Evidence for genetic heterogeneity between clinical subtypes of bipolar disorder.

We performed a genome-wide association study of 6447 bipolar disorder (BD) cases and 12 639 controls from the International Cohort Collection for Bipolar Disorder (ICCBD). Meta-analysis was performed with prior results from the Psychiatric Genomics Consortium Bipolar Disorder Working Group for a combined sample of 13 902 cases and 19 279 controls. We identified eight genome-wide significant, associated regions, including a novel associated region on chromosome 10 (rs10884920; P=3.28 × 10-8) that includes the brain-enriched cytoskeleton protein adducin 3 (ADD3), a non-coding RNA, and a neuropeptide-specific aminopeptidase P (XPNPEP1). Our large sample size allowed us to test the heritability and genetic correlation of BD subtypes and investigate their genetic overlap with schizophrenia and major depressive disorder. We found a significant difference in heritability of the two most common forms of BD (BD I SNP-h2=0.35; BD II SNP-h2=0.25; P=0.02). The genetic correlation between BD I and BD II was 0.78, whereas the genetic correlation was 0.97 when BD cohorts containing both types were compared. In addition, we demonstrated a significantly greater load of polygenic risk alleles for schizophrenia and BD in patients with BD I compared with patients with BD II, and a greater load of schizophrenia risk alleles in patients with the bipolar type of schizoaffective disorder compared with patients with either BD I or BD II. These results point to a partial difference in the genetic architecture of BD subtypes as currently defined.

Pseudo-Hermitian anti-Hermitian ensemble of Gaussian matrices.

It is shown that the ensemble of pseudo-Hermitian Gaussian matrices recently introduced gives rise in a certain limit to an ensemble of anti-Hermitian matrices whose eigenvalues have properties directly related to those of the chiral ensemble of random matrices.

Pseudo-Hermitian ensemble of random Gaussian matrices.

It is shown how pseudo-Hermiticity, a necessary condition satisfied by operators of PT symmetric systems can be introduced in the three Gaussian classes of random matrix theory. The model describes transitions from real eigenvalues to a situation in which, apart from a residual number, the eigenvalues are complex conjugate.

Influence of multiple sclerosis, age and degree of disability, in the position of the contrast sensitivity curve peak.

CONTEXT: Contrast sensitivity (CS) function is one of the most important tests available for evaluating visual impairment. Multiple sclerosis (MS) can produce highly selective losses in visual function and psychophysical studies have demonstrated CS deficits for some spatial frequencies. AIMS: This work studies the differences in CS between a group of controls and a group of MS patients, focusing on the location of the maximum sensitivity peak, shape of the curve, and determination of the most affected spatial frequencies. MATERIALS AND METHODS: Using a sinusoidal stimulus the authors assessed CS function in 28 subjects with definitive relapsing remitting MS, and in 50 controls with acuities of 20/25 or better. The peaks of the CS curves were studied by fitting third degree polynomials to individual sets of data. RESULTS: Compared with the control group, the CS function curve for MS subjects showed more deficits in extreme points (low- and high-spatial frequencies). Our results display significant CS losses, at the high-frequencies band level, in the beginning of the disease. When the disease progresses and the disabilities appear, there are greater losses at the low-frequencies band level. In average, the CS curve peaks for the MS group were shifted in relation to the control group. CONCLUSIONS: CS losses in the MS group suggest an association with ageing and disability level in the expanded disability status scale. The position of the CS function peak is influenced by MS, age, and degree of disability.

Evidence that duplications of 22q11.2 protect against schizophrenia.

A number of large, rare copy number variants (CNVs) are deleterious for neurodevelopmental disorders, but large, rare, protective CNVs have not been reported for such phenotypes. Here we show in a CNV analysis of 47 005 individuals, the largest CNV analysis of schizophrenia to date, that large duplications (1.5-3.0 Mb) at 22q11.2--the reciprocal of the well-known, risk-inducing deletion of this locus--are substantially less common in schizophrenia cases than in the general population (0.014% vs 0.085%, OR=0.17, P=0.00086). 22q11.2 duplications represent the first putative protective mutation for schizophrenia.

