Dimension-reduction simplifies the analysis of signal crosstalk in a bacterial quorum sensing pathway

Many pheromone sensing bacteria produce and detect more than one chemically distinct signal, or autoinducer. The pathways that detect these signals are typically noisy and interlocked through crosstalk and feedback. As a result, the sensing response of individual cells is described by statistical distributions that change under different combinations of signal inputs. Here we examine how signal crosstalk reshapes this response. We measure how combinations of two homoserine lactone (HSL) input signals alter the statistical distributions of individual cell responses in the AinS/R- and LuxI/R-controlled branches of the Vibrio fischeri bioluminescence pathway. We find that, while the distributions of pathway activation in individual cells vary in complex fashion with environmental conditions, these changes have a low-dimensional representation. For both the AinS/R and LuxI/R branches, the distribution of individual cell responses to mixtures of the two HSLs is effectively one-dimensional, so that a single tuning parameter can capture the full range of variability in the distributions. Combinations of crosstalking HSL signals extend the range of responses for each branch of the circuit, so that signals in combination allow population-wide distributions that are not available under a single HSL input. Dimension reduction also simplifies the problem of identifying the HSL conditions to which the pathways and their outputs are most sensitive. A comparison of the maximum sensitivity HSL conditions to actual HSL levels measured during culture growth indicates that the AinS/R and LuxI/R branches lack sensitivity to population density except during the very earliest and latest stages of growth respectively.