New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity

We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission coefficients for these potentials are obtained. We show that these potentials can also be obtained numerically. Included as an intriguing case is a shape invariant double well potential whose supersymmetric partner potential is only a single well. Our class of exactly solvable Hamiltonians is further enlarged by examining two new directions: (i) changes of parameters which are different from the previously studied cases of translation and scaling; (ii) extending the usual concept of shape invariance in one step to a multi-step situation. These extensions can be viewed as q-deformations of the harmonic oscillator or multi-soliton solutions corresponding to the Rosen-Morse potential.Comment: 26 pages, plain tex, request figures by e-mai

A novel role for CRIM1 in the corneal response to UV and pterygium development

Pterygium is a pathological proliferative condition of the ocular surface, characterised by formation of a highly vascularised, fibrous tissue arising from the limbus that invades the central cornea leading to visual disturbance and, if untreated, blindness. Whilst chronic ultraviolet (UV) light exposure plays a major role in its pathogenesis, higher susceptibility to pterygium is observed in some families, suggesting a genetic component. In this study, a Northern Irish family affected by pterygium but reporting little direct exposure to UV was identified carrying a missense variant in CRIM1 NM_016441.2: c.1235 A > C (H412P) through whole-exome sequencing and subsequent analysis. CRIM1 is expressed in the developing eye, adult cornea and conjunctiva, having a role in cell differentiation and migration but also in angiogenesis, all processes involved in pterygium formation. We demonstrate elevated CRIM1 expression in pterygium tissue from additional individual Northern Irish patients compared to unaffected conjunctival controls. UV irradiation of HCE-S cells resulted in an increase in ERK phosphorylation and CRIM1 expression, the latter further elevated by the addition of the MEK1/2 inhibitor, U0126. Conversely, siRNA knockdown of CRIM1 led to decreased UV-induced ERK phosphorylation and increased BCL2 expression. Transient expression of the mutant H412P CRIM1 in corneal epithelial HCE-S cells showed that, unlike wild-type CRIM1, it was unable to reduce the cell proliferation, increased ERK phosphorylation and apoptosis induced through a decrease of BCL2 expression levels. We propose here a series of intracellular events where CRIM1 regulation of the ERK pathway prevents UV-induced cell proliferation and may play an important role in the in the pathogenesis of pterygium

A novel nonsense CDK5RAP2 mutation in a Somali child with primary microcephaly and sensorineural hearing loss

Primary microcephaly is a genetically heterogeneous condition characterized by reduced head circumference (-3 SDS or more) and mild-to-moderate learning disability. Here, we describe clinical and molecular investigations of a microcephalic child with sensorineural hearing loss. Although consanguinity was unreported initially, detection of 13.7 Mb of copy neutral loss of heterozygosity (cnLOH) on chromosome 9 implicated the CDK5RAP2 gene. Targeted sequencing identified a homozygous E234X mutation, only the third mutation to be described in CDK5RAP2, the first in an individual of non-Pakistani descent. Sensorineural hearing loss is not generally considered to be consistent with autosomal recessive microcephaly and therefore it seems likely that the deafness in this individual is caused by the co-occurrence of a further gene mutation, independent of CDK5RAP2. Nevertheless, further detailed clinical descriptions of rare CDK5RAP2 patients, including hearing assessments will be needed to resolve fully the phenotypic range associated with mutations in this gene. This study also highlights the utility of SNP-array testing to guide disease gene identification where an autosomal recessive condition is plausible

Nuclear-mitochondrial DNA segments resemble paternally inherited mitochondrial DNA in humans.