Structure of trajectories of complex-matrix eigenvalues in the Hermitian-non-Hermitian transition.

The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues is reflected in the structure of the trajectories and also in the final distribution of the eigenvalues in the complex plane.

Hyperbolic disordered ensembles of random matrices.

Using the recently introduced simple procedure of dividing Gaussian matrices by a positive random variable, a family of random matrices is generated characterized by a behavior ruled by the generalized hyperbolic distribution. The spectral density evolves from the semicircle law to a Gaussian-like behavior while concomitantly, the local fluctuations show a transition from the Wigner-Dyson to the Poisson statistics. Long range statistics such as number variance exhibit large fluctuations typical of nonergodic ensembles.

Finite element studies of the mechanical behaviour of the diaphragm in normal and pathological cases.

The diaphragm is a muscular membrane separating the abdominal and thoracic cavities, and its motion is directly linked to respiration. In this study, using data from a 59-year-old female cadaver obtained from the Visible Human Project, the diaphragm is reconstructed and, from the corresponding solid object, a shell finite element mesh is generated and used in several analyses performed with the ABAQUS 6.7 software. These analyses consider the direction of the muscle fibres and the incompressibility of the tissue. The constitutive model for the isotropic strain energy as well as the passive and active strain energy stored in the fibres is adapted from Humphrey's model for cardiac muscles. Furthermore, numerical results for the diaphragmatic floor under pressure and active contraction in normal and pathological cases are presented.

GWA study data mining and independent replication identify cardiomyopathy-associated 5 (CMYA5) as a risk gene for schizophrenia.

We conducted data-mining analyses using the Clinical Antipsychotic Trials of Intervention Effectiveness (CATIE) and molecular genetics of schizophrenia genome-wide association study supported by the genetic association information network (MGS-GAIN) schizophrenia data sets and performed bioinformatic prioritization for all the markers with P-values ≤0.05 in both data sets. In this process, we found that in the CMYA5 gene, there were two non-synonymous markers, rs3828611 and rs10043986, showing nominal significance in both the CATIE and MGS-GAIN samples. In a combined analysis of both the CATIE and MGS-GAIN samples, rs4704591 was identified as the most significant marker in the gene. Linkage disequilibrium analyses indicated that these markers were in low LD (3 828 611-rs10043986, r(2)=0.008; rs10043986-rs4704591, r(2)=0.204). In addition, CMYA5 was reported to be physically interacting with the DTNBP1 gene, a promising candidate for schizophrenia, suggesting that CMYA5 may be involved in the same biological pathway and process. On the basis of this information, we performed replication studies for these three single-nucleotide polymorphisms. The rs3828611 was found to have conflicting results in our Irish samples and was dropped out without further investigation. The other two markers were verified in 23 other independent data sets. In a meta-analysis of all 23 replication samples (family samples, 912 families with 4160 subjects; case-control samples, 11 380 cases and 15 021 controls), we found that both markers are significantly associated with schizophrenia (rs10043986, odds ratio (OR)=1.11, 95% confidence interval (CI)=1.04-1.18, P=8.2 × 10(-4) and rs4704591, OR=1.07, 95% CI=1.03-1.11, P=3.0 × 10(-4)). The results were also significant for the 22 Caucasian replication samples (rs10043986, OR=1.11, 95% CI=1.03-1.17, P=0.0026 and rs4704591, OR=1.07, 95% CI=1.02-1.11, P=0.0015). Furthermore, haplotype conditioned analyses indicated that the association signals observed at these two markers are independent. On the basis of these results, we concluded that CMYA5 is associated with schizophrenia and further investigation of the gene is warranted.

Deformations of the Tracy-Widom distribution.

In random matrix theory, the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists of removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristic of extreme values of an uncorrelated sequence, is obtained.

Missing levels in acoustic resonators.

