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Quantitative modeling of multi-signal quorum sensing maps environment to bacterial regulatory responses

Supporting Information

Literature Search

Paper PMID →_lasI_ →_lasR_ →_rhlI_ →_rhlR_ →elastase
García-Reyes, Soberón-Chávez, and Cocotl-Yanez 2020[@GarcíaReyes2020] 31794380 ● ○ ● ● ●
Rutherford and Bassler 2012[@Rutherford2012] 23125205 ● ○ ● ●
Proctor, McCarron, and Ternan 2020[@Proctor2020] 31971503 ● ○ ○ ●
Jakobsen et al. 2013[@Jakobsen2013] 23841636 ● ○ ● ●
Soukarieh et al. 2018[@Soukarieh2018] 29999316 ● ● ● ●
Tateda 2005[@Tateda2005] 15926474 ● ○ ● ○ ●
Williams et al. 2007[@Williams2007] 19249239 ○ ○ ● ●
Heurlier, Dénervaud, and Haas 2006[@Heurlier2006] 16503417 ● ○ ● ○
Le Berre et al. 2006[@LeBerre2006] 16631332 ○ ○ ● ●
Juhas, Eberl, and Tümmler 2005[@Juhas2005] 15816912 ● ● ● ● ●
Donabedian 2003[@Donabedian2003] 12799145 ● ○ ● ● ●
Reuter, Steinbach, and Helms 2016[@Reuter2016] 26819549 ● ○ ○ ● ●
Yong and Zhong 2013[@Yong2013] 22767136 ● ○ ● ● ●
Welsh and Blackwell 2016[@Welsh2016] 27268906 ● ● ●
De Sordi and Mühlschlegel 2009[@DeSordi2009] 19845041 ● ○ ● ○
Winzer and Williams 2001[@Winzer2001] 11437336 ● ○ ○ ● ●
Schuster et al. 2013[@Schuster2013] 23682605 ● ○ ● ●
Papaioannou, Utari, and Quax 2013[@Papaioannou2013] 24065108 ● ● ○ ● ●
Roy, Adams, and Bentley 2011[@Roy2011] 22112397 ● ○ ● ●

Table: lasr {#tbl:lasr}

**Table [-@tbl:lasr]. Activation of QS genes by LasR/3‑oxo‑C12‑HSL in review of published literature.** Solid dots indicate positive activation in the paper’s diagram of gene transcription, while hollow dots indicate that the diagram shows no effect. No diagrams indicated repression. Note that some papers made no attempt to indicate particular interactions; several, for example, concentrated strictly on the QS genes themselves and did not show the effect on downstream genes such as those for elastase.

Paper PMID →_lasI_ →_lasR_ →_rhlI_ →_rhlR_ →elastase
García-Reyes, Soberón-Chávez, and Cocotl-Yanez 2020[@GarcíaReyes2020] 31794380 ○ ○ ○ ○ ●
Rutherford and Bassler 2012[@Rutherford2012] 23125205 ○ ○ ● ○
Proctor, McCarron, and Ternan 2020[@Proctor2020] 31971503 ○ ○ ● ○
Jakobsen et al. 2013[@Jakobsen2013] 23841636 ○ ○ ● ○
Soukarieh et al. 2018[@Soukarieh2018] 29999316 ○ ○ ○ ○
Tateda 2005[@Tateda2005] 15926474 ○ ○ ● ○ ●
Williams et al. 2007[@Williams2007] 19249239 ○ ○ ○ ○
Heurlier, Dénervaud, and Haas 2006[@Heurlier2006] 16503417 ○ ○ ● ○
Le Berre et al. 2006[@LeBerre2006] 16631332 ○ ○ ○ ○
Juhas, Eberl, and Tümmler 2005[@Juhas2005] 15816912 ○ ○ ● ● ●
Donabedian 2003[@Donabedian2003] 12799145 ○ ○ ○ ○ ●
Reuter, Steinbach, and Helms 2016[@Reuter2016] 26819549 ○ ○ ○ ○ ●
Yong and Zhong 2013[@Yong2013] 22767136 ○ ○ ● ○ ●
Welsh and Blackwell 2016[@Welsh2016] 27268906 ○ ○ ○
De Sordi and Mühlschlegel 2009[@DeSordi2009] 19845041 ○ ○ ● ○
Winzer and Williams 2001[@Winzer2001] 11437336 ○ ○ ● ○ ●
Schuster et al. 2013[@Schuster2013] 23682605 ○ ○ ● ○
Papaioannou, Utari, and Quax 2013[@Papaioannou2013] 24065108 ○ ○ ● ○ ●
Roy, Adams, and Bentley 2011[@Roy2011] 22112397 ○ ○ ○ ○

Table: rhlr {#tbl:rhlr}

**Table [-@tbl:rhlr]. Activation of QS genes by RhlR/C4‑HSL in review of published literature.** Same notation as previous table.

