In Silico Evaluation of the Impacts of Quorum Sensing Inhibition (QSI) on Strain Competition and Development of QSI Resistance

As understanding of bacterial regulatory systems and pathogenesis continues to increase, QSI has been a major focus of research. However, recent studies have shown that mechanisms of resistance to quorum sensing (QS) inhibitors (QSIs) exist, calling into question their clinical value. We propose a computational framework that considers bacteria genotypes relative to QS genes and QS-regulated products including private, quasi-public, and public goods according to their impacts on bacterial fitness. Our results show (1) QSI resistance spreads when QS positively regulates the expression of private or quasi-public goods. (2) Resistance to drugs targeting secreted compounds downstream of QS for a mix of private, public, and quasi-public goods also spreads. (3) Changing the micro-environment during treatment with QSIs may decrease the spread of resistance. At fundamental-level, our simulation framework allows us to directly quantify cell-cell interactions and biofilm dynamics. Practically, the model provides a valuable tool for the study of QSI-based therapies, and the simulations reveal experimental paths that may guide QSI-based therapies in a manner that avoids or decreases the spread of QSI resistance.

Dynamics of strain growth with biofilms composed of QS + , QS − , and QSI-resistant strains, when QS regulates the production of private goods (colored red, blue, and green respectively). Figure set A: Projections of biofilm growth up to 10 days. Figure set Bi-Biii: Graphs displaying the relative ratio of each strain, before and after QSI addition under various types of QSI (i, ii, iii correspond to scenarios SE8, SE9, and SE10, respectively). Figure set Biv-viii: Graphs comparing the consequences of different modes of QSI on multiple QS and bacteria population measurements. Note that resistance to QSIs targeting signal accumulation is not considered, SE19 does not have QSI-resistant strain in the mix.

Supplementary Note 1: Preliminary Success of QSIs
Previous work on using QS inhibitors can be characterized to target at least one of these three categories: (1) signal generation; 1 (2) extracellular signal accumulation; 2 (3) signal reception. 3 For targeting on the signal generation, extensive research has evaluated the mechanisms involved in AHL production. LasI synthase proteins utilize components of the amino acid and fatty acid biosynthesis pathways to produce AHLs. Recent in vitro studies have also shown that alterations in the biosynthesis of the LasI synthase proteins can decrease the production of active AHL molecules. 1 This research data demonstrate that LasI is very sensitive to environmental conditions and that controlling the LasI substrates may have a significant effect on functional AHL production. Therefore, targeting the expression of LasI substrates can prevent the production of AHL, and thus QS activation.
For targeting on the signal accumulation, another extensively studied QSI strategy is the degradation and modification of the QS signaling molecules. Most enzymes identified thus far target AHL molecules. Lactonases degrade AHLs as they leave the bacteria, thus inhibiting their activation of LasR and host cells. Indeed, when these lactonases were expressed in P. aeruginosa, once can observe a significant decrease in AHL production and virulence factors expression. 2 For targeting on the signal generation, a recent study used a reporter assay to identify a group of compounds to inhibit the activation of LasR and elastase production. 3 The antagonists are similar in structure to natural AHLs produced by P. aeruginosa and would compete for binding to LasR proteins; thus, inhibit the activation of LasR.

Supplementary Note 2: Simulations with QSI Effects and QSI Resistance, where QS Leads to Production of Non-beneficial Goods
We consider QS + and QSI-resistant cells produce non-beneficial goods in response to QS activation. Also, we consider three QSI strategies, namely, a) targeting signal generation (SE5), b) targeting signal accumulation, and no QSI-resistance mechanism (SE6), c) targeting signal reception (SE7).
When QS regulates the production of non-beneficial goods, the QS-regulated expression, QS + genotype ratio, and QSIresistant cell frequencies do not increase; in fact, the QSI-resistant can not dominate the population in all there scenarios due to the production of non-beneficial goods has a metabolic costs on QS + and QSI-resistant cells, and this is not balanced by any fitness benefit. Overall, the use of QSI in the non-beneficial goods cases can effectively inhibit the QS-regulated expressions without inducing any bad outcome. That is to say, if the virulence factors are regulated by QS, and they confer no growth benefits to the producers, then QSI therapy should work very well.

Supplementary Note 3: Simulations with QSI Effects and QSI Resistance, where QS Leads to Production of Private Goods
As discussed earlier, private goods are typically secondary metabolites that are only accessible by producer cells, including QSI-resistant cells and QS + cells (if their signal reception is not inhibited), therefore providing exclusive fitness benefits to the producer cells. In the following three scenarios, we model the 10-day biofilm evolution consisting of QS − cells, QS + cells, and QSI-resistant cells where QS + and QSI-resistant cells produce private goods in response to QS activation. Similarly, we consider three QSI strategies: a) targeting signal generation (SE8), b) targeting signal accumulation (SE9), and c) targeting signal reception (SE10).
Compared to SE5, SE6, SE7, coupling between QS-regulated products and bacterial fitness leads to dramatically different evolution results, yet each QSI strategy present distinct risks of the development of resistance. Specifically, targeting signal accumulation results in weak resistance selection while targeting signal reception results in strong selection of QSI-resistance cells. Nevertheless, targeting signal molecule accumulation in the extracellular space continue to show potential as the best approach.

Supplementary Note 4: Simulations with QSI Effects and QSI Resistance, where QS Leads to Production of Diffusive Public Goods
As previously shown, the QS-mediated production of diffusive public goods shared by all cells imposes a significant negative impact on the fitness of QS + cells. However, under QSI treatment, an important, but often overlooked detail is whether or not QS + cells remain actively producing public goods. If not, QS + cells incur no metabolic cost and are able to achieve growth rates comparable to QS − cells. In the following three scenarios, we consider the 10-day biofilm growth consisting of QS − cells, QS + cells, and QSI-resistant cells where QS + and QSI-resistant cells produce diffusive public goods in response to QS activation. Similarly, we consider three QSI strategies: a) targeting signal generation (SE11), b) targeting signal accumulation (SE12), c) targeting signal reception (SE13).
In general, QSI therapy works well when the micro-environment at infection sites encouraging QS + and QSI-resistant cells to generate public goods, and the public goods can be effectively shared by QS − cheaters. More precisely, QSI treatment not only shuts down the QS-regulated expression immediately, but also prevents the increase of resistance and QS + genotype ratio (see Supplementary Fig. 8).

Supplementary Note 5: Robustness of Simulation Parameters
We examined the impact of considering different ratios of each strain at the beginning of simulations. More precisely, we use scenario M5 as an example to illustrate that the initial ratio among genotypes does not change the long-term evolution dynamics. Here, we consider four different composition ratios of QS + , QS − and QSI-resistance cells. As shown in Supplementary Fig. 10, when the initial compositions of QSI-resistance cells increases, QSI-resistance cells enter the exponential growth phase earlier; this is due to the fact that QSI-resistance cells begin to massively produce QS-controlled public goods earlier. However, the long-term evolution dynamics is robust and not influenced by this selection of initial composition ratios of the three genotypes of cells (e.g, the QSI-resistance cells have growth advantage compared to other cell types).
We also conduct a robustness analysis of the model parameters to show the range of model parameters that can still capture the desired behavior. Since we calibrate the model parameters to fit the relative changes of the LasR-AHL concentration, the model parameters depend on the relative values. For example, the production rates k A and k R in eq (2) and (3) (in the main manuscript) are calibrated to be equal (i.e., k A = k R ) and the binding and unbinding rates are calibrated to be of the same magnitude order. Therefore, we vary the values of these parameters to verify the robustness of the model.