Percentage of parameter space where bistable responses are possible^a.

a<p>Some bidimensional sections of the multidimensional parameter space of bistability are shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031095#pone.0031095.s002" target="_blank">Figure S2</a>. The results show that in TCS with a bifunctional SK, both a TC_SK and a TC_RR cause a decrease in the size of the parametric region of bistability, with one exception: Model C has a larger parametric region of bistability when the signaling target is SK autophosphorylation (k₁). However, in systems with a monofunctional SK, a TCSK causes an increase and a TCRR causes a decrease in the size of the parametric region of bistability if the environment modulates the SK dephosphorylation (k₂). A|B stands for Model A controlled for Model B. A|C stands for Model A controlled for Model C.</p

Temporal responsiveness curves of Models A, B, and C.

<p>The systems are at an initial steady state and, at time zero, the signal, represented in the x axis, changes instantaneously and the time it takes for the system to get to within 90% of the new steady state is measured and plotted in the y axis. A–D: Response times of TCS with monofunctional SK. E–H: Response times of TCS with bifunctional SK. The OFF to ON plots start with the systems at an OFF steady state (low levels of RRP) corresponding to a low value of k₁ (A, C, E, G) or a high value of k₂ (B, D, F, H). The signal is then changed to increase the steady state level of RRP. The ON to OFF plots start with the systems at an ON steady state (high levels of RRP) corresponding to a high value of k₁ or a low value of k₂. The signal is then changed to decrease the steady state level of RRP. Peaks that indicate slower response times are located immediately outside the range of bistability. The lack of a peak in a curve can be due to monostability or irreversibility. The dashed lines indicate the signal value at which Models B and C exit its bistable range. Absence of a dashed line indicates irreversible turning ON or OFF of the system (Model B in panel C ) or absence of bistability (see the signal-response curves of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031095#pone-0031095-g002" target="_blank">Figure 2</a>).</p

Experiments to analyze the effect of changes in different parameter values and protein concentrations on the range of bistability for the alternative TCS modules^a.

a<p>The steady state(s) for the three models by scanning a)k₁ (SK autophosphorylation reaction rate constant) and b)k₂ (SKP autodephosphorylation reaction rate constant) between 10⁻⁶ and 10 at different values of the parameters named in the table (see text for details).</p

Percentage of parameter space where a bistable response is possible for Models A, B, and C^a.

a<p>A|B stands for Model A controlled for Model B. A|C stands for Model A controlled for Model C.</p><p>k_i: kinetic constants for the reactions in the systems shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031095#pone-0031095-g001" target="_blank">Figure 1</a>. SKt: total concentration of SK. RRt: total concentration of RR. TCt: total concentration of third component protein. The parameter space for k_i,k_j, and k_k was scanned between absolute values of 10⁻⁶ and 10 for each of the parameters. Sampling was uniform in logarithmic space.</p>b<p>Percentage of the parameter space of k_i, k_j and k_k where bistability is found for Models A, B, and C respectively.</p>c<p>Percentage of the parameter space where bistability is found in Model A controlled for B and for C, respectively.</p><p>NA Non Applicable. Mono functional systems have k₈ = 0. The concentration of TC = 0 in Model A. Model A can not be scanned with respect to the concentration of SK in the controlled comparisons, because SK is independently fixed to make the dynamical response of Model A more similar to those of Models B and C.</p

Stochastic time trajectories after an instantaneous change in the signal, for the three systems modeled with a monofunctional SK.

<p>A mathematically controlled comparison between Models A and B, and between Models A and C was performed as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031095#s4" target="_blank">methods</a>. The results for three individual runs for each value of k1 or k2 are plotted in each panel. Panels in the first column correspond to Model A controlled to be as similar as possible to Model B. Panels in the second column correspond to Model B. Panels in the third column correspond to Model A controlled to be as similar as possible to Model C. Panels in the fourth column correspond to Model C. The circles indicate lines that are replicates of the same simulation. Simulations marked with an arrow correspond to a signal intensity close to the bistability threshold and show slower and noisier responses. The OFF to ON plots start with the systems at an OFF steady state (low levels of RRP) corresponding to a low value of k1 or a high value of k2. At time zero, there is an instantaneous increase in k1 or decrease in k2. The ON to OFF plots start with the systems at an ON steady state (high levels of RRP) corresponding to a high value of k1 or a low value of k2. At time zero, there is an instantaneous decrease in k1 or increase in k2. The values for k1 or k2 are chosen to be below, next to and above the threshold value at which the system switches from OFF to ON, or from ON to OFF. See text for further details.</p

Steady state signal-response curves for the various TCS modules.

<p>Each plot shows the steady state levels of the phosphorylated RR in the y axis at different values of the signal k₁ (SK autophosphorylation rate constant) or k₂ (SKP dephosphorylation rate constant) in the x axis. When the signal modulates SK dephosphorylation (changes in k₂), the system behaves symmetrically to when SK phosphorylation (changes in k₁) is modulated. In the first case, increases in signal intensity cause the fraction of RRP to decrease, while in the latter, increases in signal intensity cause the fraction of RRP to increase. A, C, E: Response curves of TCS modules with monofunctional sensor. B, D, F: Response curves of TCS modules with bifunctional sensor. A, B, Response curves of Model A. C, D: Mathematically controlled comparison between the response curves of Model B and those of Model A. E, F: Mathematically controlled comparison between the response curves of Model C and those of Model A. Mathematical controls are implemented to make sure that the differences in response between the alternative modules are due to the presence of third component and not to other spurious differences.</p

Summary of the comparison of physiologically relevant criteria between the alternative designs for monofunctional TCS^a.

a<p>The model with the largest number of “+” signs for a given criterion is the one with the best performance with respect to that criterion.</p><p>A|B stands for Model A controlled for Model B. A|C stands for Model A controlled for Model C.</p

Controlled comparison of the overall response times between Models A and B, and between Models A and C^a.

a<p>The reported values represent the area below each curve in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031095#pone-0031095-g003" target="_blank">Figure 3</a>, that is, the sum of the transient times for each response. A|B stands for Model A controlled for Model B. A|C stands for Model A controlled for Model C.</p

Summary of the comparison of physiologically relevant criteria between the alternative designs for TCS with bifunctional SK^a.

a<p>The model with the largest number of “+” signs for a given criterion is the one with the best performance with respect to that criterion.</p><p>A|B stands for Model A controlled for Model B. A|C stands for Model A controlled for Model C.</p

Analyzed Two Component Systems modules.

<p>Model A represents a prototypical TCS. Model B represents a TCS with a SK-binding third component (TC_SK). Model C represents a TCS with a RR-binding third component (TC_RR). SK: sensor kinase; RR: response regulator; SKP: phosphorylated SK; RRP: phosphorylated RR; Ph: alternative phosphatase that dephosphorylates RRP; SKRR: dead-end complex, resulting from the binding of SK and RR; SKPRR: protein complex formed by the binding of SKP and RR; SKRRP: protein complex formed by the binding of SK and RRP; PhRRP: protein complex formed by the binding of Ph and RRP; SKTC and RRPTC: protein complexes formed by the binding of the third component to SK and RRP, respectively; (k₁, …, k₁₈): kinetic constants of the individual reactions. For simplicity, ATP and the release of inorganic phosphate are omitted. To analyze TCS modules with monofunctional sensors, k₈ is set to 0. To analyze TCS modules with bifunctional sensors, k₈ is set to be different from 0.</p