Mathematical Modelling of the MAP Kinase Pathway Using Proteomic Datasets

<div><p>The advances in proteomics technologies offer an unprecedented opportunity and valuable resources to understand how living organisms execute necessary functions at systems levels. However, little work has been done up to date to utilize the highly accurate spatio-temporal dynamic proteome data generated by phosphoprotemics for mathematical modeling of complex cell signaling pathways. This work proposed a novel computational framework to develop mathematical models based on proteomic datasets. Using the MAP kinase pathway as the test system, we developed a mathematical model including the cytosolic and nuclear subsystems; and applied the genetic algorithm to infer unknown model parameters. Robustness property of the mathematical model was used as a criterion to select the appropriate rate constants from the estimated candidates. Quantitative information regarding the absolute protein concentrations was used to refine the mathematical model. We have demonstrated that the incorporation of more experimental data could significantly enhance both the simulation accuracy and robustness property of the proposed model. In addition, we used the MAP kinase pathway inhibited by phosphatases with different concentrations to predict the signal output influenced by different cellular conditions. Our predictions are in good agreement with the experimental observations when the MAP kinase pathway was inhibited by phosphatase PP2A and MKP3. The successful application of the proposed modeling framework to the MAP kinase pathway suggests that our method is very promising for developing accurate mathematical models and yielding insights into the regulatory mechanisms of complex cell signaling pathways.</p> </div

Protein concentrations of the pathway models.

<p>System 1 is the model based on the proteomic data only with normalized protein concentrations. System 2 is the model based on both proteomic and other experimental data with absolute protein concentrations. Except the variables in this table, the initial conditions of other variables are zeros. The concentrations of three phosphatases were calculated based on both the absolute kinase concentration in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042230#pone.0042230-Fujioka1" target="_blank">[30]</a> and ratio of phosphatase concentration to the corresponding kinase concentration in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042230#pone.0042230-Schoeberl1" target="_blank">[26]</a>.</p

Kinase activities at 10 min inhibited by phosphatases PP2A and MKP3.

<p>(A, B, C) Simulated Raf, MEK and ERK activities at 10 min when the MAP kinase module was stimulated by different signal inputs and inhibited by phosphatase PP2A with different concentrations. (D, E, F) Simulated Raf, MEK and ERK activities at 10 min when the MAP kinase module was stimulated by different signal inputs and inhibited by the phosphatase MKP3 with different concentrations (blue-line: Ras = 0.004; red-line: Ras = 0.02; black-line: Ras = 0.04; green-line: Ras = 0.4).</p

Simulations of the normalized kinase activities.

<p>(A) Normalized Ras activity as the signal input from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042230#pone.0042230-Fujioka1" target="_blank">[30]</a>. (B) Raf activity; (C) Total MEK activity; and (D) Total ERK activity (blue-line: simulation; green-line: normalized Western blotting data <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042230#pone.0042230-Fujioka1" target="_blank">[30]</a>; red-line: proteomic data <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042230#pone.0042230-Olsen1" target="_blank">[9]</a>). (E) MEK activity and (F) ERK activity at different locations (blue-line: simulation in the cytosol, red-line: proteomic data in the cytosol, green-line: simulation in the nucleus, black-line: proteomic data in the nucleus).</p

Schematic representation of the MAK kinase pathway.

<p>Schematic representation of the MAK kinase pathway.</p

Robustness analysis.

<p>(A and B) Robustness analysis of the proposed model with 10 sets of estimated kinetic rates that were derived from the normalized proteomic data. (A) the average behavior and (B) nominal behavior of the model with perturbed kinetic rates. (C and D) Robustness analysis of the proposed model with 10 sets of estimated kinetic rates that were derived from more resources of experimental data. (C) the average behavior and (D) nominal behavior of the model with perturbed kinetic rates. (Blue-line: Raf; green-line: MEK, red-line: ERK. The horizontal dash lines in (A) and (C) are the simulated kinase activities based on the unperturbed model kinetic rates).</p

Flowchart of the proposed modeling framework for developing mathematical models of cell signaling pathways using proteomic data.

<p>Refer to the Section “Model refinement by incorporating more experimental data” for more detailed description of this flowchart.</p

The distribution of Bdifr for the fourth amino acid group (in (a)), and for the third group (in (b)), and for the first and second groups (in (d)), and the distribution of Bavgr for the third group (in (c)).

<p>The y-axes denote ΔΔ<i>G</i>. ∘: ILE, VAL, LEU, MET, ALA and GLY; ◻: CYS, THR, SER, PRO, HIS, GLN and ASN; ♢: GLU, ASP, LYS and ARG; ▿: PHE, TRP and TYR. The importance of V10, V8 and V7 is ranked as 9^<i>th</i>, 19^<i>th</i> and 24^<i>th</i>, respectively, as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0144486#pone.0144486.g002" target="_blank">Fig 2</a>, while the Pearson correlation coefficients of the three features are -0.054, -0.213 and -0.313, respectively, as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0144486#pone.0144486.t005" target="_blank">Table 5</a>. V4 and V6 are not in the top 40 important features in randomForest.</p

Additional file 1 of DiCleave: a deep learning model for predicting human Dicer cleavage sites

Additional file 1. Supplementary Tables and Figure

The ROC curves measuring the discriminative capability of the ubiquitination site indicators.

<p>The indicators include the sequence pattern, the structural propensities (local conformation, residue propensities in the microenvironment, accessibility and centrality) and their combination. For combination, individual indicators were combined by a weighted summing scheme (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083167#pone.0083167.s009" target="_blank">Table S2</a> for the weights). The AUC values were calculated according to the structural propensities, the likelihood scores derived via five-fold cross-validation of the corresponding models or their combinations (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083167#pone.0083167.s010" target="_blank">Text S1</a> for details). The larger the AUC value, the stronger the indicator.</p