9 research outputs found

    Sampling distributions of LE-LOD(max) as a function of number of families N.

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    (A) Results when data are generated under the hypothesis of (complete) disequilibrium, with s = 2, k = 1, γ = 0, and f = .5. (B) Corresponding results when data are generated under the null hypothesis of no linkage and no linkage disequilibrium.</p

    Sampling distributions and expected values of .

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    (A) Swarm plots showing sampling distributions of , as obtained from maximizing the LD-LOD, as a function of number of families N; (B) Expected values of as a function of population prevalence γ and ascertainment parameter k, for f = 0.2, 0.5 and 0.8, reading from bottom to top of the plot, respectively; (C) Expected values of the estimate of f obtained by maximizing the TBF (denoted here as fTBF) as a function of population prevalence γ and ascertainment parameter k, for f = 0.2, 0.5 and 0.8, reading from bottom to top of the plot, respectively. Data are the same as used to generate Figs 1 and 2, respectively.</p

    Expected values of alternative co-segregation measures as a function of ascertainment model and phenocopy rate for N = 20.

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    (A) Expected values of LE-LOD(max) as a function of population prevalence γ and ascertainment parameter k, for f = 0.5, s = 2 and N = 20. (B) Expected values of the TBF(gen) for the same data. (C) Expected values of the TBF evaluated at the same maximizing model used to evaluate LE-LOD in panel A. Note the different scales on the y-axis across subplots.</p

    Swarm plots showing sampling distributions of penetrance estimates as a function of number of families N.

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    Distributions of (A) and (B) are shown for simulations of 1000 replicates, with true penetrance f = 0.5. The number of sibs per family s = 2; phenocopy rate γ = 0. Users interested in varying the parameters can use the PenEst app.</p

    Expected values of penetrance estimates as a function of population prevalence <i>γ</i> and ascertainment parameter <i>k</i>.

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    Expected values of (A) and (B) when the true penetrance f = 0.5; expected values of (C) and (D) when f = 0.2 (lower line sets) or f = 0.8 (upper line sets). The number of sibs per family, s = 2. Users interested in varying the parameters can use the PenEst app.</p

    Different molecular interactions in models M1–M7 produce different temporal profiles of PIP<sub>3</sub> binding to Itk.

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    <p>(<b>A</b>) Kinetics of PIP<sub>3</sub> association of Itk for fixed initial PIP<sub>3</sub> and Itk concentrations (100 and 370 molecules, respectively) in models with feedbacks (M1–M4, and M7, left panel) and no feedbacks (M5–M6, right panel). (B) The shapes of the temporal profiles can be characterized by the parameters peak time (<i>τ</i><sub>p</sub>), peak width (<i>τ</i><sub>w</sub>), and peak value or amplitude (<i>A</i>). The dimensionless asymmetry ratio <i>R</i> = <i>τ</i><sub>w</sub>/<i>τ</i><sub>p</sub> quantifies how symmetric the shape of the time profile is. A larger R value indicates larger asymmetry. (C) Variations in R in models M1–M7 for different initial concentrations of Itk and PIP<sub>3</sub>. Color scales for R values are shown on the right of each panel.</p

    Experimentally measured PLCγ1activation kinetics in DP thymocytes stimulated with TCR ligands of different affinities and robustness of <i>in silico</i> models.

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    <p>(A) Immunoblots showing Y<sub>783</sub>-phosphorylated (upper panels) and total (lower panels) PLCγ1 protein amounts in <i>RAG2<sup>−/−</sup>MHC<sup>−/−</sup> OT1 TCR-transgenic</i> DP thymocytes stimulated for the indicated times with MHCI tetramers presenting the indicated altered peptide ligands (APL). (B) Phospho-PLCγ1 levels normalized to total PLCγ1 protein amounts plotted over time for the indicated APLs. Their TCR affinity decreases in the order OVA (black)>Q4R7 (red)>Q4H7 (blue)>G4 (green). Band intensities were quantified via scanning and analysis with <i>ImageJ</i> software. Representative of several independent experiments. (C) Variation of the Kulback-Leibler distance D<sub>KL</sub> with <i>R</i> for models M1–M3 (blue, red and black, respectively), M7 (yellow), and M4–M6 (orange, purple, and maroon, respectively) at high initial Itk (Itk<sup>0</sup> = 140 molecules) and PIP<sub>3</sub> concentrations (PIP<sub>3</sub><sup>0</sup> = 530 molecules), representing high-affinity OVA stimulation for <i>τ</i><sub>p</sub> = 2 min and <i>A</i> (shown as <i>A</i><sub>avg</sub>) = 40 molecules. Note we use <i>A</i> to represent the amplitude <i>A</i><sup>expt</sup> in experiments measuring fold change in Itk phosphorylation (see the main text for further details). The vertical orange bar indicates R<i><sup>expt</sup></i> for OVA. Color legend in (D). (D) The color map shows which model is most robust (has the lowest D<sub>KL</sub>) as <i>R<sup>expt</sup></i> and <i>A</i> (shown as <i>A</i><sub>avg</sub>) are varied for the same parameters as in (C). The color legend is depicted on the right.</p

