Model evaluation in comparison to the experimental data.

<p>Comparison of the model time course to the experimental data for nuclear -catenin dynamics. The simulation data fit the experimental ones for the first 2 hours.</p

Schematic representation of the intracellular Wnt/-catenin pathway model.

<p>A cell is composed of two compartments, the cytosol and the nucleus, separated by the dashed lane. The five species are framed in gray. Only the species <i>Wnt</i> is extra-cellular. For a given reaction, an arrow-less lane shows the reactant(s), and an arrow lane points to the product. Bended arrows represent protein production for reaction or protein decay for reactions , , , and . An open arrow coming after a large vertical bar represents a trigger effect (according to the Systems Biology Graphical Notation <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042792#pone.0042792-Novere1" target="_blank">[60]</a>) where the reactant is not consumed in the reaction, but necessary for the process to take place. The reactions' numbers correspond to the ones in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042792#pone-0042792-t001" target="_blank">Table 1</a>.</p

Comparison of -catenin dynamics between our core model and the <i>Lee model</i>.

<p>Time-dependent response of -catenin under transient Wnt signal ( introduced into the system at the steady-state, at ). The dynamics of total in the and of nuclear -catenin () in our core model are corresponding. Simulations of the <i>Lee model</i> are performed through the JWS platform <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042792#pone.0042792-Olivier1" target="_blank">[55]</a>.</p

Reactions of the intracellular Wnt/-catenin pathway model.

<p>All reactions are following Mass action kinetics, but -catenin production (1) that is a constant flux. The reaction numbers correspond to the ones in the model schema (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042792#pone-0042792-g001" target="_blank">Figure 1</a>).</p

Dynamics of nuclear -catenin in heterogeneous cell population.

<p>A population of 100 cells is simulated. (A, B, and D) represent the sum of nuclear in -catenin 100 cells as compared to the experimental data. (C) represents the number of nuclear -catenin in each cell individually for a population of 100 cells. (A) The total cell population is analyzed. The simulation data do not correlate with the experimental ones. (B) The cell population asynchrony toward the cell cycle does not give rise to a second increase of nuclear -catenin after 2 hours. (C) Single cell analysis shows the delay in -catenin dynamics due to the cell cycle asynchrony. (D) The addition of a continuous and autocrine Wnt signal to the previous experimental setting produces simulation data in perfect agreement to the experimental ones. (A, C) Parameters used are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042792#pone-0042792-t003" target="_blank">Table 3</a> (Set 3). (B, D) Parameters used for both experiments are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042792#pone-0042792-t003" target="_blank">Table 3</a> (Set 4).</p

List of model parameters.

<p>Parameters used in our model for the different <i>in silico</i> experiments. Sets 1 and 2 are the results of the parameter fitting experiments comparing to the <i>Lee model</i> and our experimental data, respectively. Sets 3 and 4 are obtained from our stochastic and our cell cycle investigation, respectively. All rate constants are in but the ones indicated by “*”: the deterministic values of are given in , and the deterministic values of are given in .</p

Parameters from the <i>Lee model</i>[23] used in our model and their stochastic conversion.

<p>Parameters' names and values are given as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042792#pone.0042792-Lee1" target="_blank">[23]</a>. Their corresponding names in our model are given with their stochastic values.</p

Nuclear -catenin dynamics with higher number of AxinP.

<p>(A) In absence of Wnt signal. (B) Under transient Wnt signal. The plots represent 10 simulation runs.</p

Nuclear -catenin during RVM cell differentiation.

<p>(A) Representative Western-blot from which the -catenin protein amount was quantified (B). Time point 0 stands for control using proliferating cells and -actin was used as a loading control. The signal intensities at 0 hour are normalized to 1.0 and the values are presented as mean standard error on the mean from at least 3 independent experiments. The figure is reproduced from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042792#pone.0042792-Mazemondet1" target="_blank">[12]</a> (Figures 8C and 8D) where details about experimentation can be found, as well as in the section <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042792#s3" target="_blank">Materials & Methods</a>.</p

Effects of AxinP on -catenin dynamics according to stochastic simulation.

<p>In absence of Wnt signal, small variations of (A) influence dynamics (B) leading to high variance. Increase of and by 1000 accelerate changes (C), but fluctuations still remain too high (D). Each plot represents a single simulation run.</p