Figure 1.
Schematic representation of the model.
The parameters and variables of the model are explained in Table 1. 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 (e.g., cytokines) and immunogenic danger signals. Danger (alerting) signals activate the autoimmune response which further triggers the autoimmune-induced (“positive”) process of β-cell loss.
Table 1.
Description of the model variables and parameters.
Figure 2.
Model predictions of age-dependent glucose profiles in disease progressors and non-progressors and model validation based on prediction of β-cell mass.
(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 [10] which are shown in the same figure. The goodness-of-fit R2 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 [19].
Figure 3.
Simulated amounts of macrophages and of activated macrophages.
The amount of macrophages increases with time and the amount of activated macrophages decreases in time (in agreement with the Copenhagen model [13]).
Figure 4.
Different time courses of autoimmune response.
Simulated (A) protective autoimmunity, (B) autoimmunity with an early shut-off and (C) delayed-onset autoimmunity. Different profiles are obtained by setting different values of and
parameters (equation 2).
Figure 5.
Protective pathway and progression to autoimmune diabetes.
(A) Interaction between protective metabolic pathway and autoimmune response. Autoimmune response with stronger intensity leads to higher concentration of metabolite of protective pathway (effective protective pathway) as compared to the autoimmune response with weak intensity (defective protective pathway). (B) Prediction of β-cell mass in disease progressors and in protected non-progressors. The simulation is based on experimental data for NOD mice. Progressors are IAA+ at 8 weeks of age and non-progressors are IAA+ at 8 weeks of age [10]. β-cell loss is slower in the presence of effective protective pathway.
Figure 6.
Schematic presentation of function used in autoimmune response equation.
is the threshold for autoimmune response activation and
is the shut-off value.
Table 2.
Description of the variables and parameters from the β-cell model.