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The development of mature, antigen-inexperienced (naive) T cells begins in the thymus and continues after export into the periphery. Post-thymic maturation of naive T cells, in humans, coincides with the progressive loss of markers such as protein tyrosine kinase 7 (PTK7) and platelet endothelial cell adhesion molecule-1 (CD31). As a consequence, subpopulations of naive T cells can be recognised raising questions about the processes that give rise to the loss of these markers and their exact relationship to recent thymic emigrants (RTE). Here, we combine a mathematical survival analysis approach and data from healthy and thymectomised humans to understand the apparent persistence of populations of 'veteran' PTK7 (+) T cells in thymectomised individuals. We show that a model of heterogeneity in rates of maturation, possibly linked to natural variation in TCR signalling thresholds or affinity for self-antigens, can explain the data. This model of maturation predicts that the average post-thymic age of PTK7 (+) T cells will increase linearly with the age of the host suggesting that, despite the immature phenotype, PTK7 (+) cells do not necessarily represent a population of RTE. Further, the model predicts an accelerated increase in the average post-thymic age of residual PTK7 (+) T cells following thymectomy and may also explain in part the prematurely aged phenotype of the naive T cell pool in individuals thymectomised early in life.

The recent development of High Throughput Sequencing technologies has enabled an individual's TCR repertoire to be efficiently analysed at the nucleotide level. However, with unique clonotypes ranging in the tens of millions per individual, this approach gives a surfeit of information that is difficult to analyse and interpret in a biological context and gives little information about TCR structural diversity. Using publicly available TCR CDR3 sequence data, we analysed TCR repertoires by converting the encoded CDR3 amino acid sequences into Kidera Factors, a set of orthogonal physico-chemical properties that reflect protein structure. This approach enabled the TCR repertoire from different individuals to be distinguished and demonstrated the close similarity of the repertoire in different samples from the same individual.

Early antiretroviral therapy (ART) and virological suppression can affect evolving antibody responses to HIV infection. We aimed to assess frequency and predictors of seronegativity in infants starting early ART. We compared HIV antibody results between two of three treatment groups of the Children with HIV Early Antiretroviral Therapy (CHER) trial, done from July, 2005, until July, 2011, in which infants with HIV infection aged 5·7–12·0 weeks with a percentage of CD4-positive T lymphocytes of at least 25% were randomly assigned to immediate ART for 96 weeks (ART-96W) or deferred ART until clinical or immunological progression (ART-Def). We measured antibody from all available stored samples for ART-96W and ART-Def at trial week 84 using three assays: fourth-generation enzyme immunoassay HIV antigen–antibody combination, HIV-1 and HIV-2 rapid antibody test, and quantitative anti-gp120 IgG ELISA. We also assessed odds of seropositivity with respect to age of ART initiation and cumulative viral load. The CHER trial was registered with ClinicalTrials.gov, number NCT00102960. The median age of the infants from when samples were taken (184 samples from 268 infants) was 92 weeks (IQR 90·6–93·4). More specimens from the ART-96W group were seronegative than from the ART-Def group by enzyme immunoassay (ART-96W 49 [46%] of 107 vs ART-Def eight [11%] of 75; p<0·0001) and rapid antibody test (54 [53%] of 101 vs eight [11%] of 74; p<0·0001). Median anti-gp120 IgG concentration was lower in the ART-96W group (230 μg/μL [IQR 133–13 129]) than in the ART-Def group (6870 μg/μL [1706–53 645]; p<0·0001). If ART was started between 12 and 24 weeks of age, odds of seropositivity were increased 13·7 times (95% CI 3·1–60·2; p=0·001) compared with starting it between 0 and 12 weeks. All children starting ART aged older than 24 weeks were seropositive. Cumulative viral load to week 84 correlated with anti-gp120 IgG concentrations (coefficient 0·54; p<0·0001) and increased odds of seropositivity (odds ratio 1·59 [95% CI 1·1–2·3]) adjusted for ART initiation age. About half of children starting ART before 12 weeks of age were HIV seronegative by almost 2 years of age. HIV antibody tests cannot be used to reconfirm HIV diagnosis in children starting early ART. Long-term effects of seronegativity need further study. Clear guidelines are needed for retesting alongside improved diagnostic tests. Wellcome Trust, Medical Research Council, and National Institutes of Health.

