Disruption of microbial communication yields a two-dimensional percolation transition

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Disruption of microbial communication yields a two-dimensional percolation transition

Kalinga Pavan T. Silva, Tahir I. Yusufaly, Prithiviraj Chellamuthu, and James Q. Boedicker

Phys. Rev. E 99, 042409 – Published 19 April 2019

Abstract

Bacteria communicate with each other to coordinate macroscale behaviors including pathogenesis, biofilm formation, and antibiotic production. Empirical evidence suggests that bacteria are capable of communicating at length scales far exceeding the size of individual cells. Several mechanisms of signal interference have been observed in nature, and how interference influences macroscale activity within microbial populations is unclear. Here we examined the exchange of quorum sensing signals to coordinate microbial activity over long distances in the presence of a variable amount of interference through a neighboring signal-degrading strain. As the level of interference increased, communication over large distances was disrupted and at a critical amount of interference, large-scale communication was suppressed. We explored this transition in experiments and reaction-diffusion models, and confirmed that this transition is a two-dimensional percolation transition. These results demonstrate the utility of applying physical models to emergence in complex biological networks to probe robustness and universal quantitative features.

Received 23 October 2018

DOI:https://doi.org/10.1103/PhysRevE.99.042409

Physics Subject Headings (PhySH)

Cell communication Cell signaling Collective behavior Emergent biological functions from complex interactions

Physics of Living Systems

Authors & Affiliations

Kalinga Pavan T. Silva¹, Tahir I. Yusufaly¹, Prithiviraj Chellamuthu¹, and James Q. Boedicker^1,2

¹Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089, USA
²Department of Biological Sciences, University of Southern California, Los Angeles, CA 90089, USA

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Vol. 99, Iss. 4 — April 2019

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Images

Figure 1
Experimental assay to measure spatial patterns of cellular communication in the presence of interference. (a) The sender (yellow) produces an acyl-homoserine lactone (AHL) signal, 3-oxo-C6-HSL, while the degrader (black shaded) produces the AHL degradative enzyme AiiA constitutively. When the senders are in monoculture, quorum sensing is uniformly activated by all cells across the plate. When degraders are introduced, AHLs are degraded resulting in regions where sender cells do not activate quorum sensing. (b) Senders and degraders are mixed at a ratio of $10^{9} : n$ (units of cells), where $n$ is varied from 0 to $2 \times 10^{9}$ cells. The mixture is loaded into a small Petri dish with LB agar.
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Figure 2
Experimental demonstration of a degrader-dependent percolation transition. (a) Here we represent the 20× microscopic GFP image of the sender cells (left) in the presence of degraders at a ratio of $10^{9} : 6 \times 10^{8}$ (sender:degrader). The GFP is due to quorum sensing activation. The dark regions in the green fluorescent image are due to the senders not activating quorum sensing due to the presence of degraders; see Fig. S1 [34]. We measured the GFP pixel intensity across the blue line, represented in the fluorescent image, and observed that the fluorescence dips below the threshold value at certain points on the line (see Fig. S2 for further details on the threshold [34]). (b) The 20× fluorescent microscopy images reveal the regions of active (green) and inactive senders (dark) as we increase the amount of degraders. (c) The number of percolation events in our images was measured as a function of the amount of degraders added to the plate. Here the data are taken from three replicate plates, with each plate having a minimum of 16 images. The error bars represent the standard error over replicates.
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Figure 3
Scaling quantities from experiments. (a) The average cluster size $〈 s 〉$ , (b) the order parameter $P_{\infty}$ , (c) and the correlation length ξ calculated from experimental data. The error bars represent the standard error from three replicate plates and a minimum of 16 images per plate. In (d–f), we have the $lo g_{10} − lo g_{10}$ transform of the points in the critical region for $〈 s 〉, P_{\infty}$ , and ξ, respectively, marked as filled blue circles. The slope of the linear fits to these points yields the critical exponents. The blue lines represent the linear fit (least square fit) with the experimentally obtained exponent while the dashed brown lines represent the values from classical percolation theory, listed in Table 1. The error bars in (d–f) are determined via propagation of the $lo g_{10}$ of the uncertainty.
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Figure 4
Simulation of quorum sensing activation in the sender and degrader community. (a) The AHL concentration of the senders from simulations are marked in green, with green indicating signal concentration that exceeded the threshold needed to activate quorum sensing. (b) The frequency of percolation events from the simulations. (c) The average cluster size $〈 s 〉$ , the order parameter $P_{\infty}$ , and the correlation length ξ obtained from simulations. The red diamond data points are simulated data while the blue circular data points are experimental data points added for comparison. The error bars for the simulations represent the standard error over 100 repeats.
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Figure 5
Changing the production rate of AiiA shifts the critical density. The percolation frequency (Perc. freq.) (a) from simulations and (b), from experiments for two different production rates $(ρ_{aiiA})$ of the AiiA enzyme. For both simulations and experiments, the green cross-marked points represent the case when the degraders with lower production rate were used. In simulations, this lower value was $0.6 ρ_{aiiA}$ . The red diamond data points in simulations represent when the production rate of the degrader enzyme was the original value $(ρ_{aiiA})$ . In experiments, the blue circular data points represent when the normal degrader with production rate $ρ_{aiiA}$ was used. For the degrader with lower production rate, the IPTG level was kept at 1.0 mM such that the production rate of the degradative enzyme was decreased (see Fig. S17 [34]). In the inset we represent the universality in the nature of transition by reducing the $x$ axis to $[\log (Amount of degraders) - \log {(Amount of degraders)}_{c}] / [\log {(Amount of degraders)}_{c}]$ . The error bars for the simulations represent the standard error over 100 iterations. The error bars for the experiments represent the standard error over three sets of experiments.
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