updated doi

Author: sathomas

README.md

@@ -41,7 +41,7 @@ We first evaluate quorum sensing behavior under the influence of a single signal
 <img src="Figures/fig2_observations.svg" alt="Figure 2: observations" />
 <figcaption aria-hidden="true">Figure 2: observations</figcaption>
 
-**Figure 2. Both the *las* signal 3‑oxo‑C<sub>12</sub>‑HSL and the *rhl* signal C<sub>4</sub>‑HSL increase the expression of *lasI* and *rhlI* in a signal null PAO1.** (A-C) *lasI* expression level as a function of defined concentrations of 3‑oxo‑C<sub>12</sub>‑HSL alone (A), C<sub>4</sub>‑HSL alone (B), and both signals together (C). (D-F) *rhlI* expression level under the same conditions. All plots show fold-change in RLU/OD (relative light units per optical density) values compared to baseline with no exogenous signals in NPAO1∆*lasI*∆*rhlI* cultures. Genomic reporter fusions *lasI:luxCDABE* and *rhlI:luxCDABE* were used to generate luminescence. Points are individual observations within the time window of peak expression; lines show predictions from the Michaelis-Menten model of Equation S1 parameterized according to Table S3. Figures S1 and S2 show the underlying expression data for the entire time course of the experiments. Additional observations at lower signal concentrations were used to validate the model parameters and showed strong agreement (R<sup>2</sup> = 0.82) as detailed in Figure S4. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.14230778.)
+**Figure 2. Both the *las* signal 3‑oxo‑C<sub>12</sub>‑HSL and the *rhl* signal C<sub>4</sub>‑HSL increase the expression of *lasI* and *rhlI* in a signal null PAO1.** (A-C) *lasI* expression level as a function of defined concentrations of 3‑oxo‑C<sub>12</sub>‑HSL alone (A), C<sub>4</sub>‑HSL alone (B), and both signals together (C). (D-F) *rhlI* expression level under the same conditions. All plots show fold-change in RLU/OD (relative light units per optical density) values compared to baseline with no exogenous signals in NPAO1∆*lasI*∆*rhlI* cultures. Genomic reporter fusions *lasI:luxCDABE* and *rhlI:luxCDABE* were used to generate luminescence. Points are individual observations within the time window of peak expression; lines show predictions from the Michaelis-Menten model of Equation S1 parameterized according to Table S3. Figures S1 and S2 show the underlying expression data for the entire time course of the experiments. Additional observations at lower signal concentrations were used to validate the model parameters and showed strong agreement (R<sup>2</sup> = 0.82) as detailed in Figure S4. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)
 
 While we find no surprises with 3‑oxo‑C<sub>12</sub>‑HSL, our experiments with C<sub>4</sub>‑HSL challenge the conventional hierarchical view. Figure 2B,E shows those results: expression of *lasI* and *rhlI* increases with higher C<sub>4</sub>‑HSL concentration. The response of *lasI* (Figure 2B) does not correspond to a strict hierarchy with *las* as the master. Here we find that the *rhl* system affects the *las* system.
 
@@ -56,7 +56,7 @@ Having established a simple Michaelis-Menten model for each signal in isolation
 <img src="Figures/fig3_reciprocal.svg" alt="Figure 3: reciprocal" />
 <figcaption aria-hidden="true">Figure 3: reciprocal</figcaption>
 
