The nonlinear ARX model of the IEGs.

<p>(A) The simulation result of the nonlinear ARX model (solid lines) together with the experimental results in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0057037#pone-0057037-g001" target="_blank">Figure 1B</a> (dots). The colour codes are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0057037#pone-0057037-g001" target="_blank">Figure 1B</a>. The experimental data in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0057037#pone-0057037-g001" target="_blank">Figure 1B</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0057037#pone.0057037.s002" target="_blank">Figure S2</a> were used for parameter estimation of the nonlinear ARX model. (B) The identified systems by the nonlinear ARX model. The upstream dependency (selected inputs), Hill functions, and frequency response curve of the nonlinear ARX model were shown. The selected inputs, pERK (solid line), pCREB (dotted line), pJNK (dashed line), and c-FOS (dashed and dotted line) were numbered.</p

The selective expression of EGR1 in response to pulsatile ERK phosphorylation.

<p>(A) The step (5 ng/ml, red), pulse (5 ng/ml, 6 min, blue), and pulsatile NGF stimulation (0.5 ng/ml, 6 min with 12-min intervals for four times, green) were given as indicated by bars (top), and pERK, pCREB, EGR1, and c-FOS were measured in experiments (dots). Using the experimental data of pERK and pCREB as the selected inputs, the outputs (c-FOS and EGR1) were simulated by the nonlinear ARX model (solid lines). (B) Interval dependency of EGR1 and c-FOS expression. The pulsatile NGF stimulation (0.5 ng/ml, 15-min duration for each pulse) with the indicated intervals were given, and pERK, EGR1, and c-FOS expression were measured in experiments. The area under the curve (AUC) (0–480 min) of EGR1 and c-FOS are shown in bars. The intervals are indicated by the colour codes. Bars represent means ±S.D.(n = 4). Note that 15-min duration of pulses was used in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0057037#pone-0057037-g004" target="_blank">Figure 4B</a> because of the technical limitation of probe numbers of the automated liquid-handling robots, and pulsatile stimulation with 6-min pulse duration and 12-min intervals were available at most four times (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0057037#pone-0057037-g004" target="_blank">Figure 4A</a>).</p

Temporal Decoding of MAP Kinase and CREB Phosphorylation by Selective Immediate Early Gene Expression

<div><p>A wide range of growth factors encode information into specific temporal patterns of MAP kinase (MAPK) and CREB phosphorylation, which are further decoded by expression of immediate early gene products (IEGs) to exert biological functions. However, the IEG decoding system remain unknown. We built a data-driven based on time courses of MAPK and CREB phosphorylation and IEG expression in response to various growth factors to identify how signal is processed. We found that IEG expression uses common decoding systems regardless of growth factors and expression of each IEG differs in upstream dependency, switch-like response, and linear temporal filters. Pulsatile ERK phosphorylation was selectively decoded by expression of EGR1 rather than c-FOS. Conjunctive NGF and PACAP stimulation was selectively decoded by synergistic JUNB expression through switch-like response to c-FOS. Thus, specific temporal patterns and combinations of MAPKs and CREB phosphorylation can be decoded by selective IEG expression via distinct temporal filters and switch-like responses. The data-driven modeling is versatile for analysis of signal processing and does not require detailed prior knowledge of pathways.</p> </div

System identification by the nonlinear ARX model.

<p>(A) The modeling scheme of the nonlinear ARX model. Upstream dependency was determined by lag order number, <i>m</i>. For example, if <i>m</i> = 0, upstream signal is not transmitted downstream, otherwise signal is transmitted downstream. The signals of the selected upstream molecules were transformed successively by Hill function and linear ARX model, that characterise a system with switch-like (solid line) or graded (dotted line) dose response, and with temporal filters such as a low-pass filter (dotted line) and that with an inverse notch (solid line), respectively (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0057037#s2" target="_blank">Materials and methods</a>). (B) Temporal signal transformation in the nonlinear ARX model. For example, signal transformation in the nonlinear ARX model of c-FOS was shown. pERK and pCREB were selected upstream molecules, but pp38 and pJNK were not (<i>m</i> = 0). The signals of pERK and pCREB were transformed by the Hill equations. Then, the transformed signals by the Hill equations were temporally transformed by the linear ARX model. The sum of the transformed signals by the linear ARX model was c-FOS, the final output of the nonlinear ARX model of c-FOS.</p

The selected inputs and parameters of the Hill function and frequency response curves of the nonlinear ARX model.

<p>The selected inputs and parameters of the Hill function and frequency response curves of the nonlinear ARX model.</p

Conjunctive stimulation of NGF and PACAP induced synergistic JUNB expression through switch-like response to c-FOS.

