A unified fluctuation formula for one-cut β\beta-ensembles of random matrices

Using a Coulomb gas approach, we compute the generating function of the covariances of power traces for one-cut $\beta$-ensembles of random matrices in the limit of large matrix size. This formula depends only on the support of the spectral density, and is therefore universal for a large class of models. This allows us to derive a closed-form expression for the limiting covariances of an arbitrary one-cut $\beta$-ensemble. As particular cases of the main result we consider the classical $\beta$-Gaussian, $\beta$-Wishart and $\beta$-Jacobi ensembles, for which we derive previously available results as well as new ones within a unified simple framework. We also discuss the connections between the problem of trace fluctuations for the Gaussian Unitary Ensemble and the enumeration of planar maps.Comment: 16 pages, 4 figures, 3 tables. Revised version where references have been added and typos correcte

Entangled random pure states with orthogonal symmetry: exact results

We compute analytically the density $\varrho_{N,M}(\lambda)$ of Schmidt eigenvalues, distributed according to a fixed-trace Wishart-Laguerre measure, and the average R\'enyi entropy $\langle\mathcal{S}_q\rangle$ for reduced density matrices of entangled random pure states with orthogonal symmetry $(\beta=1)$. The results are valid for arbitrary dimensions $N=2k,M$ of the corresponding Hilbert space partitions, and are in excellent agreement with numerical simulations.Comment: 15 pages, 5 figure

Correlators for the Wigner–Smith time-delay matrix of chaotic cavities

We study the Wigner–Smith time-delay matrix Q of a ballistic quantum dot supporting N scattering channels. We compute the v-point correlators of the power traces Tr Qk for arbitrary v>1 at leading order for large N using techniques from the random matrix theory approach to quantum chromodynamics. We conjecture that the cumulants of the Tr Qkʼs are integer-valued at leading order in N and include a MATHEMATICA code that computes their generating functions recursively

Purity distribution for generalized random Bures mixed states

We compute the distribution of the purity for random density matrices (i.e.random mixed states) in a large quantum system, distributed according to the Bures measure. The full distribution of the purity is computed using a mapping to random matrix theory and then a Coulomb gas method. We find three regimes that correspond to two phase transitions in the associated Coulomb gas. The first transition is characterized by an explosion of the third derivative on the left of the transition point. The second transition is of first order, it is characterized by the detachement of a single charge of the Coulomb gas. A key remark in this paper is that the random Bures states are closely related to the O(n) model for n=1. This actually led us to study "generalized Bures states" by keeping $n$ general instead of specializing to n=1

Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices

We compute analytically the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W=X^T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value =N/c decreases for large N as $\sim \exp[-\frac{\beta}{2}N^2 \Phi_{-}(\frac{2}{\sqrt{c}}+1;c)]$, where \beta=1,2 correspond respectively to real and complex Wishart matrices, c=N/M < 1 and \Phi_{-}(x;c) is a large deviation function that we compute explicitly. The result for the Anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of constrained Wishart matrices whose eigenvalues are forced to be smaller than a fixed barrier. The numerical simulations are in excellent agreement with the analytical predictions.Comment: Published version. References and appendix adde

Analysis of Global Sumoylation Changes Occurring during Keratinocyte Differentiation

Sumoylation is a highly dynamic process that plays a role in a multitude of processes ranging from cell cycle progression to mRNA processing and cancer. A previous study from our lab demonstrated that SUMO plays an important role in keratinocyte differentiation. Here we present a new method of tracking the sumoylation state of proteins by creating a stably transfected HaCaT keratinocyte cell line expressing an inducible SNAP-SUMO3 protein. The SNAP-tag allows covalent fluorescent labeling that is denaturation resistant. When combined with two-dimensional gel electrophoresis, the SNAP-tag technology provides direct visualization of sumoylated targets and can be used to follow temporal changes in the global cohort of sumoylated proteins during dynamic processes such as differentiation. HaCaT keratinocyte cells expressing SNAP-SUMO3 displayed normal morphological and biochemical features that are consistent with typical keratinocyte differentiation. SNAP-SUMO3 also localized normally in these cells with a predominantly nuclear signal and some minor cytoplasmic staining, consistent with previous reports for untagged SUMO2/3. During keratinocyte differentiation the total number of proteins modified by SNAP-SUMO3 was highest in basal cells, decreased abruptly after induction of differentiation, and slowly rebounded beginning between 48 and 72 hours as differentiation progressed. However, within this overall trend the pattern of change for individual sumoylated proteins was highly variable with both increases and decreases in amount over time. From these results we conclude that sumoylation of proteins during keratinocyte differentiation is a complex process which likely reflects and contributes to the biochemical changes that drive differentiation

Identifying allosteric fluctuation transitions between different protein conformational states as applied to Cyclin Dependent Kinase 2