-**Figure 3. The *las* and *rhl* QS systems have a reciprocal, synergistic, and unequal relationship.** (A,B) Single-signal models demonstrate that the summed effects of single signals (3‑oxo‑C<sub>12</sub>‑HSL alone, red; C<sub>4</sub>‑HSL alone, orange) cannot account for the maximal expression of *lasI* or *rhlI.* The upper green, flat surfaces in the plots indicate the maximum mean expression level measured across all combinations of signal concentrations while the lower semi-transparent surfaces mark the sum of single signal effects. The plotted points represent observed expression levels when C<sub>4</sub>‑HSL is withheld (red) and when 3‑oxo‑C<sub>12</sub>‑HSL is withheld (yellow). Lines indicate the model predictions (Equation S1, parameters in Table S3). (C,D) Multi-signal non-linear models capture the synergistic effects of both signals and match observed expression levels. Model estimates are shown as grid lines. Horizontal bars show the mean value of expression observed at each combination of signal concentrations. Lines extend from these mean values to the relevant grid point for clarity. The coefficient of determination (R<sup>2</sup>) for the models is 0.82 and 0.77, respectively. Figures S5 and S6 present more detailed comparisons between model and observations. (E) The data of Figure 2 shows that relationship of the *las* and *rhl* systems is reciprocal, and the multi-signal model quantifies the strength of those interactions. In particular, it reveals the contribution of bvoth signals to the maximum fold-change in expression of both synthases. The charts in this panel summarize the contribution of 3‑oxo‑C<sub>12</sub>‑HSL (red), C<sub>4</sub>‑HSL (yellow), and the synergistic combination of both (orange). (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.14230778.)
+**Figure 3. The *las* and *rhl* QS systems have a reciprocal, synergistic, and unequal relationship.** (A,B) Single-signal models demonstrate that the summed effects of single signals (3‑oxo‑C<sub>12</sub>‑HSL alone, red; C<sub>4</sub>‑HSL alone, orange) cannot account for the maximal expression of *lasI* or *rhlI.* The upper green, flat surfaces in the plots indicate the maximum mean expression level measured across all combinations of signal concentrations while the lower semi-transparent surfaces mark the sum of single signal effects. The plotted points represent observed expression levels when C<sub>4</sub>‑HSL is withheld (red) and when 3‑oxo‑C<sub>12</sub>‑HSL is withheld (yellow). Lines indicate the model predictions (Equation S1, parameters in Table S3). (C,D) Multi-signal non-linear models capture the synergistic effects of both signals and match observed expression levels. Model estimates are shown as grid lines. Horizontal bars show the mean value of expression observed at each combination of signal concentrations. Lines extend from these mean values to the relevant grid point for clarity. The coefficient of determination (R<sup>2</sup>) for the models is 0.82 and 0.77, respectively. Figures S5 and S6 present more detailed comparisons between model and observations. (E) The data of Figure 2 shows that relationship of the *las* and *rhl* systems is reciprocal, and the multi-signal model quantifies the strength of those interactions. In particular, it reveals the contribution of bvoth signals to the maximum fold-change in expression of both synthases. The charts in this panel summarize the contribution of 3‑oxo‑C<sub>12</sub>‑HSL (red), C<sub>4</sub>‑HSL (yellow), and the synergistic combination of both (orange). (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)
 
 To account for the synergy between the signals, we incorporate a cooperativity term in the gene expression model. Note that the cooperativity term is a multiplication of signals, and it alone cannot explain the full response, as the product is necessarily zero when any signal is absent. This term accounts for any non-additive interaction, for example the ability of one bound transcription factor to recruit the binding of a second transcription factor (Kaplan et al. 2008). Equation 1 shows the result. Each gene has a basal expression level, amplification from each signal alone, and additional amplification from each pair-wise combination of signals. The interaction from these pair-wise combinations captures the cooperative enhancement from the combined signals.
 
@@ -83,7 +83,7 @@ The prior literature provides a clear expectation that *lasB* expression will be
 <img src="Figures/fig4_lasb.svg" alt="Figure 4: lasb" />
 <figcaption aria-hidden="true">Figure 4: lasb</figcaption>
 
-**Figure 4. Expression of *lasB* is maximal in the presence of both C<sub>4</sub>‑HSL and 3‑oxo‑C<sub>12</sub>‑HSL.** An analysis similar to Figure 3 shows that (A) a single-signal model cannot account for the maximal expression of *lasB,* while (B) a multi-signal model incorporating synergistic effects can match observations. Panel C summarizes qualitative differences in the relative effects of each signal on *lasB* response compared to *lasI* and *rhlI.* Pie charts break down the contribution to maximum fold-change in expression levels. For both *lasI* and *rhlI,* 3‑oxo‑C<sub>12</sub>‑HSL alone is responsible for slightly more than half of their maximum expression, while for *lasB* 3‑oxo‑C<sub>12</sub>‑HSL alone accounts for less than a quarter. The combined effect of both 3‑oxo‑C<sub>12</sub>‑HSL and C<sub>4</sub>‑HSL together dominates *lasB* expression.The half concentration values also show a qualitative difference. While *lasI* and *rhl* are nearly equally sensitive to 3‑oxo‑C<sub>12</sub>‑HSL and C<sub>4</sub>‑HSL, *lasB* is substantially more sensitive to C<sub>4</sub>‑HSL than to 3‑oxo‑C<sub>12</sub>‑HSL. Figure S3 shows underlying expression data for full time course of experiments; Table S5 lists the parameter values, and Figure S7 provides a detailed comparison of model predictions and observations. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.14230778.)
+**Figure 4. Expression of *lasB* is maximal in the presence of both C<sub>4</sub>‑HSL and 3‑oxo‑C<sub>12</sub>‑HSL.** An analysis similar to Figure 3 shows that (A) a single-signal model cannot account for the maximal expression of *lasB,* while (B) a multi-signal model incorporating synergistic effects can match observations. Panel C summarizes qualitative differences in the relative effects of each signal on *lasB* response compared to *lasI* and *rhlI.* Pie charts break down the contribution to maximum fold-change in expression levels. For both *lasI* and *rhlI,* 3‑oxo‑C<sub>12</sub>‑HSL alone is responsible for slightly more than half of their maximum expression, while for *lasB* 3‑oxo‑C<sub>12</sub>‑HSL alone accounts for less than a quarter. The combined effect of both 3‑oxo‑C<sub>12</sub>‑HSL and C<sub>4</sub>‑HSL together dominates *lasB* expression.The half concentration values also show a qualitative difference. While *lasI* and *rhl* are nearly equally sensitive to 3‑oxo‑C<sub>12</sub>‑HSL and C<sub>4</sub>‑HSL, *lasB* is substantially more sensitive to C<sub>4</sub>‑HSL than to 3‑oxo‑C<sub>12</sub>‑HSL. Figure S3 shows underlying expression data for full time course of experiments; Table S5 lists the parameter values, and Figure S7 provides a detailed comparison of model predictions and observations. (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.15808353.)
 