<p>The step stimulation of NGF alone (5 ng/ml, red), PACAP alone (100 nM, blue), and both NGF and PACAP (violet) were given, and pERK, pCREB, c-FOS, JUNB, and FOSB were measured in experiments (dots). The simulation results of the nonlinear ARX model are shown (solid lines). Black dots indicate the sum of the IEG in response to NGF alone and to PACAP alone, and arrows indicate the difference from the sum.</p

System identification reveals temporal decoding systems of MAP kinase and CREB phosphorylation by selective IEG expression.

<p>We made a system identification of temporal decoding of MAP kinase and CREB phosphorylation by selective immediate early genes expression such as c-FOS, EGR1, c-JUN and JUNB using time series data and the nonlinear ARX model. We found that the expression of IEGs has a distinct upstream dependency, and there are distinct switch-like responses and temporal filters for decoding upstream signals. For example, pulsatile ERK phosphorylation was decoded by selective expression of EGR1 rather than c-FOS, and conjunctive NGF and PACAP stimulation was decoded by synergistic JUNB expression through a switch-like response to c-FOS.</p

The Extraction of Simple Relationships in Growth Factor-Specific Multiple-Input and Multiple-Output Systems in Cell-Fate Decisions by Backward Elimination PLS Regression

<div><p>Cells use common signaling molecules for the selective control of downstream gene expression and cell-fate decisions. The relationship between signaling molecules and downstream gene expression and cellular phenotypes is a multiple-input and multiple-output (MIMO) system and is difficult to understand due to its complexity. For example, it has been reported that, in PC12 cells, different types of growth factors activate MAP kinases (MAPKs) including ERK, JNK, and p38, and CREB, for selective protein expression of immediate early genes (IEGs) such as c-FOS, c-JUN, EGR1, JUNB, and FOSB, leading to cell differentiation, proliferation and cell death; however, how multiple-inputs such as MAPKs and CREB regulate multiple-outputs such as expression of the IEGs and cellular phenotypes remains unclear. To address this issue, we employed a statistical method called partial least squares (PLS) regression, which involves a reduction of the dimensionality of the inputs and outputs into latent variables and a linear regression between these latent variables. We measured 1,200 data points for MAPKs and CREB as the inputs and 1,900 data points for IEGs and cellular phenotypes as the outputs, and we constructed the PLS model from these data. The PLS model highlighted the complexity of the MIMO system and growth factor-specific input-output relationships of cell-fate decisions in PC12 cells. Furthermore, to reduce the complexity, we applied a backward elimination method to the PLS regression, in which 60 input variables were reduced to 5 variables, including the phosphorylation of ERK at 10 min, CREB at 5 min and 60 min, AKT at 5 min and JNK at 30 min. The simple PLS model with only 5 input variables demonstrated a predictive ability comparable to that of the full PLS model. The 5 input variables effectively extracted the growth factor-specific simple relationships within the MIMO system in cell-fate decisions in PC12 cells.</p></div

Loadings and scores of the principal components of the inputs and outputs.

<p>(<b>A</b>) Input loadings. A wedge indicates the temporal evolution of the indicated molecules from 0 to 360 min (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072780#pone-0072780-t001" target="_blank">Table 1</a>). (<b>B</b>) Input scores. A wedge indicates the doses of the stimulant. (<b>C</b>) Output loadings. A wedge indicates the temporal evolution (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072780#pone-0072780-t001" target="_blank">Table 1</a>). (<b>D</b>) Output scores. A wedge indicates the doses of the indicated molecules (Fig. 1). The red and blue colors indicate positive and negative values, respectively (<b>A</b>–<b>D</b>). Scatter plots of input loadings (<b>E</b>), input scores (<b>F</b>), output loadings (<b>G</b>) and output scores (<b>H</b>) of the first and second principal components. The colors correspond to the latent variables (<b>E</b>, <b>G</b>) and stimuli (<b>F</b>, <b>H</b>). The numbers indicate the time (minute for pERK, pCREB, pJNK, pAKT, pp38, c-FOS, c-JUN, EGR1, JUNB and FOSB and hour for neurite lengths, cell viability, cell cycle and cell death).</p

Validation of the PLS model using inhibitor experiments.

<p>Correlation plots between the measured outputs and predicted outputs with NGF (<b>A</b>), PACAP (<b>B</b>) and anisomycin (<b>C</b>). The correlation coefficient, <i>r</i>, is indicated in each plot. Each dot represents a single time point. The data sets with PD0325901 (MEK inhibitor), H89 (PKA inhibitor), LY294002 (PI3K inhibitor), SB203580 (p38 inhibitor), SP600125 (JNK inhibitor) (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072780#pone.0072780.s004" target="_blank">Table S2</a>) are indicated by the various colors.</p