Early treatment of HIV-infected children and adults is important for optimal immune reconstitution. Infants' immune systems are more plastic and dynamic than older children's or adults', and deserve particular attention. This study aimed to understand the response of the HIV-infected infant immune system to early antiretroviral therapy (ART) and planned ART interruption and restart. Data from HIV-infected children enrolled the CHER trial, starting ART aged between 6 and 12 weeks, were used to explore the effect of ART on immune reconstitution. We used linear and non-linear regression and mixed-effects models to describe children's CD4 trajectories and to identify predictors of CD4 count during early and interrupted ART. Early treatment arrested the decline in CD4 count but did not fully restore it to the levels observed in HIV-uninfected children. Treatment interruption at 40 or 96 weeks resulted in a rapid decline in CD4 T-cells, which on retreatment returned to levels observed before interruption. Naïve CD4 T-cell count was an important determinant of overall CD4 levels. A strong correlation was observed between thymic output and the stable CD4 count both before and after treatment interruption. Early identification and treatment of HIV-infected infants is important to stabilize CD4 counts at the highest levels possible. Once stabilized, children's CD4 counts appear resilient, with good potential for recovery following treatment interruption. The naïve T-cell pool and thymic production of naive cells are key determinants of children's CD4 levels.

Spectratyping assays are well recognized as the clinical gold standard for assessing the T cell receptor (TCR) repertoire in haematopoietic stem cell transplant (HSCT) recipients. These assays use length distributions of the hyper variable complementarity-determining region 3 (CDR3) to characterize a patient's T cell immune reconstitution post-transplant. However, whilst useful, TCR spectratyping is notably limited by its resolution, with the technique unable to provide data on the individual clonotypes present in a sample. High-resolution clonotype data are necessary to provide quantitative clinical TCR assessments and to better understand clonotype dynamics during clinically relevant events such as viral infections or GvHD. In this study we developed and applied a CDR3 Next Generation Sequencing (NGS) methodology to assess the TCR repertoire in cord blood transplant (CBT) recipients. Using this, we obtained comprehensive TCR data from 16 CBT patients and 5 control cord samples at Great Ormond Street Hospital (GOSH). These were analyzed to provide a quantitative measurement of the TCR repertoire and its constituents in patients post-CBT. We were able to both recreate and quantify inferences typically drawn from spectratyping data. Additionally, we demonstrate that an NGS approach to TCR assessment can provide novel insights into the recovery of the immune system in these patients. We show that NGS can be used to accurately quantify TCR repertoire diversity and to provide valuable inference on clonotypes detected in a sample. We serially assessed the progress of T cell immune reconstitution demonstrating that there is dramatic variation in TCR diversity immediately following transplantation and that the dynamics of T cell immune reconstitution is perturbed by the presence of GvHD. These findings provide a proof of concept for the adoption of NGS TCR sequencing in clinical practice.

Long-term immune reconstitution on antiretroviral therapy (ART) has important implications for HIV-infected children, who increasingly survive into adulthood. Children's response to ART differs from adults', and better descriptive and predictive models of reconstitution are needed to guide policy and direct research. We present statistical models characterising, qualitatively and quantitatively, patterns of long-term CD4 recovery. CD4 counts every 12 wk over a median (interquartile range) of 4.0 (3.7, 4.4) y in 1,206 HIV-infected children, aged 0.4-17.6 y, starting ART in the Antiretroviral Research for Watoto trial (ISRCTN 24791884) were analysed in an exploratory analysis supplementary to the trial's pre-specified outcomes. Most (n = 914; 76%) children's CD4 counts rose quickly on ART to a constant age-corrected level. Using nonlinear mixed-effects models, higher long-term CD4 counts were predicted for children starting ART younger, and with higher CD4 counts (p<0.001). These results suggest that current World Health Organization-recommended CD4 thresholds for starting ART in children ≥5 y will result in lower CD4 counts in older children when they become adults, such that vertically infected children who remain ART-naïve beyond 10 y of age are unlikely ever to normalise CD4 count, regardless of CD4 count at ART initiation. CD4 profiles with four qualitatively distinct reconstitution patterns were seen in the remaining 292 (24%) children. Study limitations included incomplete viral load data, and that the uncertainty in allocating children to distinct reconstitution groups was not modelled. Although younger ART-naïve children are at high risk of disease progression, they have good potential for achieving high CD4 counts on ART in later life provided ART is initiated following current World Health Organization (WHO), Paediatric European Network for Treatment of AIDS, or US Centers for Disease Control and Prevention guidelines. In contrast, to maximise CD4 reconstitution in treatment-naïve children >10 y, ART should ideally be considered even if there is a low risk of immediate disease progression. Further exploration of the immunological mechanisms for these CD4 recovery profiles should help guide management of paediatric HIV infection and optimise children's immunological development. Please see later in the article for the Editors' Summary.