Data Analysis

Gene expression data for lasI, rhlI, and lasB was collected every hour for a 24-hour period. Observations used for analysis were limited to a two-hour window that contained the peak expression level for each gene. Figs [-@fig:lasi_time], [-@fig:rhli_time], and [-@fig:lasb_time] show the full time course of expression levels and highlight the intervals used for analysis. Those windows were 8–10 hours, 3–5 hours, and 4–6 hours for lasI, rhlI, and lasB, respectively.

lasi_time{#fig:lasi_time number=1}

**Figure [-@fig:lasi_time]. Expression level of _lasI_ over time course of experiment.** Shaded regions highlight peak expression and indicate two-hour period used in analysis. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)

rhli_time{#fig:rhli_time}

**Figure [-@fig:rhli_time]. Expression level of _rhlI_ over time course of experiment.** Shaded regions highlight peak expression and indicate two-hour period used in analysis. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)

lasb_time{#fig:lasb_time}

**Figure [-@fig:lasb_time]. Expression level of _lasB_ over time course of experiment.** Shaded regions highlight peak expression and indicate two-hour period used in analysis. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)

Single-Signal Models

Table [-@tbl:singlesignal] shows the parameter estimates for the single-signal model below as maximum fold-change ((ɑ + ɑ0) / ɑ0) and half-concentration values (K) for both signals. $$ E(S) = \alpha_0 + \alpha \frac{[S]}{[S] + K} \qquad{(\mathrm{A})} $$

**Equation A. Expression level as a function of a single signal's concentration.**

Gene Signal Parameter Derivation Estimate 95% C.I.
lasI Basal expression ɑ0 1670 RLU/OD 1619 – 1721
3‑oxo‑C12‑HSL Max fold-change (ɑ + ɑ0) / ɑ0 38 × 36 – 40
½ conc. K 0.24 μM 0.17 – 0.30
C4‑HSL Max fold-change (ɑ + ɑ0) / ɑ0 6.4 × 5.8 – 7.0
½ conc. K 1.0 μM 0.7 – 1.4
rhlI Basal expression ɑ0 1861 RLU/OD 1798 – 1923
3‑oxo‑C12‑HSL Max fold-change (ɑ + ɑ0) / ɑ0 35 × 34 – 36
½ conc. K 0.052 μM 0.031 – 0.073
C4‑HSL Max fold-change (ɑ + ɑ0) / ɑ0 6.4 × 5.3 – 7.4
½ conc. K 1.6 μM 0.8 – 2.4

Table: singlesignal {#tbl:singlesignal}

**Table [-@tbl:singlesignal]. Single Signal Parameter Estimates.** Estimated fold-change, derived from raw parameters of Eq A as (*ɑ* + *ɑ*0) / *ɑ*0 , and half-concentration, *K*, values for gene expression as a function of a single signal in isolation. Values shown with 95% confidence intervals.

The primary data set focuses on a full range of signal concentrations from 0 to 5μM. To further validate the model, additional measurements were collected for low values of signal concentration. Fig [-@fig:lowconc] overlays those observations on the primary data set, demonstrating further strong agreement between observations and model predictions.

model1{#fig:lowconc}

**Figure [-@fig:lowconc]. Effect of each signal in isolation on the expression level of _lasI_** Plotted points are observations and dashed lines show model (Eq A) predictions when parameterized per Table [-@tbl:singlesignal]. Dark blue points are additional observations collected using low signal concentrations. (A single data point identified as a faulty outlier is indicated in light blue and excluded from the analysis.) These data points are not used in estimating model parameters yet still show strong agreement with the model. Coefficient of determination R2 between additional observations and initial model predictions is 0.82. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)

Multi-Signal Models

Table [-@tbl:multisignal] shows the parameter estimates for the multi-signal model of Eq 1 (main text).

