The Chirality-Flow Formalism and Optimising Scattering Amplitudes

This thesis is composed of five papers, which all attempt to optimise calculations of scattering amplitudes in high-energy-physics collisions. These scattering amplitudes are a key part of theoretical predictions for particle-physics experiments like the Large Hadron Collider at CERN. The first four papers are the main topic of the thesis, and describe a novel method called chirality flow. Chirality flow simplifies Feynman-diagram calculations and makes them more intuitive. Papers I, II, and IV describe chirality flow in detail at both tree-level and one-loop level, while paper III shows a first implementation of it in the event generator MadGraph5_aMC@NLO. The final paper instead explores the speed, accuracy, and precision of an approximation of the colour part of a scattering amplitude.Paper I introduces the chirality-flow formalism, a new pictorial method used to calculate tree-level helicity amplitudes by drawing lines and connecting them to find spinor inner products, instead of doing algebraic manipulations. This method makes calculations more transparent, and often allows one to go from Feynman diagram to spinor inner products in a single line. Massless QED and QCD are treated in full. Paper II extends the chirality-flow formalism of paper I to deal with massive particles, and therefore allows chirality flow to be used for any tree-level Standard Model calculation. Paper III describes our implementation of chirality flow in massless QED in MadGraph5_aMC@NLO. A speed comparison is made showing up to a factor of 10 increase in evaluation speed. Paper IV extends the chirality-flow formalism to the one-loop level for any Standard Model calculation, showing the simplifications in the numerator algebra and the tensor reduction. Paper V describes an extension to the MadGraph5_aMC@NLO event generator in which the kinematics are calculated using Berends-Giele recursions instead of Feynman diagrams, and the colour matrix can be expanded in the number of colours Nc. The speed of the extension, and the accuracy and precision of the colour expansion are explored

The chirality-flow formalism

We take a fresh look at Feynman diagrams in the spinor-helicity formalism. Focusing on tree-level massless QED and QCD, we develop a new and conceptually simple graphical method for their calculation. In this pictorial method, which we dub the chirality-flow formalism, Feynman diagrams are directly represented in terms of chirality-flow lines corresponding to spinor inner products, without the need to resort to intermediate algebraic manipulations.Comment: 44 pages, 3 figure

Simplifying QCD event generation with chirality flow, reference vectors and spin directions

The chirality-flow formalism, combined with good choices of gauge reference vectors, simplifies tree-level calculations to the extent that it is often possible to write down amplitudes corresponding to Feynman diagrams immediately. It has also proven to give a very sizable speedup in a proof of concept implementation of massless tree-level QED in MadGraph5_aMC@NLO. In the present paper we extend this analysis to QCD, including massive quarks. We define helicity-dependent versions of the gluon vertices, derive constraints on the spinor structure of propagating gluons, and explore the Schouten identity to simplify the four-gluon vertex further. For massive quarks, the chirality-flow formalism sheds light on how to exploit the freedom to measure spin along any direction to shorten the calculations. Overall, this results in a clear speedup for treating the Lorentz structure at high multiplicities.Comment: 30 pages, 4 figure

Lifelongα-tocopherol supplementation increases the median life span of C57BL/6 mice in the cold but has only minor effects on oxidative damage

The effects of dietary antioxidant supplementation on oxidative stress and life span are confused. We maintained C57BL/6 mice at 7 ± 2°C and supplemented their diet with α-tocopherol from 4 months of age. Supplementation significantly increased (p = 0.042) median life span by 15% (785 days, n = 44) relative to unsupplemented controls (682 days, n = 43) and also increased maximum life span (oldest 10%, p = 0.028). No sex or sex by treatment interaction effects were observed on life span, with treatment having no effect on resting or daily metabolic rate. Lymphocyte and hepatocyte oxidative DNA damage and hepatic lipid peroxidation were unaffected by supplementation, but hepatic oxidative DNA damage increased with age. Using a cDNA macroarray, genes associated with xenobiotic metabolism were significantly upregulated in the livers of female mice at 6 months of age (2 months supplementation). At 22 months of age (18 months supplementation) this response had largely abated, but various genes linked to the p21 signaling pathway were upregulated at this time. We suggest that α-tocopherol may initially be metabolized as a xenobiotic, potentially explaining why previous studies observe a life span extension generally when lifelong supplementation is initiated early in life. The absence of any significant effect on oxidative damage suggests that the life span extension observed was not mediated via any antioxidant properties of α-tocopherol. We propose that the life span extension observed following α-tocopherol supplementation may be mediated via upregulation of cytochrome p450 genes after 2 months of supplementation and/or upregulation of p21 signaling genes after 18 months of supplementation. However, these signaling pathways now require further investigation to establish their exact role in life span extension following α-tocopherol supplementation

