Dependence on parameters.

<p>We vary two key parameter values (keeping the rest fixed at the values shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0062254#pone-0062254-t001" target="_blank">Table 1</a>): <i>α</i>, the expression level of the constitutive promoter; and <i>n</i>, the Hill coefficient of LuxR-DNA binding. As we move through this space of parameters, the effect of inhibitor combinations will change. Dark curves show transitions between qualitatively different inhibitor effects: emergence of smooth or sharp transitions, or a change of curvature of the inhibitory boundary. Examples of different inhibitor effects are shown as 2-dimensional plots, as in Fig. 3, with light connecting lines indicating the parameter values that give rise to each plot. (A,C,E) LuxI-feedback systems. (B,D,F) LuxR-feedback systems. (A,B) LuxI inhibitors and LuxR non-competitive inhibitors. (C,D) LuxR non-competitive inhibitors and LuxR competitive inhibitors. (E,F) LuxI inhibitors and LuxR competitive inhibitors. (A) The two inhibitors act essentially multiplicatively. The response is abrupt for low values of <i>α</i> (below the curve) but is a mixture of smooth and abrupt for high values of <i>α</i> (above the curve). (B) The two inhibitors act multiplicatively, with no qualitative changes over the parameter range. The response is abrupt. (C) The two inhibitors show complicated interactions. For low values of competitive inhibition ( close to 1), the interaction with the non-competitive inhibitor is antagonistic. For higher values of competitive inhibition ( close to 0) the interaction with the non-competitive inhibitor is multiplicative. The dark curve in {<i>α</i>,<i>n</i>} space separates purely abrupt responses from a mixture of smooth and abrupt responses. (D) Above the value <i>α</i> = 0.125, both the LuxR competitive and non-competitive inhibitors act to suppress virulence. However, it is mainly the level of the LuxR non-competitive inhibitor which is important. Below the value <i>α</i> = 0.125, the competitive inhibitor acts antagonistically with the non-competitive inhibitor. For <i>n</i> >1.4 the response is abrupt; for <i>n</i> <1.4 the response is smooth. (E) The two inhibitors show similar interactions as in panel (C). The dark curves separate regions where the response is completely smooth (top), completely abrupt (bottom left) or a mixture of the two (bottom right). (F) Virulence expression is high over all inhibitor combinations and parameter values shown. The distinction between cooperative and antagonistic behavior is hardly visible.</p

<b>Table 2.</b> Classes of QS inhibitors.

<p><b>Table 2.</b> Classes of QS inhibitors.</p

Effect of inhibitors in combination.

<p>Each panel shows the steady-state expression level at the virulence promoter as two inhibitors are varied. Parameter values are taken from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0062254#pone-0062254-t001" target="_blank">Table 1</a>. Both <i>x</i>- and <i>y</i>-axes are logarithmic. Virulence expression is represented by the shade, ranging from low virulence (light) to high virulence (dark). When two stable branches co-exist, the upper branch is shown (except in panels G,H, where the lower branch is shown). Sharp transitions represent bifurcation points where the upper branch vanishes. (A,C,E,G) LuxI-feedback systems with <i>α</i> = 0.11. (B,D,F,H) LuxR-feedback systems with <i>α</i> = 0.05. (A,B) LuxI inhibitors and LuxR non-competitive inhibitors. (C,D) LuxR non-competitive inhibitors and LuxR competitive inhibitors. (E,F) LuxI inhibitors and LuxR competitive inhibitors. (G,H) External AHL is varied along the <i>x</i>-axis, while cell density is varied along the <i>y</i>-axis. The dark curve shows the contour of constant total AHL from external and internal sources.</p

Experimentally validated parameter values.

<p>Experimentally validated parameter values.</p

An overview of model checkers and CBMC as a tool.

<p>CBMC’s front end (CFE) converts a program and a property into a Boolean formula which is then verified using a SAT solver. CBMC will produce a counterexample in the case of violation of the property.</p

Number of simple 3-edge-connected unlabeled N-node graphs.

<p>Number of simple 3-edge-connected unlabeled N-node graphs.</p

SNARE regulation and graph connectedness.

<p>SNARE regulation and graph connectedness.</p

The vesicle traffic graph in steady state.

<p>Nodes (large circles) are compartments; vesicles (small circles) are associated with directed edges. The binary labels represent the presence/absence of four molecular types in this example. The actual amounts of these molecules on each compartment, and actual fluxes along each vesicle edge, can be positive real numbers. By construction, the total incoming flux can be made to balance the total outgoing flux of each molecular type at every node. Note that no pair of vesicles has identical compositions, yet all molecular components move in closed cycles. This is related to the fact that this graph is 3-connected (see section 2.2).</p

Exploiting Cell-To-Cell Variability To Detect Cellular Perturbations

<div><p>Any single-cell-resolved measurement generates a population distribution of phenotypes, characterized by a mean, a variance, and a shape. Here we show that changes in the shape of a phenotypic distribution can signal perturbations to cellular processes, providing a way to screen for underlying molecular machinery. We analyzed images of a Drosophila S2R+ cell line perturbed by RNA interference, and tracked 27 single-cell features which report on endocytic activity, and cell and nuclear morphology. In replicate measurements feature distributions had erratic means and variances, but reproducible shapes; RNAi down-regulation reliably induced shape deviations in at least one feature for 1072 out of 7131 genes surveyed, as revealed by a Kolmogorov-Smirnov-like statistic. We were able to use these shape deviations to identify a spectrum of genes that influenced cell morphology, nuclear morphology, and multiple pathways of endocytosis. By preserving single-cell data, our method was even able to detect effects invisible to a population-averaged analysis. These results demonstrate that cell-to-cell variability contains accessible and useful biological information, which can be exploited in existing cell-based assays.</p></div

Well-to-well and cell-to-cell variability.

<p>(<b>A,B</b>) Population distributions (histograms) of features I3 (A) and G3 (B), for three negative control wells from a single slide. Hollow bars show raw distributions; solid bars show the data when distributions are normalized to have zero mean and unit variance. (<b>C,D</b>) Heat maps of population-averaged mean values for features I3 (C) and G3 (D). The positional effects in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0090540#pone-0090540-g002" target="_blank">Figure 2C</a> likely arise from labeling and imaging artifacts. (<b>E</b>) ANOVA F-statistic for inter-row variance versus within-row variance of distribution means (x-axis) or skewnesses (y-axis), for all 27 features. Each point shows the median F-statistic over 84 slides; intensity features are colored orange, geometric features are colored purple. Data for each slide are shown in Figure S1B,C in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0090540#pone.0090540.s001" target="_blank">File S1</a>. (<b>F</b>) Cumulative distributions of feature I3, from a negative control well (grey) and a positive control well (Arf1; blue). The left panel shows raw data; the right panel shows that cumulative distributions are still distinguishable after normalization.</p