Gene Signal Parameter Derivation Estimate 95% C.I.
lasI Basal expression ɑ1,0 1670 RLU/OD 1619 – 1721
3‑oxo‑C12‑HSL Max fold-change (ɑ1,1 + ɑ1,0) / ɑ1,0 38 × 36 – 40
½ conc. K1,1 0.24 μM 0.17 – 0.30
C4‑HSL Max fold-change (ɑ1,2 + ɑ1,0) / ɑ1,0 6.4 × 5.8 – 7.0
½ conc. K1,2 1.0 μM 0.7 – 1.4
Combined Max fold-change (ɑ1,1,2 + ɑ1,0) / ɑ1,0 30 × 29 – 31
½ conc. for 3‑oxo‑C12‑HSL KQ1,1,2 < 0.001 μM
½ conc. for C4-HSL KQ1,2,1 0.003 μM 0 – 0.011
rhlI Basal expression ɑ2,0 1861 RLU/OD 1798 – 1923
3‑oxo‑C12‑HSL Max fold-change (ɑ2,1 + ɑ2,0) / ɑ2,0 35 × 34 – 36
½ conc. K2,1 0.052 μM 0.031 – 0.073
C4‑HSL Max fold-change (ɑ2,2 + ɑ2,0) / ɑ2,0 6.4 × 5.3 – 7.4
½ conc. K2,2 1.6 μM 0.8 – 2.4
Combined Max fold-change (ɑ2,1,2 + ɑ1,0) / ɑ1,0 27 × 26 – 28
½ conc. for 3‑oxo‑C12‑HSL KQ2,1,2 < 0.001 μM
½ conc. for C4-HSL KQ2,2,1 < 0.001 μM

Table: multisignal {#tbl:multisignal}

**Table [-@tbl:multisignal]. Multi-signal parameter estimates.** Model parameters for gene expression as a function of multiple signal concentrations. Parameter definitions are the same as in Table [-@tbl:singlesignal] with addition of cooperative fold-change, again derived from raw parameters as (*ɑ* + *ɑ*0) / *ɑ*0 , and cooperative half-concentration *KQ.* Values shown with 95% confidence intervals.

Figs 3C and 3D in the main text summarize the predictions of the multi-signal models for lasI and rhlI expression. The following figures provide a more detailed comparison of the model predictions for both genes.

model_lasi{#fig:model_lasi}

**Figure [-@fig:model_lasi]. Multi-signal model for _lasI_ expression.** Panels compare model predictions to observations for all combinations of signal concentrations. Horizontal bars indicate model predictions, while plotted points show observed values. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)

model_rhli{#fig:model_rhli}

**Figure [-@fig:model_rhli]. Multi-signal model for _rhlI_ expression.** Panels compare model predictions to observations for all combinations of signal concentrations. Horizontal bars indicate model predictions, while plotted points show observed values. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)

Table [-@tbl:explasb] shows the parameter estimates for lasB expression.

Signal Parameter Derivation Estimate 95% C.I.
Basal Expression ɑ3,0 1588 RLU/OD 1516 –1660
3‑oxo‑C12‑HSL Max fold-change (ɑ3,1 + ɑ3,0) / ɑ3,0 6.1 × 5.6 – 6.7
½ conc. K3,1 2.5 μM 1.0 – 3.0
C4‑HSL Max fold-change (ɑ3,2 + ɑ3,0) / ɑ3,0 1.1 × 1.1 – 1.1
½ conc. K3,2 < 0.001 μM
Combined Max fold-change (ɑ3,1,2 + ɑ3,0) / ɑ3,0 23 × 22 – 24
½ conc. for 3‑oxo‑C12‑HSL KQ3,1,2 0.42 μM 0.35 – 0.48
½ conc. for C4-HSL KQ3,2,1 0.22 μM 0.18 – 0.25

Table: explasb {#tbl:explasb}

**Table [-@tbl:explasb]. Multi-signal parameter estimates for *lasB.*** Model parameters for *lasB* expression as a function of multiple signal concentrations. Parameter definitions are the same as in Table [-@tbl:multisignal]. Values shown with 95% confidence intervals. Half-concentration estimates less than 0.001 μM are below the limits of precision of the experimental data.

