Model of Aslam: Eigenvalues and ratio .

<p>Model of Aslam: Eigenvalues and ratio .</p

Model of Aslam et al. [6].

<p>(A) The model describes the positive feedback loop between the protein -CaMKII and the translation factor CPEB1. The protein -CaMKII can be in one of three states: inactive (X), active (X) and phosphorylated (X). When active and phosphorylated, -CaMKII phosphorylates CPBE1 which in turn can initiate the translation of a new -CaMKII protein <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033110#pone.0033110-Aslam1" target="_blank">[6]</a>. (B) Trajectories for increasing inputs showing the delay close to the threshold (C) Magnitude of the real part of the eigenvalues of the Jacobian matrix at the saddle point, the stable ones are depicted in black while the unstable one is depicted in red. The inlet zooms in on the three slowest eigenvalues. (D) Sensitivity at saddle point and (E) degrees of robustness (DOR). Parameters with a high sensitivity (red) have a low degree of robustness. Conversely, parameters with a low sensitivity (dark blue) have a high DOR.</p

Results of the analysis of the model of apoptosis proposed by Eißing et al. [3].

<p>(A) Model description. In response to a pro-apoptotic input signal, initiator caspases C8 become activated and activate the effector caspase C3. Activated C3, C3*, activate C8 in return through a positive feedback loop. Inhibitors CARP and IAP bind to C8* and C3* to prevent apoptosis. (B) Time-scale separation at saddle point. Trajectories rapidly converge to the unstable manifold (red dashed line) of the saddle point (red dot) and then slowly escape to reach either the life (green square) or the death steady-states. For the grey trajectory, equally distributed time markers are depicted () showing how trajectories are delayed in the vicinity of the saddle point. (C) Sum of relative sensitivities at saddle point. The saddle point is insensitive to parameters and (see Supplementary <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033110#pone-0033110-t001" target="_blank">table 1</a>). These parameters have a high degree of robustness (D). (E) Output trajectories for increasing input. For input above the threshold, the system switches to the unexcited state, see the corresponding trajectories in the phase plane (B). Trajectories have been normalized such that the output equals zero in the unexcited state and equals one in the exited state. Depending on the input strength, the switch is more or less delayed. By observing trajectories in the phase plane (D), one can see that trajectories starting close to the stable manifold of the saddle point fast converge in the neighborhood of the saddle point where there are delayed before converging to the excited state creating a mechanism of delayed decision making.</p

Results of the analysis of the model of Schliemann et al. [9].

<p>(A) Magnitude of the real part of the eigenvalues of the Jacobian matrix at the saddle point, the stable ones are depicted in black while the unstable one is depicted in red. The zooms in on the three slowest eigenvalues. (B) Output trajectories for impulse inputs, slightly below (light blue solid curve), slightly above (dark grey dashed curve), above (dark grey solid curve) and significantly above (black solid curve) the decision making threshold, (C) Corresponding trajectories in the phase plane. Trajectories passing close to the saddle point are delayed. Trajectories follow the unstable manifold of the saddle point (red dashed curve) before reaching the survival or death state.</p

Influence of the distance to a bifurcation on the switching for the model of Aslam et al. [6].

<p>(A)-(D) Switching responses for the Aslam model for different input intensities above the threshold : (doted line), (dashed-doted line), (dashed line), (solid line). (A) Nominal model. (B)-(D) Perturbed models with single parameter set to 0.99 of its upper bifurcation value. (E)-(G) Bifurcation diagrams for the parameters -CaM, k and k. (B) and (E) -CaM, (C) and (F) and (D) and (G) k.</p

Model of Eißing: Eigenvalues and ratio .

<p>Model of Eißing: Eigenvalues and ratio .</p

Spheroid assays in different collagen matrices.

<p>Two types of lymphatic endothelial cells, hTERT-HDLECs (a, b) and hMVEC-dly cells (c), were embedded in native collagen (2 mg/ml) (a) or in pepsinized collagen at a low (1,5 mg/ml) (b) or high concentration (2 mg/ml) (c). Cells were cultured in the absence (control) or presence of MMP-inhibitors (RO-28-2653 or MMP2 inhibitor) for 24 h (a, b) or a stimulator (PMA) for 48 h (c). For each assay, the initial spheroid (0 h) and the spheroid at the end of the assay (24 h or 48 h) are shown. Graphs on the right represent the density cell distributions measured around the spheroids. For clarity, the cell density distribution curves for each assay were rendered in three colours (blue, spheroid core; green, edging cells; red, detached cells) as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097019#pone-0097019-g001" target="_blank">Figure 1</a>. r_i and r_f correspond to the radius of the initial and final spheroid, respectively. Bars = 500 µm.</p

Global and local measurements of spheroid components upon treatment with a broad-spectrum MMP inhibitor.

<p>Lymphatic hTERT-HDLEC spheroids were embedded in a native collagen matrix with or without (control) an MMP inhibitor (RO-28-2653) for 24 h. The parameters measured are those determined through the assay illustrated in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097019#pone-0097019-g002" target="_blank">Figure 2a</a>.</p><p>**P<0,01;</p><p>****P<0,0001;</p><p>*****P<0,00001 (inhibitor versus control).</p

Global and local measurements of spheroid components upon treatment with an MMP2 inhibitor.

<p>Lymphatic hTERT-HDLEC spheroids were embedded in a pepsinized collagen gel with or without (control) an MMP inhibitor (MMP2 inhibitor) for 24 h. The parameters measured are those determined through the assay illustrated in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097019#pone-0097019-g002" target="_blank">Figure 2b</a>.</p><p>*P<0,05;</p><p>****P<0,0001 (inhibitor versus control).</p

Description of the spheroid assay and the method of quantification.

<p>(a) Schematic representation of spheroid evolution during cell culture. The initial spheroid is shown on the left (yellow circle) and the different modes of cell sprouting and invasion are depicted on the right panel after 24 h of culture. (b–e) Representative pictures of spheroids after embedding into the collagen matrix (t = 0 h, b) and after 24 h of culture (t = 24 h, d), along with their corresponding binarised images (c, e). (f–h) Decomposition of the binarised image into three components: spheroid core (f), edging cells (g) and detached cells (h). (i) Representation of the whole spheroid and its components: the initial spheroid delineated by a yellow circle, the expanded spheroid core (blue), edging cells (green) and detached cells (red). (j) Illustration of the parameters used for global measurements: convex envelope (green) and total distance of cell invasion starting from the spheroid centre (d₁) or border (d₂). (k) Grid used for local measurements: a circular grid is superimposed on the coloured spheroid representation. (l) Comparison of global and local measurements at t = 0 and t = 24 h. (m) Graph representing the cell density distribution measured from the image. The colours of the curves correspond to the different spheroid components described in the other panels (a, i and k). Bars = 500 µm.</p