F-test to compare best fits with the Dornhorst model (the null hypothesis) versus the DLS model (one extra parameter – the alternative hypothesis).

<p>F-test to compare best fits with the Dornhorst model (the null hypothesis) versus the DLS model (one extra parameter – the alternative hypothesis).</p

Platelet counts (±s.e.m.) and best-fit Dornhorst model parameters from fits to population survival data for each genotype, with 95% C.I.'s from the Monte Carlo technique in brackets.

<p>Platelet counts (±s.e.m.) and best-fit Dornhorst model parameters from fits to population survival data for each genotype, with 95% C.I.'s from the Monte Carlo technique in brackets.</p

The effect of experimental uncertainty on the ability to constrain the value of the random loss fraction.

<p>Fits to simulated data with Gaussian random noise of varying standard error of the mean (s.e.m.) added to simulate experimental uncertainty. (A)–(E) Simulated model parameters: <i>μ</i> = 100 hr, <i>σ</i> = 25 hr, with (A) <i>f</i> = 0.2, (B) <i>f</i> = 0.8. For each value of <i>f</i> and each value of the s.e.m. of the noise, the fit was repeated 1000 times with independently-generated noise – the box-and-whisker plots indicate median, interquartile range, 2.5 and 97.5 percentiles, and outliers are plotted as individual dots. (C) Interquartile range as a function of random loss fraction for the various levels of noise added to the simulated data. For a given value of the s.e.m. of the noise, higher values of the random loss fraction are generally better constrained than lower (non-zero) values.</p

F-test to compare best fits with the LS model (the null hypothesis) versus the DLS model (one extra parameter – the alternative hypothesis).

<p>F-test to compare best fits with the LS model (the null hypothesis) versus the DLS model (one extra parameter – the alternative hypothesis).</p

Illustration of the difficulty in constraining the value of the random loss fraction using the Dornhorst-Lognormal-Senescent model.

<p>(<b>A</b>) Theoretical population survival curves from the DLS model as the mean and standard deviation of natural life span are kept constant (<i>μ</i> = 100 hr, <i>σ</i> = 25 hr) while the random loss fraction, <i>f</i>, is varied. Small values of the random loss fraction produce subtle changes in the shape of the population survival curve. (<b>B</b>) Strong correlation between values of the random loss fraction (<i>f</i>) and the mean natural life span (<i>μ</i>) in the Monte Carlo simulation – r² is the square of Pearson's correlation coefficient; Slope is the gradient of the linear regression with 95% confidence intervals in brackets [,]. The correlation with other parameters of the model is much less – (<b>B</b>) random loss fraction (<i>f</i>) versus standard deviation natural life span (<i>σ</i>), and (<b>C</b>) random loss fraction (<i>f</i>) versus labeling efficiency (<i>e₁</i>).</p

Platelet counts (±s.e.m) and best-fit DLS model parameters from fits to population survival data for each genotype, with 95% C.I.'s from the Monte Carlo technique in brackets.

<p>Platelet counts (±s.e.m) and best-fit DLS model parameters from fits to population survival data for each genotype, with 95% C.I.'s from the Monte Carlo technique in brackets.</p

Values of absolute random loss rate (fixed requirement for platelets), extracted from the same fits of the DLS model to survival data as illustrated in <b>Figure 3</b>.

<p>1000 Monte Carlo simulations were performed and fit to obtain parameters – box-and-whisker plots indicate median, interquartile range, 2.5 and 97.5 percentiles, and outliers are plotted as individual dots.</p

Dornhorst model fits of platelet survival data predict that a large proportion of platelets are destroyed randomly.

<p>(<b>A</b>) Population survival data and Dornhorst model best fits for <i>Bcl-x^+/Plt20</i> (blue), wild-type (green) and <i>Bak^−/−</i> (red) mice. A Monte Carlo technique was used to generate estimates of confidence intervals for the model parameters – (<b>B</b>) natural life span, <i>T</i>, (<b>C</b>) standard deviation of natural life span (always 0 hr for this model), (<b>D</b>) random loss rate constant, <i>r</i>, and (<b>E</b>) random loss fraction, <i>f</i>. 1000 Monte Carlo simulations were performed and fit to obtain parameters – box-and-whisker plots indicate median, interquartile range, 2.5 and 97.5 percentiles, and outliers are plotted as individual dots.</p

Lognormal-Senescent model fits of platelet survival data.

<p>(<b>A</b>) Population survival data and LS model best fits for <i>Bcl-x^+/Plt20</i> (blue), wild-type (green) and <i>Bak^−/−</i> (red) mice. A Monte Carlo technique was used to generate estimates of confidence intervals for the model parameters – (<b>B</b>) mean natural life span, <i>μ</i>, (<b>C</b>) standard deviation of natural life span, <i>σ</i>, (<b>D</b>) random loss rate constant, <i>r</i> (always 0 hr⁻¹ for this model), and (<b>E</b>) random loss fraction, <i>f</i> (always 0 for this model). 1000 Monte Carlo simulations were performed and fit to obtain parameters – box-and-whisker plots indicate median, interquartile range, 2.5 and 97.5 percentiles, and outliers are plotted as individual dots.</p

Dornhorst-Lognormal-Senescent model fits of platelet survival data reveals a smaller random loss fraction than the classic Dornhorst model but wide confidence intervals.

<p>(<b>A</b>) Population survival data and DLS model best fits for <i>Bcl-x^+/Plt20</i> (blue), wild-type (green) and <i>Bak^−/−</i> (red) mice. A Monte Carlo technique was used to generate estimates of confidence intervals for the model parameters – (<b>B</b>) natural life span, <i>T</i>, (<b>C</b>) standard deviation of natural life span, (<b>D</b>) random loss rate constant, <i>r</i>, and (<b>E</b>) random loss fraction, <i>f</i>. 1000 Monte Carlo simulations were performed and fit to obtain parameters – box-and-whisker plots indicate median, interquartile range, 2.5 and 97.5 percentiles, and outliers are plotted as individual dots.</p