A Macaque Model to Study Vaginal HSV-2/Immunodeficiency Virus Co-Infection and the Impact of HSV-2 on Microbicide Efficacy

Herpes simplex virus type-2 (HSV-2) infection enhances the transmission and acquisition of human immunodeficiency virus (HIV). This occurs in symptomatic and asymptomatic stages of HSV-2 infection, suggesting that obvious herpetic lesions are not required to increase HIV spread. An animal model to investigate the underlying causes of the synergistic action of the two viruses and where preventative strategies can be tested under such complex physiological conditions is currently unavailable.We set out to establish a rhesus macaque model in which HSV-2 infection increases the susceptibility to vaginal infection with a model immunodeficiency virus (simian-human immunodeficiency virus, SHIV-RT), and to more stringently test promising microbicides. HSV-2 exposure significantly increased the frequency of vaginal SHIV-RT infection (n = 6). Although cervical lesions were detected in only approximately 10% of the animals, long term HSV-2 DNA shedding was detected (in 50% of animals followed for 2 years). Vaginal HSV-2 exposure elicited local cytokine/chemokine (n = 12) and systemic low-level HSV-2-specific adaptive responses in all animals (n = 8), involving CD4(+) and CD8(+) HSV-specific T cells (n = 5). Local cytokine/chemokine responses were lower in co-infected animals, while simian immunodeficiency virus (SIV)-specific adaptive responses were comparable in naïve and HSV-2-infected animals (n = 6). Despite the increased frequency of SHIV-RT infection, a new generation microbicide gel, comprised of Carraguard(R) and a non-nucleoside reverse transcriptase inhibitor MIV-150 (PC-817), blocked vaginal SHIV-RT infection in HSV-2-exposed animals (n = 8), just as in naïve animals.We established a unique HSV-2 macaque model that will likely facilitate research to define how HSV-2 increases HIV transmission, and enable more rigorous evaluation of candidate anti-viral approaches in vivo

Insufficient Production and Tissue Delivery of CD4+Memory T Cells in Rapidly Progressive Simian Immunodeficiency Virus Infection

The mechanisms linking human immunodeficiency virus replication to the progressive immunodeficiency of acquired immune deficiency syndrome are controversial, particularly the relative contribution of CD4+ T cell destruction. Here, we used the simian immunodeficiency virus (SIV) model to investigate the relationship between systemic CD4+ T cell dynamics and rapid disease progression. Of 18 rhesus macaques (RMs) infected with CCR5-tropic SIVmac239 (n = 14) or CXCR4-tropic SIVmac155T3 (n = 4), 4 of the former group manifested end-stage SIV disease by 200 d after infection. In SIVmac155T3 infections, naive CD4+ T cells were dramatically depleted, but this population was spared by SIVmac239, even in rapid progressors. In contrast, all SIVmac239-infected RMs demonstrated substantial systemic depletion of CD4+ memory T cells by day 28 after infection. Surprisingly, the extent of CD4+ memory T cell depletion was not, by itself, a strong predictor of rapid progression. However, in all RMs destined for stable infection, this depletion was countered by a striking increase in production of short-lived CD4+ memory T cells, many of which rapidly migrated to tissue. In all rapid progressors (P < 0.0001), production of these cells initiated but failed by day 42 of infection, and tissue delivery of new CD4+ memory T cells ceased. Thus, although profound depletion of tissue CD4+ memory T cells appeared to be a prerequisite for early pathogenesis, it was the inability to respond to this depletion with sustained production of tissue-homing CD4+ memory T cells that best distinguished rapid progressors, suggesting that mechanisms of the CD4+ memory T cell generation play a crucial role in maintaining immune homeostasis in stable SIV infection

Progressive CD4+ central–memory T cell decline results in CD4+ effector–memory insufficiency and overt disease in chronic SIV infection

