Numerical renormalization group calculation of impurity internal energy and specific heat of quantum impurity models

We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model, we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat, $C_{\rm imp}$, to be calculated accurately from local static correlation functions; specifically via $C_{\rm imp}=\frac{\partial E_{\rm ionic}}{\partial T} + 1/2\frac{\partial E_{\rm hyb}}{\partial T}$, where $E_{\rm ionic}$ and $E_{\rm hyb}$ are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to $C_{\rm imp}$. For the non-degenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The new approach could also be of interest within other impurity solvers, e.g., within quantum Monte Carlo techniques.Comment: 16 pages, 15 figures, published versio

Cyclic nucleotide specificity of the activator and catalytic sites of a cGMP-stimulated cGMP phosphodiesterase from Dictyostelium discoideum

The cellular slime mold Dictyostelium discoideum has an intracellular phosphodiesterase which specifically hydrolyzes cGMP. The enzyme is activated by low cGMP concentrations, and is involved in the reduction of chemoattractant-mediated elevations of cGMP levels. The interaction of 20 cGMP derivatives with the activator site and with the catalytic site of the enzyme has been investigated. Binding of cGMP to the activator site is strongly reduced (more than 80-fold) if cGMP is no longer able to form a hydrogen bond at N2H2 or O2’H. Modifications at N7, C8, O3’ and O5’ induce only a small reduction of binding affinity. A cyclic phosphate structure, as well as a negatively charged oxygen atom at phosphorus, are essential to obtain activation of the enzyme. Substitution of the axial exocyclic oxygen atom by sulphur is tolerated; modification of the equatorial oxygen atom reduces the binding activity of cGMP to the activator site by 90-fold. Binding of cGMP to the catalytic site is strongly reduced if cGMP is modified at N1H, C6O, C8 and O3’, while modifications at N2H2, N3, N7, O2’H, and O5’ have minor effects. Both exocyclic oxygen atoms are important to obtain binding of cGMP to the catalytic site. The results indicate that activation of the enzyme by cGMP and hydrolysis of cGMP occur at different sites of the enzyme. cGMP is recognized at these sites by different types of molecular interaction between cGMP and the protein. cGMP derivatives at concentrations which saturate the activator site do not induce the same degree of activation of the enzyme (activation 2.3-6.6-fold). The binding affinities of the analogues for the activator site and their maximal activation are not correlated. Our results suggest that the enzyme is activated because cGMP bound to the activator site stabilizes a state of the enzyme which has a higher affinity for cGMP at the catalytic site.

Pancancer analysis of DNA methylation-driven genes using MethylMix.

Aberrant DNA methylation is an important mechanism that contributes to oncogenesis. Yet, few algorithms exist that exploit this vast dataset to identify hypo- and hypermethylated genes in cancer. We developed a novel computational algorithm called MethylMix to identify differentially methylated genes that are also predictive of transcription. We apply MethylMix to 12 individual cancer sites, and additionally combine all cancer sites in a pancancer analysis. We discover pancancer hypo- and hypermethylated genes and identify novel methylation-driven subgroups with clinical implications. MethylMix analysis on combined cancer sites reveals 10 pancancer clusters reflecting new similarities across malignantly transformed tissues

Immortalization of T-cells is accompanied by gradual changes in CpG methylation resulting in a profile resembling a subset of T-cell leukemias

We have previously described gene expression changes during spontaneous immortalization of T-cells, thereby identifying cellular processes important for cell growth crisis escape and unlimited proliferation. Here, we analyze the same model to investigate the role of genome-wide methylation in the immortalization process at different time points pre-crisis and post-crisis using high-resolution arrays. We show that over time in culture there is an overall accumulation of methylation alterations, with preferential increased methylation close to transcription start sites (TSSs), islands, and shore regions. Methylation and gene expression alterations did not correlate for the majority of genes, but for the fraction that correlated, gain of methylation close to TSS was associated with decreased gene expression. Interestingly, the pattern of CpG site methylation observed in immortal T-cell cultures was similar to clinical T-cell acute lymphoblastic leukemia (T-ALL) samples classified as CpG island methylator phenotype positive. These sites were highly overrepresented by polycomb target genes and involved in developmental, cell adhesion, and cell signaling processes. The presence of non-random methylation events in in vitro immortalized T-cell cultures and diagnostic T-ALL samples indicates altered methylation of CpG sites with a possible role in malignant hematopoiesis

Negative Impurity Magnetic Susceptibility and Heat Capacity in a Kondo Model with Narrow Peaks in the Local Density of Electron States

Temperature dependencies of the impurity magnetic susceptibility, entropy, and heat capacity have been obtained by the method of numerical renormalization group and exact diagonalization for the Kondo model with peaks in the electron density of states near the Fermi energy (in particular, with logarithmic Van Hove singularities). It is shown that these quantities can be {\it negative}. A new effect has been predicted (which, in principle, can be observed experimentally), namely, the decrease in the magnetic susceptibility and heat capacity of a nonmagnetic sample upon the addition of magnetic impurities into it