Zimmermann's Forest Formula, Infrared Divergences and the QCD Beta Function

We review Zimmermann's forest formula, which solves Bogoliubov's recursive $R$-operation for the subtraction of ultraviolet divergences in perturbative Quantum Field Theory. We further discuss a generalisation of the $R$-operation which subtracts besides ultraviolet also Euclidean infrared divergences. This generalisation, which goes under the name of the $R^*$-operation, can be used efficiently to compute renormalisation constants. We will discuss several results obtained by this method with focus on the QCD beta function at five loops as well as the application to hadronic Higgs boson decay rates at N${}^4$LO. This article summarizes a talk given at the Wolfhart Zimmermann Memorial Symposium.Comment: 17 pages, 5 figures; based on a talk given at the Wolfhart Zimmermann Memorial Symposium on the 22nd of May 2017 in Munic

The Soft-Virtual Higgs Cross-section at N3LO and the Convergence of the Threshold Expansion

We discuss the validity of the soft-virtual approximation and the threshold expansion for the Higgs boson production cross-section at hadron colliders in perturbative QCD up to next-to- next-to-next-to-leading order (N3LO).Comment: Proceedings of Moriond QCD 2014; contains several interesting plot

Renormalization of gluonic leading-twist Operators in covariant Gauges

We provide the all-loop structure of gauge-variant operators required for the renormalisation of Green's functions with insertions of twist-two operators in Yang-Mills theory. Using this structure we work out an explicit basis valid up to 4-loop order for an arbitrary compact simple gauge group. To achieve this we employ a generalised gauge symmetry, originally proposed by Dixon and Taylor, which arises after adding to the Yang-Mills Lagrangian also operators proportional to its equation of motion. Promoting this symmetry to a generalised BRST symmetry allows to generate the ghost operator from a single exact operator in the BRST-generalised sense. We show that our construction complies with the theorems by Joglekar and Lee. We further establish the existence of a generalised anti-BRST symmetry which we employ to derive non-trivial relations among the anomalous dimension matrices of ghost and equation-of-motion operators. For the purpose of demonstration we employ the formalism to compute the N=2,4 Mellin moments of the gluonic splitting function up to 4 loops and its N=6 Mellin moment up to 3 loops, where we also take advantage of additional simplifications of the background field formalism.Comment: 44 pages, 7 table

compleXView: a server for the interpretation of protein abundance and connectivity information to identify protein complexes

The molecular understanding of cellular processes requires the identification and characterization of the involved protein complexes. Affinity-purification and mass spectrometric analysis (AP-MS) are performed on a routine basis to detect proteins assembled in complexes. In particular, protein abundances obtained by quantitative mass spectrometry and direct protein contacts detected by crosslinking and mass spectrometry (XL-MS) provide complementary datasets for revealing the composition, topology and interactions of modules in a protein network. Here, we aim to combine quantitative and connectivity information by a webserver tool in order to infer protein complexes. In a first step, modeling protein abundances and functional annotations from Gene Ontology (GO) results in a network which, in a second step, is integrated with connectivity data from XL-MS analysis in order to complement and validate the protein complexes in the network. The output of our integrative approach is a quantitative protein interaction map which is supplemented with topological information of the detected protein complexes. compleXView is built up by two independent modules which are dedicated to the analysis of label-free AP-MS data and to the visualization of the detected complexes in a network together with crosslink-derived distance restraints. compleXView is available to all users without login requirements at http://xvis.genzentrum.lmu.de/compleXView

Soft Expansion of Double-Real-Virtual Corrections to Higgs Production at N3^3LO

We present methods to compute higher orders in the threshold expansion for the one-loop production of a Higgs boson in association with two partons at hadron colliders. This process contributes to the N$^3$LO Higgs production cross section beyond the soft-virtual approximation. We use reverse unitarity to expand the phase-space integrals in the small kinematic parameters and to reduce the coefficients of the expansion to a small set of master integrals. We describe two methods for the calculation of the master integrals. The first was introduced for the calculation of the soft triple-real radiation relevant to N$^3$LO Higgs production. The second uses a particular factorization of the three body phase-space measure and the knowledge of the scaling properties of the integral itself. Our result is presented as a Laurent expansion in the dimensional regulator, although some of the master integrals are computed to all orders in this parameter.Comment: 30 page

Molecular architecture of human polycomb repressive complex 2.

