Regulatory network of a single gene.

<p>Regulatory mechanisms of gene expression include: binding of TF to a promoter site of the DNA; recruitment of RNAP to the promoter region to form the pre-initiation complex; binding of a number of RNAP molecules leading to multiple transcription re-initiations during a time period of gene activation, which is realized by the transcription memory window; gene inactivity period during which RNAP molecule is unable to bind to the promoter region, which is characterized as the second memory window.</p

Averaged bursting numbers under various conditions.

<p>The averaged bursting number per simulation based on different numbers of TF but a fixed number of RNAP with either constant lengths of memory windows in (A) or lengths following the exponential distributions in (B). Rate constant are the same as those in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052029#pone-0052029-g002" target="_blank">Figure 2</a>. The averaged bursting number per simulation based on different numbers of RNAP but a fixed TF number with the binding rate of RNAP to DNA as in (C) or in (D). The corresponding rate constant in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052029#pone-0052029-g002" target="_blank">Figure 2</a> is (solid line: mean; dash-line: ).</p

Damped oscillation of the p53 module in a population of cells.

<p>(A) Fractions of cells showing different pulse numbers of ATM activity when cells were irradiated by different gamma doses. The averaged copy numbers of p53 (B) and MDM2 (C) based on 1000 simulations. (Solid-line: gamma dose 10 Gy, dash-dot-line: 2.5 Gy, and dash-line: 0.3 Gy).</p

Stochastic simulations of single-gene expression using the same rate constants.

<p>(A) Gene On/Off states; (B) mRNA numbers; (C) protein numbers. Two simulations when the lengths of memory windows are constants (length of transcription window and length of gene inactivity window ). (D) Gene On/Off states; (E) mRNA numbers; (F) protein numbers. Two simulations when the lengths of memory windows follow the exponential distributions with mean . (G) Gene On/Off states; (H) mRNA numbers; (I) protein numbers. Two simulations when the lengths of memory windows follow the Gaussian distributions with </p

Simulated noise in protein abundance.

<p>Noise in protein abundance derived from stochastic simulations with different TF numbers (solid-line: lengths of memory windows are constant; dash-line: lengths of windows follow the exponential distributions; dash-dot line: theoretical prediction from a simpler stochastic model in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052029#pone.0052029-Pedraza1" target="_blank">[19]</a>).</p

Stochastic simulations of the p53-MDM2 core module.

<p>The upstream signal represented by the ATM kinase activities (measured from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052029#pone-0052029-g001" target="_blank">Fig. 1</a> in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052029#pone.0052029-Batchelor1" target="_blank">[50]</a>) has two pulses in (A) or four pulses in (D). Five simulations of the p53 copy numbers based on two pulses (B) and four pulses (E) of the upstream signal; and the corresponding MDM2 copy numbers in five simulations induced by two pulses (C) and four pulses (F) of p53 activities.</p

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

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

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