Extended Modelling of Molecular Calcium Signalling in Platelets by Combined Recurrent Neural Network and Partial Least Squares Analyses

Figures

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  Figure 1. Assignment matrix of variables of 72 numbered experimental conditions. Calibrated curves of Fura-2-loaded platelets from one donor, representative for 5 donors, were used as input data. The conditions highlighted in blue (solid borders) were used as validation set, and those in red (dashed borders) were used as test set. Abbreviations: Col, collagen (μg/mL); CRP, collagen-related peptide (μg/mL); Thr, thrombin (nM); EG, EGTA: 0.1 mM if assigned to 1 or 1 mM CaCl2 if assigned to 0; AI, apyrase (0.1 U/mL) plus indomethacin (20 μM) if assigned to 1; Thap, thapsigargin (1 μM) if assigned to 1.

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  Figure 2. Workflow used for the data processing, neural network construction, and scalar model development. For explanation, see text.

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  Figure 3. Construction of two neural networks. (A) Setup of MLP network as a fully connected feedforward neural network, which was used for magnitude prediction of the [Ca2+]i time curves. (B) Setup of closed-loop non-linear autoregressive network with exogenous inputs (NARX), which was developed as a recurrent neural network for the trend prediction of [Ca2+]i time curves.

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  Figure 4. Test results of the NARX network to predict curve shapes. (A–G) Testing of trend prediction of 0–1 scaled [Ca2+]i curves. Experiments of the test set are shown in Figure 1. Red solid lines = experimental values, blue dashed lines = predicted values. Indicated per condition are the calculated R2 values (a negative R2 indicates an explained variance worse than random). (H) For comparison, results from the same test set are given as obtained by the MLP network. Shown here are the target and predicted nM [Ca2+]i levels in log scale.

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  Figure 5. Combined effects of magnitude and trend prediction of platelet [Ca2+]i curves at varying agonist concentrations. (A) Panels of prediction efficacy of scaled curves per agonist concentration. Lightest grey lines represent basal levels, while darker lines point to predicted curves in the presence of agonist at 1–10% of the maximum concentration in the training set. Columns show conditions with indicated agonists, collagen (Col), CRP, or thrombin (Thr). Rows represent different inhibitor conditions: + or − mean presence or not; from top to bottom: EGTA, apyrase plus indomethacin (AI), and thapsigargin (Thap). (B) Sensitivity characteristics of the scalar curves generated by MLP and NARX. Columns indicate: [Ca2+]i level at log10 base (magnitude), time of [Ca2+]i (tmax), final [Ca2+]i level (ylast), and mean deviation from linear (absdev).

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  Figure 6. Scalar characteristic of the [Ca2+]i time curves. Scaling resulted in the following parameters: magnitude (nM) points to the maximal minus minimal value of a curve; tmax refers to the time point where the maximal value is reached, scaled by time range (540 s). The parameter ylast indicates the end value, scaled according to the magnitude; absdev represents the mean deviation of the time curve from linear (red line). The deviation from this line (green) was calculated per time point, in which absdev means the average of all deviations.

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  Figure 7. Loading coefficients of experimental variables in the PLS regression analysis. PLS regression analysis was performed for the prediction of curve magnitude (A), tmax (B), ylast (C), and absdev (D). Colours indicate contributions per variable. Plots show for two principal components the contribution of six experimental variables (collagen dose, CRP dose, thrombin dose, EGTA/CaCl2, AI, thapsigargin).