 ### Mathematical Models Incorporating Multi-signal Interactions Predict Wildtype Quorum Sensing Response to Environmental Variation
 
@@ -112,7 +112,7 @@ In Figure 5A,B we illustrate our integrated model prediction of wildtype *lasB*
 <img src="Figures/fig5_environment.svg" alt="Figure 5: environment" />
 <figcaption aria-hidden="true">Figure 5: environment</figcaption>
 
-**Figure 5. The models of Equations 1 and 2 in combination can quantitatively predict wildtype QS-controlled *lasB* response to environmental variation.** (A) Mathematical model schematic: Given values for population density and mass transfer rate, Equation 2 (parameterized by Table S6) predicts equilibrium concentrations of 3‑oxo‑C<sub>12</sub>‑HSL and C<sub>4</sub>‑HSL. With those values Equation 1 (parameterized by Table S5) can predict the resulting *lasB* expression level. (B) Independently parameterized model predictions compared to experimental observations. The plot shows a reaction norm (Stearns 1989) of predicted *lasB* expression level (solid line) as a function of population carrying capacity. The figure also shows independent experimental observations of wildtype *lasB* expression as a function of bacterial carrying capacity, manipulated by varying the concentration of limiting carbon (J. Rattray et al. 2022). Model predictions are in good agreement with independent experimental data (R<sup>2</sup> = 0.91), together showing that *lasB* responds to changes in population density and mass transfer in a graded manner. Note that the model parameters are not fitted to the data in this figure. (C-H) Heat maps of model predicted *lasB* expression level as a function of both mass transfer *m* and population density *N* given three quorum sensing architectures. (C-E) Architectures without rescaling; (F-H) architectures with rescaling to standardize maximum expression levels. The lines on each heat map indicate density and mass transfer values for which *lasB* expression is constant, either 50% of its maximum value (white) or 5% of its maximum value (black). (The data underlying this Figure and the code used to analyze it can be found in https://doi.org/10.5281/zenodo.14230778.)
+**Figure 5. The models of Equations 1 and 2 in combination can quantitatively predict wildtype QS-controlled *lasB* response to environmental variation.** (A) Mathematical model schematic: Given values for population density and mass transfer rate, Equation 2 (parameterized by Table S6) predicts equilibrium concentrations of 3‑oxo‑C<sub>12</sub>‑HSL and C<sub>4</sub>‑HSL. With those values Equation 1 (parameterized by Table S5) can predict the resulting *lasB* expression level. (B) Independently parameterized model predictions compared to experimental observations. The plot shows a reaction norm (Stearns 1989) of predicted *lasB* expression level (solid line) as a function of population carrying capacity. The figure also shows independent experimental observations of wildtype *lasB* expression as a function of bacterial carrying capacity, manipulated by varying the concentration of limiting carbon (J. Rattray et al. 2022). Model predictions are in good agreement with independent experimental data (R<sup>2</sup> = 0.91), together showing that *lasB* responds to changes in population density and mass transfer in a graded manner. Note that the model parameters are not fitted to the data in this figure. (C-H) Heat maps of model predicted *lasB* expression level as a function of both mass transfer *m* and population density *N* given three quorum sensing architectures. (C-E) Architectures without rescaling; (F-H) architectures with rescaling to standardize maximum expression levels. The lines on each heat map indicate density and mass transfer values for which *lasB* expression is constant, either 50% of its maximum value (white) or 5% of its maximum value (black). (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 Architectures Govern Functional Responses to Environmental Variation