On the arithmetic sums of Cantor sets

Let C_\la and C_\ga be two affine Cantor sets in $\mathbb{R}$ with similarity dimensions d_\la and d_\ga, respectively. We define an analog of the Bandt-Graf condition for self-similar systems and use it to give necessary and sufficient conditions for having \Ha^{d_\la+d_\ga}(C_\la + C_\ga)>0 where C_\la + C_\ga denotes the arithmetic sum of the sets. We use this result to analyze the orthogonal projection properties of sets of the form C_\la \times C_\ga. We prove that for Lebesgue almost all directions $\theta$ for which the projection is not one-to-one, the projection has zero (d_\la + d_\ga)-dimensional Hausdorff measure. We demonstrate the results on the case when C_\la and C_\ga are the middle-(1-2\la) and middle-(1-2\ga) sets

Coenzyme Q ₁₀ and L-Carnitine Disturbances in Children with Mitochondrial Diseases

Coenzyme Q10 (CoQ10) and L-carnitine are very important biologically active compounds involved in energy metabolism. L-carnitine and coenzyme Q10 disturbances in mitochondrial diseases require the correction. Patients and methods: The levels of coenzyme Q10 and L-carnitine (total carnitine, free carnitine, and acylcarnitines) were determined in children with mitochondrial diseases (25 children and 16 children, respectively). High-performance liquid chromatography with UV detection (chromatograph Shimadzu Nexera LC-30) and chromatography-mass spectrometry (Agilent 6410 QQQ , USA) were used. As an additional parameter of possible coenzyme Q10 and carnitine insufficiency, the coenzyme Q10/cholesterol ratio and acylcarnitines/free carnitine ratio were calculated. Results: A significantly low ratio of coenzyme Q10/cholesterol in children with mitochondrial diseases was revealed—0.10 ± 0.01 vs. 0.19 ± 0.01 in the control group (p < 0.001). A lower absolute level of coenzyme Q10 and tendency toward a more pronounced decrease in the Q10/cholesterol ratio in older patients (6–16 years) were shown. The free carnitine blood level was within the normal range and averaged at 29.8 ± 2.6 μmol/l; however, the level was lower than that in the control group (44 ± 5.2 μmol/l, p < 0.05). A pronounced significant increase in the acylcarnitines/free carnitine ratio was determined—1.5 ± 0.05 (the normal range < 0.6)

Longitudinal high-throughput TCR repertoire profiling reveals the dynamics of T cell memory formation after mild COVID-19 infection

COVID-19 is a global pandemic caused by the SARS-CoV-2 coronavirus. T cells play a key role in the adaptive antiviral immune response by killing infected cells and facilitating the selection of virus-specific antibodies. However neither the dynamics and cross-reactivity of the SARS-CoV-2-specific T cell response nor the diversity of resulting immune memory are well understood. In this study we use longitudinal high-throughput T cell receptor (TCR) sequencing to track changes in the T cell repertoire following two mild cases of COVID-19. In both donors we identified CD4+ and CD8+ T cell clones with transient clonal expansion after infection. The antigen specificity of CD8+ TCR sequences to SARS-CoV-2 epitopes was confirmed by both MHC tetramer binding and presence in large database of SARS-CoV-2 epitope-specific TCRs. We describe characteristic motifs in TCR sequences of COVID-19-reactive clones and show preferential occurence of these motifs in publicly available large dataset of repertoires from COVID-19 patients. We show that in both donors the majority of infection-reactive clonotypes acquire memory phenotypes. Certain T cell clones were detected in the memory fraction at the pre-infection timepoint, suggesting participation of pre-existing cross-reactive memory T cells in the immune response to SARS-CoV-2

Precise tracking of vaccine-responding T-cell clones reveals convergent and personalized response in identical twins

T-cell receptor (TCR) repertoire data contain information about infections that could be used in disease diagnostics and vaccine development, but extracting that information remains a major challenge. Here we developed a statistical framework to detect TCR clone proliferation and contraction from longitudinal repertoire data. We applied this framework to data from three pairs of identical twins immunized with the yellow fever vaccine. We identified 500-1500 responding TCRs in each donor and validated them using three independent assays. While the responding TCRs were mostly private, albeit with higher overlap between twins, they could be well predicted using a classifier based on sequence similarity. Our method can also be applied to samples obtained post-infection, making it suitable for systematic discovery of new infection-specific TCRs in the clinic

Implementing the European Sports Leadership Programme: A vehicle to help development graduate workplace competencies

