Interactions among quorum sensing inhibitors

Abstract

Many pathogenic bacteria use quorum sensing (QS) systems to regulate the expression of virulence genes in a density-dependent manner. In one widespread QS paradigm the enzyme LuxI generates a small diffusible molecule of the acyl-homoserine lactone (AHL) family; high cell densities lead to high AHL levels; AHL binds the transcription factor LuxR, triggering it to activate gene expression at a virulence promoter. The emergence of antibiotic resistance has generated interest in alternative anti-microbial therapies that target QS. Inhibitors of LuxI and LuxR have been developed and tested in vivo, and can act at various levels: inhibiting the synthesis of AHL by LuxI, competitively or non-competitively inhibiting LuxR, or increasing the turnover of LuxI, LuxR, or AHL. Here use an experimentally validated computational model of LuxI/LuxR QS to study the effects of using inhibitors individually and in combination. The model includes the effect of transcriptional feedback, which generates highly non-linear responses as inhibitor levels are increased. For the ubiquitous LuxI-feedback virulence systems, inhibitors of LuxI are more effective than those of LuxR when used individually. Paradoxically, we find that LuxR competitive inhibitors, either individually or in combination with other inhibitors, can sometimes increase virulence by weakly activating LuxR. For both LuxI-feedback and LuxR-feedback systems, a combination of LuxR non-competitive inhibitors and LuxI inhibitors act multiplicatively over a broad parameter range. In our analysis, this final strategy emerges as the only robust therapeutic option.

Figure 1. Quorum sensing feedback systems and density-dependent responses.

(A,B) The enzyme LuxI generates AHL, a diffusible signaling molecule. The transcription factor LuxR, when bound to AHL, activates transcription of virulence genes at promoter pR. (A) LuxI-feedback system: LuxI is expressed from promoter pR, while LuxR is expressed from a constitutive promoter pX. (B) LuxR-feedback system: LuxR is expressed from promoter pR, while LuxI is expressed from a constitutive promoter pX. (C,D) Virulence gene expression as a function of cell density (computed from Eqs. 4, 5, 16) for: the wild type system (solid); with a LuxI inhibitor (; dot-dashed); with a LuxR non-competitive inhibitor (; dashed); and with a LuxR competitive inhibitor (; dotted). Positive feedback produces induction curves with stable upper and lower branches separated by an unstable middle branch. Cells which start off on the un-induced lower branch will jump to the highly-induced upper branch when their density crosses a critical threshold. (C) LuxI-feedback system. (D) LuxR-feedback system.

Figure 2. Effect of individual inhibitors.

Each panel shows the steady-state expression level at the virulence promoter as a single inhibitor is varied ( in the absence of inhibitors, at high inhibitor levels). Parameter values are taken from Table 1. The x-axis is logarithmic. Due to positive feedback, the equations sometimes admit three solutions for a fixed level of inhibition: the upper and lower branches are stable (solid curves); the middle branch is unstable (dotted curve). (A,C,E) LuxI-feedback systems with α = 0.11. (B,D,F) LuxR-feedback systems with α = 0.05. (A,B) LuxI inhibitors (varying ). (C,D) LuxR non-competitive inhibitors (varying ). (E,F) LuxR competitive inhibitors (varying ).

Figure 3. Effect of inhibitors in combination.

Each panel shows the steady-state expression level at the virulence promoter as two inhibitors are varied. Parameter values are taken from Table 1. Both x- and y-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 α = 0.11. (B,D,F,H) LuxR-feedback systems with α = 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 x-axis, while cell density is varied along the y-axis. The dark curve shows the contour of constant total AHL from external and internal sources.

Figure 4. Dependence on parameters.

We vary two key parameter values (keeping the rest fixed at the values shown in Table 1): α, the expression level of the constitutive promoter; and n, 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 α (below the curve) but is a mixture of smooth and abrupt for high values of α (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 {α,n} space separates purely abrupt responses from a mixture of smooth and abrupt responses. (D) Above the value α = 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 α = 0.125, the competitive inhibitor acts antagonistically with the non-competitive inhibitor. For n >1.4 the response is abrupt; for n <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.