The asymptomatic phase of HIV infection is characterised by a slow decline of peripheral blood CD4(+) T cells. Why this decline is slow is not understood. One potential explanation is that the low average rate of homeostatic proliferation or immune activation dictates the pace of a \"runaway\" decline of memory CD4(+) T cells, in which activation drives infection, higher viral loads, more recruitment of cells into an activated state, and further infection events. We explore this hypothesis using mathematical models. Using simple mathematical models of the dynamics of T cell homeostasis and proliferation, we find that this mechanism fails to explain the time scale of CD4(+) memory T cell loss. Instead it predicts the rapid attainment of a stable set point, so other mechanisms must be invoked to explain the slow decline in CD4(+) cells. A runaway cycle in which elevated CD4(+) T cell activation and proliferation drive HIV production and vice versa cannot explain the pace of depletion during chronic HIV infection. We summarize some alternative mechanisms by which the CD4(+) memory T cell homeostatic set point might slowly diminish. While none are mutually exclusive, the phenomenon of viral rebound, in which interruption of antiretroviral therapy causes a rapid return to pretreatment viral load and T cell counts, supports the model of virus adaptation as a major force driving depletion.

Decisions by uncommitted cells to differentiate down one lineage pathway or another is fundamental to developmental biology. In the immune system, lymphocyte precursors commit to T‐ or B‐cell lineages and T‐cell precursors to CD4 or CD8 independently of foreign antigen. T and B cells must also decide whether or not to respond to antigen and when a response is initiated, what sort of response to make such as the type of antibody, CD4 or CD8, and CD4 Th1 or Th2. The two basic mechanisms for these decision‐making processes are selection and instruction. Selection depends on prior stochastic production of precommitted cells, which are then selected to respond by an appropriate signal; for example, CD8 and CD4 responses selected by peptide presented in association with major histocompatibility complex class I or II. In contrast, instruction occurs when an uncommitted precursor embarks upon a differentiation pathway in response to a particular set of signals; for example, Th1 and Th2 lineage commitment. In this paper, the signals that determine Th1 and Th2 differentiation are examined with a mathematical model and shown to act as a bistable switch permitting either Tbet or Gata3 to be expressed in an individual cell but not both. The model is used to show how the Tbet Gata3 network within an individual cell interacts with cytokine signals between cells and suggests how Th1 and Th2 lineage commitment can become irreversible. These considerations provide an example of how mathematical models can be used to gain a better understanding of lymphocyte differentiation in an immune response.

The size and composition of the T lymphocyte compartment is subject to strict homeostatic regulation and is remarkably stable throughout life in spite of variable dynamics in cell production and death during T cell development and immune responses. Homeostasis is achieved by careful orchestration of lymphocyte survival and cell division. New T cells are generated from the thymus and the number of peripheral T cells is regulated by controlling survival and proliferation. How these processes combine is however very complex. Thymic output increases in the first year of life and then decreases but is crucial for establishing repertoire diversity. Proliferation of new naive T cells plays a crucial role for maintaining numbers but at a potential cost to TCR repertoire diversity. A mechanistic two-compartment model of T cell homeostasis is described here that includes specific terms for thymic output, cell proliferation, and cell death of both resting and dividing cells. The model successfully predicts the homeostatic set point for T cells in adults and identifies variables that determine the total number of T cells. It also accurately predicts T cell numbers in children in early life despite rapid changes in thymic output and growth over this period.

Ordinary differential equations (ODEs) are widely used to model many systems in physics, chemistry, engineering and biology. Often one wants to compare such equations with observed time course data, and use this to estimate parameters. Surprisingly, practical algorithms for doing this are relatively poorly developed, particularly in comparison with the sophistication of numerical methods for solving both initial and boundary value problems for differential equations, and for locating and analysing bifurcations. A lack of good numerical fitting methods is particularly problematic in the context of systems biology where only a handful of time points may be available. In this paper, we present a survey of existing algorithms and describe the main approaches. We also introduce and evaluate a new efficient technique for estimating ODEs linear in parameters particularly suited to situations where noise levels are high and the number of data points is low. It employs a spline-based collocation scheme and alternates linear least squares minimization steps with repeated estimates of the noise-free values of the variables. This is reminiscent of expectation-maximization methods widely used for problems with nuisance parameters or missing data.