Using the parameter values, the model predicts lasB expression as shown in Fig [-@fig:model_lasb].

model_lasb{#fig:model_lasb}

**Figure [-@fig:model_lasb]. Multi-signal model for _lasB_ expression.** Panels compare model predictions to observations for all combinations of signal concentrations. Horizontal bars indicate model predictions, while plotted points show observed values. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)

Signal Dynamics

We analyze signal dynamics using the model from the main text where the per-capita single production rater is assumed to be proportional to the synthase expression level, $E_i(\mathbf{S})$. The proportionality constant is $c_i$.

$$ \frac{\mathrm{d}S_i}{\mathrm{dt}} \ \ = \ \ c_i E_i(\mathbf{S})\cdot N \ \ - \ \ \delta_i \cdot S_i \ \ - \ \ m \cdot S_i \qquad{(\mathrm{B})} $$

We consider the equilibrium signal concentration (where $\mathrm{d}S/\mathrm{dt} = 0$) and normalize to the decay rate of C4‑HSL ($\delta_2$). When there is no mass transfer ($m = 0$), these simplifications result in an equation for C4‑HSL,

$$ 0 \ \ = \ \ \frac{ c_2 }{ \delta_2 } E_2(\mathbf{S})\cdot N \ \ - \ \ S_2 \qquad{(\mathrm{C})} $$

which can be solved for $c_2 / \delta_2$ in terms of rhlI expression $E_2(\mathbf{S})$, density $N$, and C4‑HSL concentration $S_2$. The corresponding equation for 3‑oxo‑C12‑HSL includes an additional factor $\delta_1/\delta_2$ which, from [@Cornforth2014], we take to be approximately 1.7.

$$ 0 \ \ = \ \ \frac{ c_1 }{ \delta_2 } E_1(\mathbf{S})\cdot N \ \ - \ \ \frac{ \delta_1 }{ \delta_2 } S_1 \qquad{(\mathrm{D})} $$

Data from [@Rattray2022] includes measurements of equilibrium signal concentrations at multiple population densities. We combine those measurements of $N$ and $S_i$ with our model’s estimate of synthase expression level $E_i(\mathbf{S})$ and use non-linear least squares to estimate the proportionality constants.

Signal i Proportionality Constant $c_i/\delta_2$
3‑oxo‑C12‑HSL 12.7 pM/RLU
C4‑HSL 25.4 pM/RLU

Table: const {#tbl:const}

**Table [-@tbl:const]. Estimated proportionality constants that relate synthase expression levels to per-capita signal production rates.** Final column shows adjusted R2 of non-linear least squares estimate.

constants{#fig:constants}

**Figure [-@fig:constants]. Equilibrium signal concentration predicted using proportionality constants.** Individual data points show experimental observations and dashed lines indicate model predictions. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)

Analytic Solutions for Equilibrium

It is possible to derive analytic solutions of Eq 2 (main text) for equilibrium concentrations in all architectures; however, the results are not especially helpful for deriving insights into the system behavior. For example, the independent architecture, which is the simplest considered, has the following equilibrium concentration of 3‑oxo‑C 12‑HSL. $$ S_1^* = \frac{ \begin{align} c_1,N,(\alpha_{1,0} +\alpha_{1,1}) \ - K_{1,1},(m+\delta_1) \end{align} ;+\sqrt{ \begin{aligned} {K_{1,1} }^2 ,{\delta_1 }^2 +2,{K_{1,1} }^2 ,\delta_1 ,m+{K_{1,1} }^2 ,m^2 +2,K_{1,1} ,N,\alpha_{1,0} ,c_1 ,\delta_1 \ +2,K_{1,1} ,N,\alpha_{1,0} ,c_1 ,m -2,K_{1,1} ,N,\alpha_{1,1} ,c_1 ,\delta_1 -2,K_{1,1} ,N,\alpha_{1,1} ,c_1 ,m \ +N^2 ,{\alpha_{1,0} }^2 ,{c_1 }^2 +2,N^2 ,\alpha_{1,0} ,\alpha_{1,1} ,{c_1 }^2 +N^2 ,{\alpha_{1,1} }^2 ,{c_1 }^2 \end{aligned} } }{2,{\left(\delta_1 +m\right)}} \qquad{(\mathrm{E})} $$

Alternate QS Architectures

Table [-@tbl:architectures] shows the parameter values that allow Eq 1 (main text) to represent various QS architectures.

