Model predictions of age-dependent glucose profiles in disease progressors and non-progressors and model validation based on prediction of β-cell mass.

<p>(A) Model prediction of glucose levels in autoantibody positive cases. (B) Model prediction of glucose levels in autoantibody positive cases. The profiles are fitted to glucose measurements in NOD mice from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0051909#pone.0051909-SysiAho1" target="_blank">[10]</a> which are shown in the same figure. The goodness-of-fit <i>R²</i> values are 0.83 (IAA+ progessors), 0.55 (IAA+ non-progressors), 0.59 (IAA- progressors) and 0.18 (IAA- non-progressors). Fitting was performed using the fminsearch function in Matlab (Mathworks, Inc., Natick, MA). Because the number of experimental data points is small (17 data points for IAA+ progressors, 30 data points for IAA+ non progressors, 21 data points for IAA- progressors and 31 data points for IAA- non progressors), we fit the trends of data rather than their exact behaviour. (C) Prediction of β-cell mass: model performances with a set of qualitatively estimated parameters for IAA+ progressors case and with and parameter value taken from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0051909#pone.0051909-Maree1" target="_blank">[19]</a>.</p

Description of the model variables and parameters.

<p>Description of the model variables and parameters.</p

Schematic presentation of function used in autoimmune response equation.

<p> is the threshold for autoimmune response activation and is the shut-off value.</p

Different time courses of autoimmune response.

<p>Simulated (<b>A</b>) protective autoimmunity, (<b>B</b>) autoimmunity with an early shut-off and (<b>C</b>) delayed-onset autoimmunity. Different profiles are obtained by setting different values of and parameters (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0051909#pone.0051909.e035" target="_blank">equation 2</a>).</p

Simulated amounts of macrophages and of activated macrophages.

<p>The amount of macrophages increases with time and the amount of activated macrophages decreases in time (in agreement with the Copenhagen model <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0051909#pone.0051909-FreieslebenDeBlasio1" target="_blank">[13]</a>).</p

Schematic representation of the model.

<p>The parameters and variables of the model are explained in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0051909#pone-0051909-t001" target="_blank"><b>Table 1</b></a>. Proteins released by the environmental triggers attack the β-cells and start the degenerative process of tissue loss. These proteins are detected by macrophages in the islets of Langerhans, leading to formation of activated macrophages. Activated macrophages release signal molecules (<i>e.g.</i>, cytokines) and immunogenic danger signals. Danger (alerting) signals activate the autoimmune response which further triggers the autoimmune-induced (“positive”) process of β-cell loss.</p

Description of the variables and parameters from the β-cell model.

<p>Description of the variables and parameters from the β-cell model.</p