It is shown that the deviations of the experimental statistics of six chaotic acoustic resonators from Wigner-Dyson random matrix theory predictions are explained by a recent model of random missing levels. In these resonatorsa made of aluminum plates a the larger deviations occur in the spectral rigidity (SRs) while the nearest-neighbor distributions (NNDs) are still close to the Wigner surmise. Good fits to the experimental NNDs and SRs are obtained by adjusting only one parameter, which is the fraction of remaining levels of the complete spectra. For two Sinai stadiums, one Sinai stadium without planar symmetry, two triangles, and a sixth of the three-leaf clover shapes, was found that 7%, 4%, 7%, and 2%, respectively, of eigenfrequencies were not detected.

Disordered ensembles of random matrices.

It is shown that the families of generalized matrix ensembles recently considered which give rise to an orthogonal invariant stable Lévy ensemble can be generated by the simple procedure of dividing Gaussian matrices by a random variable. The nonergodicity of this kind of disordered ensembles is investigated. It is shown that the same procedure applied to random graphs gives rise to a family that interpolates between the Erdös-Renyi and the scale free models.

Finite element studies of the deformation of the pelvic floor.

This article describes research involving finite element simulations of women's pelvic floor, undertaken in the engineering schools of Lisbon and Oporto, in collaboration with the medical school of Oporto. These studies are motivated by the pelvic floor dysfunctions that lead namely to urinary incontinence and pelvic organ prolapse. This research ultimately aims at: (i) contributing to clarify the primary mechanism behind such disorders; (ii) providing tools to simulate the pelvic floor function and the effects of its dysfunctions; (iii) contributing to planning and performing surgeries in a more controlled and reliable way. The finite element meshes of the levator ani are based on a publicly available geometric data set, and use triangular thin shell or special brick elements. Muscle and soft tissues are assumed as (quasi-)incompressible hyperelastic materials. Skeletal muscles are transversely isotropic with a single fiber direction, embedded in an isotropic matrix. The fibers considered in this work may be purely passive, or active with input of neuronal excitation and consideration of the muscle activation process. The first assumption may be adequate to simulate passive deformations of the pelvic muscles and tissues (namely, under the extreme loading conditions of childbirth). The latter may be adequate to model faster contractions that occur in time intervals of the same order as those of muscle activation and deactivation (as in preventing urinary incontinence in coughing or sneezing). Numerical simulations are presented for the active deformation of the levator ani muscle under constant pressure and neural excitation, and for the deformation induced by a vaginal childbirth.

Integrating genetic, functional genomic, and bioinformatics data in a systems biology approach to complex diseases: application to schizophrenia.

The search for DNA alterations that cause human disease has been an area of active research for more than 50 years, since the time that the genetic code was first solved. In the absence of data implicating chromosomal aberrations, researchers historically have performed whole genome linkage analysis or candidate gene association analysis to develop hypotheses about the genes that most likely cause a specific phenotype or disease. Whereas whole genome linkage analysis examines all chromosomal locations without a priori predictions regarding what genes underlie susceptibility, candidate gene association studies require a researcher to know in advance the genes that he or she wishes to test (based on their knowledge of a disease). To date, very few whole genome linkage studies and candidate gene studies have produced results that lead to generalizable findings about common diseases. One factor contributing to this lack of results has certainly been the previously limited resolution of the techniques. Recent technological advances, however, have made it possible to perform highly informative whole genome linkage and association analyses, as well as whole genome transcription (transcriptome) analysis. In addition, for the first time we can detect structural DNA aberrations throughout the genome on a fine scale. Each of these four approaches has its own strengths and weaknesses, but taken together, the results from an integrated analysis can implicate highly promising novel candidate genes. Here, we provide an overview of the integrated methodology that we have used to combine high-throughput genetic and functional genomic data with bioinformatics data that have produced new insights into the potential biological basis for schizophrenia. We believe that the potential of this combined approach is greater than that of a single mode of discovery, particularly for complex genetic diseases.

Symmetry-breaking study with deformed ensembles.

A random matrix model to describe the coupling of m -fold symmetry is constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that such an experimental and theoretical study may supply a powerful means to discern the intrinsic symmetry of physical systems.

Randomly incomplete spectra and intermediate statistics.