BACKGROUND: The mechanisms underlying protein function and associated conformational change are dominated by a series of local entropy fluctuations affecting the global structure yet are mediated by only a few key residues. Transitional Dynamic Analysis (TDA) is a new method to detect these changes in local protein flexibility between different conformations arising from, for example, ligand binding. Additionally, Positional Impact Vertex for Entropy Transfer (PIVET) uses TDA to identify important residue contact changes that have a large impact on global fluctuation. We demonstrate the utility of these methods for Cyclin-dependent kinase 2 (CDK2), a system with crystal structures of this protein in multiple functionally relevant conformations and experimental data revealing the importance of local fluctuation changes for protein function. RESULTS: TDA and PIVET successfully identified select residues that are responsible for conformation specific regional fluctuation in the activation cycle of Cyclin Dependent Kinase 2 (CDK2). The detected local changes in protein flexibility have been experimentally confirmed to be essential for the regulation and function of the kinase. The methodologies also highlighted possible errors in previous molecular dynamic simulations that need to be resolved in order to understand this key player in cell cycle regulation. Finally, the use of entropy compensation as a possible allosteric mechanism for protein function is reported for CDK2. CONCLUSION: The methodologies embodied in TDA and PIVET provide a quick approach to identify local fluctuation change important for protein function and residue contacts that contributes to these changes. Further, these approaches can be used to check for possible errors in protein dynamic simulations and have the potential to facilitate a better understanding of the contribution of entropy to protein allostery and function

Genome-wide interaction study of smoking and bladder cancer risk

Bladder cancer is a complex disease with known environmental and genetic risk factors. We performed a genome-wide interaction study (GWAS) of smoking and bladder cancer risk based on primary scan data from 3002 cases and 4411 controls from the National Cancer Institute Bladder Cancer GWAS. Alternative methods were used to evaluate both additive and multiplicative interactions between individual single nucleotide polymorphisms (SNPs) and smoking exposure. SNPs with interaction P values < 5 x 10(-) (5) were evaluated further in an independent dataset of 2422 bladder cancer cases and 5751 controls. We identified 10 SNPs that showed association in a consistent manner with the initial dataset and in the combined dataset, providing evidence of interaction with tobacco use. Further, two of these novel SNPs showed strong evidence of association with bladder cancer in tobacco use subgroups that approached genome-wide significance. Specifically, rs1711973 (FOXF2) on 6p25.3 was a susceptibility SNP for never smokers [combined odds ratio (OR) = 1.34, 95% confidence interval (CI) = 1.20-1.50, P value = 5.18 x 10(-) (7)]; and rs12216499 (RSPH3-TAGAP-EZR) on 6q25.3 was a susceptibility SNP for ever smokers (combined OR = 0.75, 95% CI = 0.67-0.84, P value = 6.35 x 10(-) (7)). In our analysis of smoking and bladder cancer, the tests for multiplicative interaction seemed to more commonly identify susceptibility loci with associations in never smokers, whereas the additive interaction analysis identified more loci with associations among smokers-including the known smoking and NAT2 acetylation interaction. Our findings provide additional evidence of gene-environment interactions for tobacco and bladder cancer

Synergistic induction of cell death in liver tumor cells by TRAIL and chemotherapeutic drugs via the BH3-only proteins Bim and Bid

Although death receptors and chemotherapeutic drugs activate distinct apoptosis signaling cascades, crosstalk between the extrinsic and intrinsic apoptosis pathway has been recognized as an important amplification mechanism. Best known in this regard is the amplification of the Fas (CD95) signal in hepatocytes via caspase 8-mediated cleavage of Bid and activation of the mitochondrial apoptosis pathway. Recent evidence, however, indicates that activation of other BH3-only proteins may also be critical for the crosstalk between death receptors and mitochondrial triggers. In this study, we show that TNF-related apoptosis-inducing ligand (TRAIL) and chemotherapeutic drugs synergistically induce apoptosis in various transformed and untransformed liver-derived cell lines, as well as in primary human hepatocytes. Both, preincubation with TRAIL as well as chemotherapeutic drugs could sensitize cells for apoptosis induction by the other respective trigger. TRAIL induced a strong and long lasting activation of Jun kinase, and activation of the BH3-only protein Bim. Consequently, synergistic induction of apoptosis by TRAIL and chemotherapeutic drugs was dependent on Jun kinase activity, and expression of Bim and Bid. These findings confirm a previously defined role of TRAIL and Bim in the regulation of hepatocyte apoptosis, and demonstrate that the TRAIL–Jun kinase–Bim axis is a major and important apoptosis amplification pathway in primary hepatocytes and liver tumor cells

Variants of the EAAT2 Glutamate Transporter Gene Promoter Are Associated with Cerebral Palsy in Preterm Infants

© 2017, The Author(s). Preterm delivery is associated with neurodevelopmental impairment caused by environmental and genetic factors. Dysfunction of the excitatory amino acid transporter 2 (EAAT2) and the resultant impaired glutamate uptake can lead to neurological disorders. In this study, we investigated the role of single nucleotide polymorphisms (SNPs; g.-200CCloseSPigtSPiA and g.-181ACloseSPigtSPiC) in the EAAT2 promoter in susceptibility to brain injury and neurodisability in very preterm infants born at or before 32-week gestation. DNA isolated from newborns’ dried blood spots were used for pyrosequencing to detect both SNPs. Association between EAAT2 genotypes and cerebral palsy, cystic periventricular leukomalacia and a low developmental score was then assessed. The two SNPs were concordant in 89.4% of infants resulting in three common genotypes all carrying two C and two A alleles in different combinations. However, in 10.6% of cases, non-concordance was found, generating six additional rare genotypes. The A alleles at both loci appeared to be detrimental and consequently, the risk of developing cerebral palsy increased four- and sixfold for each additional detrimental allele at -200 and -181bp, respectively. The two SNPs altered the regulation of the EAAT2 promoter activity and glutamate homeostasis. This study highlights the significance of glutamate in the pathogenesis of preterm brain injury and subsequent development of cerebral palsy and neurodevelopmental disabilities. Furthermore, the described EAAT2 SNPs may be an early biomarker of vulnerability to neurodisability and may aid the development of targeted treatment strategies