Several strands of evidence question the dogma that human mitochondrial DNA (mtDNA) is inherited exclusively down the maternal line, most recently in three families where several individuals harbored a 'heteroplasmic haplotype' consistent with biparental transmission. Here we report a similar genetic signature in 7 of 11,035 trios, with allelic fractions of 5-25%, implying biparental inheritance of mtDNA in 0.06% of offspring. However, analysing the nuclear whole genome sequence, we observe likely large rare or unique nuclear-mitochondrial DNA segments (mega-NUMTs) transmitted from the father in all 7 families. Independently detecting mega-NUMTs in 0.13% of fathers, we see autosomal transmission of the haplotype. Finally, we show the haplotype allele fraction can be explained by complex concatenated mtDNA-derived sequences rearranged within the nuclear genome. We conclude that rare cryptic mega-NUMTs can resemble paternally mtDNA heteroplasmy, but find no evidence of paternal transmission of mtDNA in humans

A family with autism and rare copy number variants disrupting the Duchenne/Becker muscular dystrophy gene DMD and TRPM3

Autism spectrum disorder is a genetically complex and clinically heterogeneous neurodevelopmental disorder. A recent study by the Autism Genome Project (AGP) used 1M single-nucleotide polymorphism arrays to show that rare genic copy number variants (CNVs), possibly acting in tandem, play a significant role in the genetic aetiology of this condition. In this study, we describe the phenotypic and genomic characterisation of a multiplex autism family from the AGP study that was found to harbour a duplication of exons 31–44 of the Duchenne/Becker muscular dystrophy gene DMD and also a rare deletion involving exons 1–9 of TRPM3. Further characterisation of these extremely rare CNVs was carried out using quantitative PCR, fluorescent in situ hybridisation, long-range PCR amplification and sequencing of junction fragments. The maternal chrX:32,097,213-32,321,945 tandem duplication and paternal chr9:72,480,413-73,064,196 deletion (NCBI build 36 coordinates) were transmitted to both affected boys, potentially signifying a multi-hit mechanism. The DMD reading frame rule predicts a Becker phenotype, characterised by later onset and milder symptoms. When last evaluated, neither child had developed signs of muscular dystrophy. These data are consistent with a degree of comorbidity between autism and muscular dystrophy and suggest that genomic background as well as the position of the mutation within the DMD gene may impact on the neurological correlates of Duchenne/Becker muscular dystrophy. Finally, communicating unexpected findings such as these back to families raises a number of ethical questions, which are discussed

Homozygous microdeletion of exon 5 in ZNF277 in a girl with specific language impairment

Peer reviewedPublisher PD

A genome-wide scan for common alleles affecting risk for autism

Although autism spectrum disorders (ASDs) have a substantial genetic basis, most of the known genetic risk has been traced to rare variants, principally copy number variants (CNVs). To identify common risk variation, the Autism Genome Project (AGP) Consortium genotyped 1558 rigorously defined ASD families for 1 million single-nucleotide polymorphisms (SNPs) and analyzed these SNP genotypes for association with ASD. In one of four primary association analyses, the association signal for marker rs4141463, located within MACROD2, crossed the genome-wide association significance threshold of P < 5 × 10−8. When a smaller replication sample was analyzed, the risk allele at rs4141463 was again over-transmitted; yet, consistent with the winner's curse, its effect size in the replication sample was much smaller; and, for the combined samples, the association signal barely fell below the P < 5 × 10−8 threshold. Exploratory analyses of phenotypic subtypes yielded no significant associations after correction for multiple testing. They did, however, yield strong signals within several genes, KIAA0564, PLD5, POU6F2, ST8SIA2 and TAF1C

Delineation of dominant and recessive forms of LZTR1-associated Noonan syndrome.