By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitions towards Poisson from random matrix theory (RMT) spectra and picket fence spectra. It is shown that the Fredholm determinant formalism of RMT extends naturally to describe incomplete RMT spectra.

Genetic investigation of chromosome 5q GABAA receptor subunit genes in schizophrenia.

We previously performed a genome-wide linkage scan in Portuguese schizophrenia families that identified a risk locus on chromosome 5q31-q35. This finding was supported by meta-analysis of 20 other schizophrenia genome-wide scans that identified 5q23.2-q34 as the second most compelling susceptibility locus in the genome. In the present report, we took a two-stage candidate gene association approach to investigate a group of gamma-aminobutyric acid (GABA) A receptor subunit genes (GABRA1, GABRA6, GABRB2, GABRG2, and GABRP) within our linkage peak. These genes are plausible candidates based on prior evidence for GABA system involvement in schizophrenia. In the first stage, associations were detected in a Portuguese patient sample with single nucleotide polymorphisms (SNPs) and haplotypes in GABRA1 (P=0.00062-0.048), GABRP (P=0.0024-0.042), and GABRA6 (P=0.0065-0.0088). The GABRA1 and GABRP findings were replicated in the second stage in an independent German family-based sample (P=0.0015-0.043). Supportive evidence for association was also obtained for a previously reported GABRB2 risk haplotype. Exploratory analyses of the effects of associated GABRA1 haplotypes on transcript levels found altered expression of GABRA6 and coexpressed genes of GABRA1 and GABRB2. Comparison of transcript levels in schizophrenia patients and unaffected siblings found lower patient expression of GABRA6 and coexpressed genes of GABRA1. Interestingly, the GABRA1 coexpressed genes include synaptic and vesicle-associated genes previously found altered in schizophrenia prefrontal cortex. Taken together, these results support the involvement of the chromosome 5q GABAA receptor gene cluster in schizophrenia, and suggest that schizophrenia-associated haplotypes may alter expression of GABA-related genes.

Level density for deformations of the Gaussian orthogonal ensemble.

Formulas are derived for the average level density of deformed, or transition, Gaussian orthogonal random matrix ensembles. After some general considerations about Gaussian ensembles, we derive formulas for the average level density for (i) the transition from the Gaussian orthogonal ensemble (GOE) to the Poisson ensemble and (ii) the transition from the GOE to m GOEs.

Universality of rescaled curvature distributions.

We applied a recently proposed rescaling of curvatures of eigenvalues of parameter-dependent random matrices to experimental data from acoustic systems and to a theoretical result. It is found that the data from four different experiments, ranging from isotropic plates to anisotropic three-dimensional objects, and the theoretical result always agree with the universal curvature distribution, if only the curvatures are rescaled such that the average of their absolute values is unity.

Support for involvement of neuregulin 1 in schizophrenia pathophysiology.

Schizophrenia is a common, multigenic psychiatric disorder. Linkage studies, including a recent meta-analysis of genome scans, have repeatedly implicated chromosome 8p12-p23.1 in schizophrenia susceptibility. More recently, significant association with a candidate gene on 8p12, neuregulin 1 (NRG1), has been reported in several European and Chinese samples. We investigated NRG1 for association in schizophrenia patients of Portuguese descent to determine whether this gene is a risk factor in this population. We tested NRG1 markers and haplotypes for association in 111 parent-proband trios, 321 unrelated cases, and 242 control individuals. Associations were found with a haplotype that overlaps the risk haplotype originally reported in the Icelandic population ("Hap(ICE)"), and two haplotypes located in the 3' end of NRG1 (all P<0.05). However, association was not detected with Hap(ICE) itself. Comparison of NRG1 transcript expression in peripheral leukocytes from schizophrenia patients and unaffected siblings identified 3.8-fold higher levels of the SMDF variant in patients (P=0.039). Significant positive correlations (P<0.001) were found between SMDF and HRG-beta 2 expression and between HRG-gamma and ndf43 expression, suggesting common transcriptional regulation of NRG1 variants. In summary, our results suggest that haplotypes across NRG1 and multiple NRG1 variants are involved in schizophrenia.