Gene Signal Parameter Derivation Reciprocal Architecture Hierarchical Architecture Independent Architecture
lasI 3‑oxo‑C12‑HSL Max fold-change (ɑ1,1 + ɑ1,0) / ɑ1,0 38 × 38 × 38 ×
C4‑HSL Max fold-change (ɑ1,2 + ɑ1,0) / ɑ1,0 6.4 × 1 × 1 ×
Combined Max fold-change (ɑ1,1,2 + ɑ1,0) / ɑ1,0 30 × 1 × 1 ×
rhlI 3‑oxo‑C12‑HSL Max fold-change (ɑ2,1 + ɑ2,0) / ɑ2,0 35 × 35 × 1 ×
C4‑HSL Max fold-change (ɑ2,2 + ɑ2,0) / ɑ2,0 6.4 × 6.4 × 6.4 ×
Combined Max fold-change (ɑ2,1,2 + ɑ1,0) / ɑ1,0 27 × 27 × 1 ×

Table: architectures {#tbl:architectures}

**Table [-@tbl:architectures]. Hierarchical and independent architectures are special cases of the reciprocal architecture.** The multi-signal model of Eq 1 (main text) can represent hypothetical, alternative QS architectures by setting appropriate *ɑ* values to zero. Zero *ɑ* values result in a corresponding maximum fold-change of 1. For a hierarchical architecture, this setting nullifies the effect of C4‑HSL on *lasI.* For an independent architecture, this setting additionally nullifies the effect of 3‑oxo‑C12‑HSL on *rhlI.*

Normalizing Alternate QS Architectures

Table [-@tbl:architectures] analyzes hypothetical, alternative architectures by eliminating the influence of specific signals on specific genes. For example, the hierarchical architecture nullifies the influence of C4‑HSL on lasI without modifying the effect of 3‑oxo‑C12‑HSL on lasI. This change necessarily reduces the maximum expression level of lasI, and that reduction partially explains the different lasB response in a hierarchical architecture. Reducing maximum lasI expression alone, however, does not explain all of the differences in the lasB response. To expose those additional differences, we make additional adjustments to the model. In particular, we increase the expression of lasI due to 3‑oxo‑C12‑HSL to precisely compensate for the loss of expression due to C4‑HSL. Table [-@tbl:architectures2] shows the full set of adjustments required to normalize the maximum synthase expression levels across all architectures.

Gene Signal Parameter Derivation Reciprocal Architecture Hierarchical Architecture Independent Architecture
lasI 3‑oxo‑C12‑HSL Max fold-change (ɑ1,1 + ɑ1,0) / ɑ1,0 38 × 73 × 73 ×
C4‑HSL Max fold-change (ɑ1,2 + ɑ1,0) / ɑ1,0 6.4 × 1 × 1 ×
Combined Max fold-change (ɑ1,1,2 + ɑ1,0) / ɑ1,0 30 × 1 × 1 ×
rhlI 3‑oxo‑C12‑HSL Max fold-change (ɑ2,1 + ɑ2,0) / ɑ2,0 35 × 35 × 1 ×
C4‑HSL Max fold-change (ɑ2,2 + ɑ2,0) / ɑ2,0 6.4 × 6.4 × 66 ×
Combined Max fold-change (ɑ2,1,2 + ɑ1,0) / ɑ1,0 27 × 27 × 1 ×

Table: architectures {#tbl:architectures2}

**Table [-@tbl:architectures2]. Models of hierarchical and independent architectures can be normalized to ensure that maximum synthase expression is the same for all architectures.** Parameters are the same as those in Table [-@tbl:architectures] but with increased values where appropriate.