Polycomb Repressive Complex 2 (PRC2) is essential for gene silencing, establishing transcriptional repression of specific genes by tri-methylating Lysine 27 of histone H3, a process mediated by cofactors such as AEBP2. In spite of its biological importance, little is known about PRC2 architecture and subunit organization. Here, we present the first three-dimensional electron microscopy structure of the human PRC2 complex bound to its cofactor AEBP2. Using a novel internal protein tagging-method, in combination with isotopic chemical cross-linking and mass spectrometry, we have localized all the PRC2 subunits and their functional domains and generated a detailed map of interactions. The position and stabilization effect of AEBP2 suggests an allosteric role of this cofactor in regulating gene silencing. Regions in PRC2 that interact with modified histone tails are localized near the methyltransferase site, suggesting a molecular mechanism for the chromatin-based regulation of PRC2 activity.DOI:http://dx.doi.org/10.7554/eLife.00005.001

Translocation arrest by reversible folding of a precursor protein imported into mitochondria

Passage of precursor proteins through translocation contact sites of mitochondria was investigated by studying the import of a fusion protein consisting of the NH2-terminal 167 amino acids of yeast cytochrome b2 precursor and the complete mouse dihydrofolate reductase. Isolated mitochondria of Neurospora crassa readily imported the fusion protein. In the presence of methotrexate import was halted and a stable intermediate spanning both mitochondrial membranes at translocation contact sites accumulated. The complete dihydrofolate reductase moiety in this intermediate was external to the outer membrane, and the 136 amino acid residues of the cytochrome b2 moiety remaining after cleavage by the matrix processing peptidase spanned both outer and inner membranes. Removal of methotrexate led to import of the intermediate retained at the contact site into the matrix. Thus unfolding at the surface of the outer mitochondrial membrane is a prerequisite for passage through translocation contact sites. The membrane-spanning intermediate was used to estimate the number of translocation sites. Saturation was reached at 70 pmol intermediate per milligram of mitochondrial protein. This amount of translocation intermediates was calculated to occupy approximately 1% of the total surface of the outer membrane. The morphometrically determined area of close contact between outer and inner membranes corresponded to approximately 7% of the total outer membrane surface. Accumulation of the intermediate inhibited the import of other precursor proteins suggesting that different precursor proteins are using common translocation contact sites. We conclude that the machinery for protein translocation into mitochondria is present at contact sites in limited number

Crosslinking-MS analysis reveals RNA polymerase I domain architecture and basis of rRNA cleavage

RNA polymerase (Pol) I contains a 10-subunit catalytic core that is related to the core of Pol II and includes subunit A12.2. In addition, Pol I contains the heterodimeric subcomplexes A14/43 and A49/34.5, which are related to the Pol II subcomplex Rpb4/7 and the Pol II initiation factor TFIIF, respectively. Here we used lysine-lysine crosslinking, mass spectrometry (MS) and modeling based on five crystal structures, to extend the previous homology model of the Pol I core, to confirm the location of A14/43 and to position A12.2 and A49/34.5 on the core. In the resulting model of Pol I, the C-terminal ribbon (C-ribbon) domain of A12.2 reaches the active site via the polymerase pore, like the C-ribbon of the Pol II cleavage factor TFIIS, explaining why the intrinsic RNA cleavage activity of Pol I is strong, in contrast to the weak cleavage activity of Pol II. The A49/34.5 dimerization module resides on the polymerase lobe, like TFIIF, whereas the A49 tWH domain resides above the cleft, resembling parts of TFIIE. This indicates that Pol I and also Pol III are distantly related to a Pol II-TFIIS-TFIIF-TFIIE comple