The lexicographically least square-free word with a given prefix

The lexicographically least square-free infinite word on the alphabet of non-negative integers with a given prefix $p$ is denoted $L(p)$. When $p$ is the empty word, this word was shown by Guay-Paquet and Shallit to be the ruler sequence. For other prefixes, the structure is significantly more complicated. In this paper, we show that $L(p)$ reflects the structure of the ruler sequence for several words $p$. We provide morphisms that generate $L(n)$ for letters $n=1$ and $n\geq3$, and $L(p)$ for most families of two-letter words $p$

Accuracy of Immunofluorescence in the Diagnosis of Primary Ciliary Dyskinesia

RATIONALE The standard approach to diagnosis of primary ciliary dyskinesia (PCD) in the UK consists of assessing ciliary function by high-speed-microscopy and ultrastructure by election microscopy, but equipment and expertise is not widely available internationally. The identification of bi-allelic disease causing mutations is also diagnostic, but many disease causing genes are unknown, and testing is not widely available outside the USA. Fluorescent antibodies to ciliary proteins are used to validate research genetic studies, but diagnostic utility in this disease has not been systematically evaluated. OBJECTIVES: Determine utility of a panel of six fluorescent labelled antibodies as a diagnostic tool for PCD. METHODS: Immunofluorescent labelling of nasal brushings from a discovery cohort of 35 patients diagnosed with PCD by ciliary ultrastructure, and a diagnostic accuracy cohort of 386 patients referred with symptoms suggestive of disease. The results were compared to diagnostic outcome. MEASUREMENTS AND MAIN RESULTS: Immunofluorescence correctly identified mislocalised or absent staining in 100% of the discovery cohort. In the diagnostic cohort immunofluorescence successfully identified 22 of 25 patients with PCD and normal staining in all 252 in whom PCD was considered highly unlikely. Immunofluorescence additionally provided a result in 55% (39) of cases which were previously inconclusive. Immunofluorescence results were available within 14 days, costing $187 per sample compared to electron microscopy (27 days, cost$1452). CONCLUSIONS: Immunofluorescence is a highly specific diagnostic test for PCD, and improves the speed and availability of diagnostic testing, however, sensitivity is limited and immunofluorescence is not suitable as a stand-alone test

Primary ciliary dyskinesia with normal ultrastructure:three-dimensional tomography detects absence of DNAH11

In primary ciliary dyskinesia (PCD), motile ciliary dysfunction arises from ciliary defects usually confirmed by transmission electron microscopy (TEM). In 30% of patients, such as those with DNAH11 mutations, apparently normal ultrastructure makes diagnosis difficult. Genetic analysis supports diagnosis, but may not identify definitive causal variants. Electron tomography, an extension of TEM, produces three-dimensional ultrastructural ciliary models with superior resolution to TEM. Our hypothesis is that tomography using existing patient samples will enable visualisation of DNAH11-associated ultrastructural defects. Dual axis tomograms from araldite-embedded nasal cilia were collected in 13 PCD patients with normal ultrastructure (DNAH11 n=7, HYDIN n=2, CCDC65 n=3 and DRC1 n=1) and six healthy controls, then analysed using IMOD and Chimera software. DNAH11 protein is localised to the proximal ciliary region. Within this region, electron tomography indicated a deficiency of >25% of proximal outer dynein arm volume in all patients with DNAH11 mutations (n=7) compared to other patients with PCD and normal ultrastructure (n=6) and healthy controls (n=6). DNAH11 mutations cause a shared abnormality in ciliary ultrastructure previously undetectable by TEM. Advantageously, electron tomography can be used on existing diagnostic samples and establishes a structural abnormality where ultrastructural studies were previously normal

Targeted NGS gene panel identifies mutations in RSPH1 causing primary ciliary dyskinesia and a common mechanism for ciliary central pair agenesis due to radial spoke defects.

Primary ciliary dyskinesia (PCD) is an inherited chronic respiratory obstructive disease with randomized body laterality and infertility, resulting from cilia and sperm dysmotility. PCD is characterized by clinical variability and extensive genetic heterogeneity, associated with different cilia ultrastructural defects and mutations identified in >20 genes. Next generation sequencing (NGS) technologies therefore present a promising approach for genetic diagnosis which is not yet in routine use. We developed a targeted panel-based NGS pipeline to identify mutations by sequencing of selected candidate genes in 70 genetically undefined PCD patients. This detected loss-of-function RSPH1 mutations in four individuals with isolated central pair (CP) agenesis and normal body laterality, from two unrelated families. Ultrastructural analysis in RSPH1-mutated cilia revealed transposition of peripheral outer microtubules into the 'empty' CP space, accompanied by a distinctive intermittent loss of the central pair microtubules. We find that mutations in RSPH1, RSPH4A and RSPH9, which all encode homologs of components of the 'head' structure of ciliary radial spoke complexes identified in Chlamydomonas, cause clinical phenotypes that appear to be indistinguishable except at the gene level. By high-resolution immunofluorescence we identified a loss of RSPH4A and RSPH9 along with RSPH1 from RSPH1-mutated cilia, suggesting RSPH1 mutations may result in loss of the entire spoke head structure. CP loss is seen in up to 28% of PCD cases, in whom laterality determination specified by CP-less embryonic node cilia remains undisturbed. We propose this defect could arise from instability or agenesis of the ciliary central microtubules due to loss of their normal radial spoke head tethering