Temporal Dynamics

lasb_time_response{#fig:lasb_time_response}

**Figure [-@fig:lasb_time_response]. Time response of *lasB* expression for reciprocal, rescaled hierarchical, and rescaled independent architectures.** Dynamics are those of Eq 2 (main text) with parameters from Table [-@tbl:architectures2]. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)

Signal Concentration Response

2signals{#fig:2signals}

**Figure [-@fig:2signals]. Extracellular signal concentration as a function of density and mass transfer varies based on the quorum sensing architecture.** Heat maps of equilibrium 3‑oxo‑C12‑HSL (A-C) and C4‑HSL (D-F) concentration for three quorum sensing architectures. Both population density and mass transfer rate are varied over the same ranges for all heatmaps. The lines on each heat map indicate density and mass transfer values for which equilibrium concentration is constant, either 50% of its maximum value (white) or 5% of its maximum value (black). Equilibrium concentrations calculated from Eq 2 model with parameters from Table [-@tbl:multisignal] and architectural parameters normalized according to Table [-@tbl:architectures2]. These results follow from the same model parameterization presented in Figs 5F-5H, which showcased the predicted outcome behavior of _lasB_ expression. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)

signal_ratio{#fig:signal_ratio}

**Figure [-@fig:signal_ratio]. Ratio of signal concentrations as a function of density and mass transfer varies based on the quorum sensing architecture.** The figure shows heat maps of the ratio of equilibrium 3‑oxo‑C12‑HSL to C4‑HSL concentration for the reciprocal architecture. Equilibrium concentrations calculated from Eq 2 model with parameters from Table [-@tbl:multisignal]. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)

Three Signal Models

The hypothetical three-signal models of the main text’s discussion are based oh a simplified version of the las and rhl interactions. Table [-@tbl:multisignal] provides the starting point for the models. For ease of computation, the second-order effects are ignored by setting ɑi,j,j` to zero. Parameters for the third signal (i = 3) are initailly based on convenient intermediate values between those of las and rhl and then varied as neccessary to demontrate the various responses. Table [-@tbl:three_signal] shows the values for all non-zero parameters in all models.

Parameter Weak Strong Limited Damped
𝛼1,0 1670 1670 1670 1670
𝛼2,0 1861 1861 1861 1861
𝛼3,0 10000 10000 10000 10000
𝛼1,1 61000 61000 61000 61000
𝛼2,2 10000 10000 10000 10000
𝛼3,3 10000 10000 10000 10000
𝛼1,2 9000 9000 9000 9000
𝛼2,1 63000 63000 63000 63000
𝛼2,3 10000 10000 10000 10000
𝛼3,1 10000 1000000 158000 630000
𝛼3,2 -10000 -10000 -245 -1580000
K1,1 0.24 0.24 0.24 0.24
K2,2 1.6 1.6 1.6 1.6
K3,3 1 1 1 1
K1,2 1 1 1 1
K2,1 0.052 0.052 0.052 0.052
K2,3 0.32 0.32 0.32 0.32
K3,1 0.32 0.32 0.032 0.032
K3,2 0.32 0.32 4.0 3.2
c1/𝛿2 1.3⨉10-5 1.3⨉10-5 1.3⨉10-5 1.3⨉10-5
c2/𝛿2 2.5⨉10-5 2.5⨉10-5 2.5⨉10-5 2.5⨉10-5
c3/𝛿2 1.9⨉10-5 1.9⨉10-5 1.9⨉10-5 1.9⨉10-5
𝛿1/𝛿2 1.7 1.7 1.7 1.7
𝛿2/𝛿2 1 1 1 1
𝛿3/𝛿2 1.35 1.35 1.35 1.35

Table: three_signal {#tbl:three_signal}

**Table [-@tbl:three_signal]. Model parameters for hypothetical three-signal architectures.** Different parameter values result in the different responses of the third QS system's synthase expression level as population density increases.

3signals{#fig:3signals}

**Figure [-@fig:3signals]. Interaction strength for both induction and repression determines population behavior.** The figure considers hypothetical architectures for a quorum sensing network with three QS systems. The first two, mimicking the architecture of _las_ and _rhl,_ are mutually reinforcing. The third system is both induced and repressed by the other two, matching the reported interactions of _pqs._ The panels show all three synthase expression levels as a function of population density. As the four panels show, even within the constraints of a particular architecture, a wide variety of responses are possible. (A) Baseline case with weak activation of system 3 by system 1 (low 𝛼3,1). (B) Strong activation (high 𝛼3,1). (C) Limited activation with weak repression of system 3 by system 2 (moderately negative 𝛼3,2). (D) Damped activation (strongly negative 𝛼3,2). (The data underlying this Figure and the code used to generate it can be found in https://doi.org/10.5281/zenodo.15808353.)

References