Noonan syndrome (NS) is characterised by distinctive facial features, heart defects, variable degrees of intellectual disability and other phenotypic manifestations. Although the mode of inheritance is typically dominant, recent studies indicate LZTR1 may be associated with both dominant and recessive forms. Seeking to describe the phenotypic characteristics of LZTR1-associated NS, we searched for likely pathogenic variants using two approaches. First, scrutiny of exomes from 9624 patients recruited by the Deciphering Developmental Disorders (DDDs) study uncovered six dominantly-acting mutations (p.R97L; p.Y136C; p.Y136H, p.N145I, p.S244C; p.G248R) of which five arose de novo, and three patients with compound-heterozygous variants (p.R210*/p.V579M; p.R210*/p.D531N; c.1149+1G>T/p.R688C). One patient also had biallelic loss-of-function mutations in NEB, consistent with a composite phenotype. After removing this complex case, analysis of human phenotype ontology terms indicated significant phenotypic similarities (P = 0.0005), supporting a causal role for LZTR1. Second, targeted sequencing of eight unsolved NS-like cases identified biallelic LZTR1 variants in three further subjects (p.W469*/p.Y749C, p.W437*/c.-38T>A and p.A461D/p.I462T). Our study strengthens the association of LZTR1 with NS, with de novo mutations clustering around the KT1-4 domains. Although LZTR1 variants explain ~0.1% of cases across the DDD cohort, the gene is a relatively common cause of unsolved NS cases where recessive inheritance is suspected

Novel method for combined linkage and genome-wide association analysis finds evidence of distinct genetic architecture for two subtypes of autism

The Autism Genome Project has assembled two large datasets originally designed for linkage analysis and genome-wide association analysis, respectively: 1,069 multiplex families genotyped on the Affymetrix 10 K platform, and 1,129 autism trios genotyped on the Illumina 1 M platform. We set out to exploit this unique pair of resources by analyzing the combined data with a novel statistical method, based on the PPL statistical framework, simultaneously searching for linkage and association to loci involved in autism spectrum disorders (ASD). Our analysis also allowed for potential differences in genetic architecture for ASD in the presence or absence of lower IQ, an important clinical indicator of ASD subtypes. We found strong evidence of multiple linked loci; however, association evidence implicating specific genes was low even under the linkage peaks. Distinct loci were found in the lower IQ families, and these families showed stronger and more numerous linkage peaks, while the normal IQ group yielded the strongest association evidence. It appears that presence/absence of lower IQ (LIQ) demarcates more genetically homogeneous subgroups of ASD patients, with not just different sets of loci acting in the two groups, but possibly distinct genetic architecture between them, such that the LIQ group involves more major gene effects (amenable to linkage mapping), while the normal IQ group potentially involves more common alleles with lower penetrances. The possibility of distinct genetic architecture across subtypes of ASD has implications for further research and perhaps for research approaches to other complex disorders as well

Analysis of exome data for 4293 trios suggests GPI-anchor biogenesis defects are a rare cause of developmental disorders.

Over 150 different proteins attach to the plasma membrane using glycosylphosphatidylinositol (GPI) anchors. Mutations in 18 genes that encode components of GPI-anchor biogenesis result in a phenotypic spectrum that includes learning disability, epilepsy, microcephaly, congenital malformations and mild dysmorphic features. To determine the incidence of GPI-anchor defects, we analysed the exome data from 4293 parent-child trios recruited to the Deciphering Developmental Disorders (DDD) study. All probands recruited had a neurodevelopmental disorder. We searched for variants in 31 genes linked to GPI-anchor biogenesis and detected rare biallelic variants in PGAP3, PIGN, PIGT (n=2), PIGO and PIGL, providing a likely diagnosis for six families. In five families, the variants were in a compound heterozygous configuration while in a consanguineous Afghani kindred, a homozygous c.709G>C; p.(E237Q) variant in PIGT was identified within 10-12 Mb of autozygosity. Validation and segregation analysis was performed using Sanger sequencing. Across the six families, five siblings were available for testing and in all cases variants co-segregated consistent with them being causative. In four families, abnormal alkaline phosphatase results were observed in the direction expected. FACS analysis of knockout HEK293 cells that had been transfected with wild-type or mutant cDNA constructs demonstrated that the variants in PIGN, PIGT and PIGO all led to reduced activity. Splicing assays, performed using leucocyte RNA, showed that a c.336-2A>G variant in PIGL resulted in exon skipping and p.D113fs*2. Our results strengthen recently reported disease associations, suggest that defective GPI-anchor biogenesis may explain ~0.15% of individuals with developmental disorders and highlight the benefits of data sharing