Primary simian immunodeficiency virus (SIV) infections of rhesus macaques result in the dramatic depletion of CD4+ CCR5+ effector–memory T (TEM) cells from extra-lymphoid effector sites, but in most infections, an increased rate of CD4+ memory T cell proliferation appears to prevent collapse of effector site CD4+ TEM cell populations and acute-phase AIDS. Eventually, persistent SIV replication results in chronic-phase AIDS, but the responsible mechanisms remain controversial. Here, we demonstrate that in the chronic phase of progressive SIV infection, effector site CD4+ TEM cell populations manifest a slow, continuous decline, and that the degree of this depletion remains a highly significant correlate of late-onset AIDS. We further show that due to persistent immune activation, effector site CD4+ TEM cells are predominantly short-lived, and that their homeostasis is strikingly dependent on the production of new CD4+ TEM cells from central–memory T (TCM) cell precursors. The instability of effector site CD4+ TEM cell populations over time was not explained by increasing destruction of these cells, but rather was attributable to progressive reduction in their production, secondary to decreasing numbers of CCR5− CD4+ TCM cells. These data suggest that although CD4+ TEM cell depletion is a proximate mechanism of immunodeficiency, the tempo of this depletion and the timing of disease onset are largely determined by destruction, failing production, and gradual decline of CD4+ TCM cells

A cellular trafficking signal in the SIV envelope protein cytoplasmic domain is strongly selected for in pathogenic infection

The HIV/SIV envelope glycoprotein (Env) cytoplasmic domain contains a highly conserved Tyr-based trafficking signal that mediates both clathrin-dependent endocytosis and polarized sorting. Despite extensive analysis, the role of these functions in viral infection and pathogenesis is unclear. An SIV molecular clone (SIVmac239) in which this signal is inactivated by deletion of Gly-720 and Tyr-721 (SIVmac239ΔGY), replicates acutely to high levels in pigtail macaques (PTM) but is rapidly controlled. However, we previously reported that rhesus macaques and PTM can progress to AIDS following SIVmac239ΔGY infection in association with novel amino acid changes in the Env cytoplasmic domain. These included an R722G flanking the ΔGY deletion and a nine nucleotide deletion encoding amino acids 734–736 (ΔQTH) that overlaps the rev and tat open reading frames. We show that molecular clones containing these mutations reconstitute signals for both endocytosis and polarized sorting. In one PTM, a novel genotype was selected that generated a new signal for polarized sorting but not endocytosis. This genotype, together with the ΔGY mutation, was conserved in association with high viral loads for several months when introduced into naïve PTMs. For the first time, our findings reveal strong selection pressure for Env endocytosis and particularly for polarized sorting during pathogenic SIV infection in vivo

Folding by Numbers: Primary Sequence Statistics and Their Use in Studying Protein Folding

The exponential growth over the past several decades in the quantity of both primary sequence data available and the number of protein structures determined has provided a wealth of information describing the relationship between protein primary sequence and tertiary structure. This growing repository of data has served as a prime source for statistical analysis, where underlying relationships between patterns of amino acids and protein structure can be uncovered. Here, we survey the main statistical approaches that have been used for identifying patterns within protein sequences, and discuss sequence pattern research as it relates to both secondary and tertiary protein structure. Limitations to statistical analyses are discussed, and a context for their role within the field of protein folding is given. We conclude by describing a novel statistical study of residue patterning in β-strands, which finds that hydrophobic (i,i+2) pairing in β-strands occurs more often than expected at locations near strand termini. Interpretations involving β-sheet nucleation and growth are discussed

Recombinant HIV Envelope Proteins Fail to Engage Germline Versions of Anti-CD4bs bNAbs

Vaccine candidates for HIV-1 so far have not been able to elicit broadly neutralizing antibodies (bNAbs) although they express the epitopes recognized by bNAbs to the HIV envelope glycoprotein (Env). To understand whether and how Env immunogens interact with the predicted germline versions of known bNAbs, we screened a large panel (N:56) of recombinant Envs (from clades A, B and C) for binding to the germline predecessors of the broadly neutralizing anti-CD4 binding site antibodies b12, NIH45-46 and 3BNC60. Although the mature antibodies reacted with diverse Envs, the corresponding germline antibodies did not display Env-reactivity. Experiments conducted with engineered chimeric antibodies combining the mature and germline heavy and light chains, respectively and vice-versa, revealed that both antibody chains are important for the known cross-reactivity of these antibodies. Our results also indicate that in order for b12 to display its broad cross-reactivity, multiple somatic mutations within its VH region are required. A consequence of the failure of the germline b12 to bind recombinant soluble Env is that Env-induced B-cell activation through the germline b12 BCR does not take place. Our study provides a new explanation for the difficulties in eliciting bNAbs with recombinant soluble Env immunogens. Our study also highlights the need for intense efforts to identify rare naturally occurring or engineered Envs that may engage the germline BCR versions of bNAbs