator of SRNS.ope

Hormone-like (endocrine) Fgfs: their evolutionary history and roles in development, metabolism, and disease

Fibroblast growth factors (Fgfs) are proteins with diverse functions in development, repair, and metabolism. The human Fgf gene family with 22 members can be classified into three groups, canonical, intracellular, and hormone-like Fgf genes. In contrast to canonical and intracellular Fgfs identified in invertebrates and vertebrates, hormone-like Fgfs, Fgf15/19, Fgf21, and Fgf23, are vertebrate-specific. The ancestral gene of hormone-like Fgfs was generated from the ancestral gene of canonical Fgfs by gene duplication early in vertebrate evolution. Later, Fgf15/19, Fgf21, and Fgf23 were generated from the ancestral gene by genome duplication events. Canonical Fgfs act as autocrine/paracrine factors in an Fgf receptor (Fgfr)-dependent manner. In contrast, hormone-like Fgfs act as endocrine factors in an Fgfr-dependent manner. Canonical Fgfs have a heparin-binding site necessary for the stable binding of Fgfrs and local signaling. In contrast, hormone-like Fgfs acquired endocrine functions by reducing their heparin-binding affinity during their evolution. Fgf15/19 and Fgf23 require βKlotho and αKlotho as cofactors, respectively. However, Fgf21 might physiologically require neither. Hormone-like Fgfs play roles in metabolism at postnatal stages, although they also play roles in development at embryonic stages. Fgf15/19 regulates bile acid metabolism in the liver. Fgf21 regulates lipid metabolism in the white adipose tissue. Fgf23 regulates serum phosphate and active vitamin D levels. Fgf23 signaling disorders caused by hereditary diseases or tumors result in metabolic disorders. In addition, serum Fgf19 or Fgf21 levels are significantly increased by metabolic disorders. Hormone-like Fgfs are newly emerging and quite unique in their evolution and function

Primary hyperoxaluria type I: a model for multiple mutations in a monogenic disease within a distinct ethnic group

Primary hyperoxaluria type 1 is an autosomal recessive inherited metabolic disease in which excessive oxalates are formed by the liver and excreted by the kidneys, causing a wide spectrum of phenotypes ranging from renal failure in infancy to mere renal stones in late adulthood. Mutations in the AGXT gene, encoding the liver-specific enzyme alanine:glyoxylate aminotransferase, are responsible for the disease. Seven mutations were detected in eight families in Israel. Four of these mutations are novel and three occur in children living in single-clan villages. The mutations are scattered along various exons (1, 4, 5, 7, 9, 10), and on different alleles comprising at least five different haplotypes. All but one of the mutations are in a homozygous pattern, reflecting the high rate of consanguinity in our patient population. Two affected brothers are homozygous for two different mutations expressed on the same allele. The patients comprise a distinct ethnic group (Israeli Arabs) residing in a confined geographic area. These results, which are supported by previous data, suggest for the first time that the phenomenon of multiple mutations in a relatively closed isolate is common and almost exclusive to the Israeli-Arab population. Potential mechanisms including selective advantage to heterozygotes, digenic inheritance, and the recent emergence of multiple mutations are discusse

Recurrent nephrotic syndrome in homozygous truncating NPHS2 mutation is not due to anti-podocin antibodies.

Mutations in NPHS2 are a common cause of focal segmental glomerulosclerosis (FSGS). It was initially assumed that FSGS caused by a genetically defective protein in the native kidney would not recur after transplantation; however, description of three patients with NPHS2 missense mutations challenged the validity of this assumption. A possible mechanism of recurrence in cases with stop-codon mutations is the formation of auto-antibodies against the truncated protein. In this case report, we describe a 9-year-old girl with the R138X NPHS2 mutation who presented with recurrent nephrotic syndrome 4 years after renal transplantation from a deceased donor, and was treated with plasmapheresis with a partial response. Renal histology did not demonstrate glomerular immunoglobulin deposition and an extensive search for anti-podocin antibodies based on indirect Western blot with recombinant podocin, was negative, as was the test for glomerular permeability factor (Palb). Taken together these findings confirm the possibility of post transplantation nephrotic syndrome in patients with NPHS2 mutations. Lack of immunoglobulin deposition, absence of circulating anti-podocin antibodies, and normal Palb suggest that other, unknown pathogenetic mechanisms are implicated