This research was part of a large intervention study implementing the European Sports Leadership Programme (ESLP). This paper reports the outcomes of the qualitative study that employed focus groups to assess the students’ perceptions of the 15 competencies determined according to the Framework for qualifications of the European Higher Education Area, before and after the ESLP. Focus groups were carried out at each of the five universities. The ESLP involved university students working as a sports leader for 24 months with the aim to engage more students in university sport, whilst they took part in a graduate employability programme. Each university recruited five sports leaders in their second year at university, to deliver 10 new sport and recreational activities targeting the wider inactive or semi-active student population. Findings highlighted that Organization and planning, Oral and written communication, Development of planning and decision making, and Teamworking, followed closely by Emotional control and Adapting to new situations, were the most commonly reported competencies. They affirmed that this programme had helped to develop these competencies. Use of information, communication and technology, Communication in a foreign language, Research and Emotional control were the most common competencies that students stated they needed to improve further. This research found that implementing the ESLP helped to develop students’ perceptions of their workplace and career competencies. The ESLP is therefore, recommended as one approach to helping universities to develop student’s workplace and career competencies

Primary and secondary anti-viral response captured by the dynamics and phenotype of individual T cell clones

The diverse repertoire of T-cell receptors (TCR) plays a key role in the adaptive immune response to infections. Previous studies show that secondary responses to the yellow fever vaccine - the model for acute infection in humans - are weaker than primary ones, but only quantitative measurements can describe the concentration changes and lineage fates for distinct T-cell clones in vivo over time. Using TCR alpha and beta repertoire sequencing for T-cell subsets, as well as single-cell RNAseq and TCRseq, we track the concentrations and phenotypes of individual T-cell clones in response to primary and secondary yellow fever immunization showing their large diversity. We confirm the secondary response is an order of magnitude weaker, albeit $\sim10$ days faster than the primary one. Estimating the fraction of the T-cell response directed against the single immunodominant epitope, we identify the sequence features of TCRs that define the high precursor frequency of the two major TCR motifs specific for this particular epitope. We also show the consistency of clonal expansion dynamics between bulk alpha and beta repertoires, using a new methodology to reconstruct alpha-beta pairings from clonal trajectories

A novel unconventional T cell population enriched in Crohn's disease

Objective One of the current hypotheses to explain the proinflammatory immune response in IBD is a dysregulated T cell reaction to yet unknown intestinal antigens. As such, it may be possible to identify disease-associated T cell clonotypes by analysing the peripheral and intestinal T-cell receptor (TCR) repertoire of patients with IBD and controls. Design We performed bulk TCR repertoire profiling of both the TCR alpha and beta chains using high-throughput sequencing in peripheral blood samples of a total of 244 patients with IBD and healthy controls as well as from matched blood and intestinal tissue of 59 patients with IBD and disease controls. We further characterised specific T cell clonotypes via single-cell RNAseq. Results We identified a group of clonotypes, characterised by semi-invariant TCR alpha chains, to be significantly enriched in the blood of patients with Crohn's disease (CD) and particularly expanded in the CD8+ T cell population. Single-cell RNAseq data showed an innate-like phenotype of these cells, with a comparable gene expression to unconventional T cells such as mucosal associated invariant T and natural killer T (NKT) cells, but with distinct TCRs. Conclusions We identified and characterised a subpopulation of unconventional Crohn-associated invariant T (CAIT) cells. Multiple evidence suggests these cells to be part of the NKT type II population. The potential implications of this population for CD or a subset thereof remain to be elucidated, and the immunophenotype and antigen reactivity of CAIT cells need further investigations in future studies

Functionally specialized human CD4+ T-cell subsets express physicochemically distinct TCRs

The organizational integrity of the adaptive immune system is determined by functionally discrete subsets of CD4+ T cells, but it has remained unclear to what extent lineage choice is influenced by clonotypically expressed T-cell receptors (TCRs). To address this issue, we used a high-throughput approach to profile the αβ TCR repertoires of human naive and effector/memory CD4+ T-cell subsets, irrespective of antigen specificity. Highly conserved physicochemical and recombinatorial features were encoded on a subset-specific basis in the effector/memory compartment. Clonal tracking further identified forbidden and permitted transition pathways, mapping effector/memory subsets related by interconversion or ontogeny. Public sequences were largely confined to particular effector/memory subsets, including regulatory T cells (Tregs), which also displayed hardwired repertoire features in the naive compartment. Accordingly, these cumulative repertoire portraits establish a link between clonotype fate decisions in the complex world of CD4+ T cells and the intrinsic properties of somatically rearranged TCRs