    Models containing Itk dimers and dueling feedbacks also show higher robustness for polyclonal T cells stimulated by anti-CD3 antibodies.

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    <p>PLCγ1 phosphorylation kinetics in <i>MHC<sup>−/−</sup></i> T cells stimulated by antibodies against (A) CD3 or (B) CD3 and CD4 at 1 µg/ml versus 5 µg/ml. (C) Variation of D<sub>KL</sub> with R for the <i>in silico models</i> M1–M3 (blue, red and black, respectively), M7 (yellow), and M5–M6 (purple and maroon, respectively) at initial Itk (Itk<sup>0</sup> = 100 molecules) and PIP<sub>3</sub> concentrations (PIP<sub>3</sub><sup>0</sup> = 370 molecules) at <i>τ</i><sub>p</sub> = 1 min and <i>A</i><sub>avg</sub> = 60 molecules, representing anti-CD3 stimulation at 5 µg/ml. The orange bar indicates R<i><sup>expt</sup></i>. Note we use <i>A</i><sub>avg</sub> to represent the amplitude A<sup>expt</sup> in experiments measuring fold change in Itk phosphorylation (see the main text for further details). (D) Variation of D<sub>KL</sub> with R for anti-CD3/CD4 stimulation at 5 µg/ml at <i>τ</i><sub>p</sub> = 1 min and <i>A</i><sub>avg</sub> = 80 molecules. The initial Itk (Itk<sup>0</sup> = 140 molecules) and PIP<sub>3</sub> concentrations (PIP<sub>3</sub><sup>0</sup> = 530 molecules) were used. The orange bar indicates R<i><sup>expt</sup></i>. (E) and (F) show maps of the most robust models (with the lowest D<sub>KL</sub>) as R<i><sup>expt</sup></i> and <i>A</i> (shown as <i>A</i><sub>avg</sub>) are varied for the same parameters as in (C) and (D), respectively.</p

    Relevant basic interactions between Itk, PIP<sub>3</sub> and IP<sub>4</sub>.

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    <p>Following TCR-pMHC binding, Itk molecules are bound by the LAT signalosome via SLP-76 (not shown). Itk molecules (monomers or dimers, blue diamonds), bind the membrane lipid PIP<sub>3</sub> with low affinity through their PH domains. PIP<sub>3</sub> bound Itk phosphorylates and thereby activates LAT-bound PLCγ1. Activated PLCγ1 then hydrolyzes the membrane lipid PIP<sub>2</sub> into the soluble second messenger IP<sub>3</sub>, a key mediator of Ca<sup>2+</sup> mobilization. IP<sub>3</sub> 3-kinase B (ItpkB) converts IP<sub>3</sub> into IP<sub>4</sub> (red filled circle). For our <i>in silico</i> models, we simplified this series of reactions, encircled by the orange oval, into a single second order reaction where PIP<sub>3</sub> bound Itk converts PIP<sub>2</sub> into IP<sub>4</sub>. In models M1–M4 and M7, IP<sub>4</sub> modifies the Itk PH domain (denoted as Itk<sup>C</sup>, purple diamonds) to promote PIP<sub>3</sub> and IP<sub>4</sub> binding to the Itk PH domain. At the onset of the signaling, when the concentration of IP<sub>4</sub> is smaller than that of PIP<sub>3</sub>, IP<sub>4</sub> helps Itk<sup>C</sup> to bind to PIP<sub>3</sub> (left lower panel). However, as the concentration of IP<sub>4</sub> is increased at later times, IP<sub>4</sub> outcompetes PIP<sub>3</sub> for binding to Itk<sup>C</sup> and sequesters Itk<sup>C</sup> to the cytosol (right lower panel). In models M5/M6, IP<sub>4</sub> and PIP<sub>3</sub> do not augment each other’s binding to Itk. However, IP<sub>4</sub> still outcompetes PIP<sub>3</sub> for Itk PH domain binding when the number of IP<sub>4</sub> molecules becomes much larger than that of PIP<sub>3</sub> molecules at later times.</p
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