Majority sensing in synthetic microbial consortia

As synthetic biocircuits become more complex, distributing computations within multi-strain microbial consortia becomes increasingly beneficial. However, designing distributed circuits that respond predictably to variation in consortium composition remains a challenge. Here we develop a two-strain gene circuit that senses and responds to which strain is in the majority. This involves a co-repressive system in which each strain produces a signaling molecule that signals the other strain to down-regulate production of its own, orthogonal signaling molecule. This co-repressive consortium links gene expression to ratio of the strains rather than population size. Further, we control the cross-over point for majority via external induction. We elucidate the mechanisms driving these dynamics by developing a mathematical model that captures consortia response as strain fractions and external induction are varied. These results show that simple gene circuits can be used within multicellular synthetic systems to sense and respond to the state of the population.

These methods expand upon the mathematical model presented in the main text. The majority wins circuits are shown in the main text in Figure 1. In our mathematical model of the consortium, we describe the dynamics of fluorescence, as well as the growth of the two strains within the population. We model the size of the total population using the logistic equation, where N denotes the total number of cells in the liquid culture, λ is the cell growth rate coefficient, and C denotes the carrying capacity of the container. The logistic growth model is appropriate for cells growing in a liquid culture: The population goes through a period of exponential growth, followed by a saturation phase wherein cells run out of nutrients and start dying or using secondary carbon sources. In this second phase, cell growth rate slows and tends to zero, while the cell count approaches the carrying capacity C. Cell growth dynamics in the saturation phase is complicated. We did not model saturation phase growth dynamics in detail, as we took our experimental measurements during the exponential phase.
The consortium is composed of two strains, and therefore N = N 1 +N 2 , where N 1 and N 2 are the number of yellow and blue cells, respectively. By setting r = N 1 /N (the ratio of yellow strain cell count to total cell count), we have N 1 = rN and N 2 = (1 − r)N . Here we assume that the ratio r remains constant throughout the experiment at the value we set when we mix the strains in the beginning of the experiment. We verified this assumption by counting the number of cells in the yellow and blue colonies that were taken from the liquid culture and plated on agar plates (See Supplementary Fig. 5).
We model the dynamics of the protein synthesis and degradation in cells with the following ODEs, where h(I) = 1 1 + ( I  K ) (4) Supplementary Equations (2) and (3)  The model includes protein loss due to both dilution and enzymatic degradation. The terms −βx i (i = 1, 2) model protein dilution due to cell growth. Here β is the instantaneous cell growth rate that satisfieṡ N = βN and is given explicitly by Supplementary Equation (5). The term Dixi Q+xi represents enzymatic degradation of protein x i (i = 1, 2). We obtain this term by using Michaelis-Menten dynamics for the enzymatic degradation mechanism. The parameter D i is the degradation rate coefficient for protein x i , and Q is the Michaelis-Menten constant.
The protein synthesis rate for strain 1 (the yellow strain) is given as a product of the maximal production rate, α 0 , and a regulatory function that takes into account the effects of the inhibition by the quorum sensing molecule, the inducer, and the leakiness. In particular, the effect of the inducer is modeled by a Hill function given in Supplementary Equation (4), with parameters and K. In the absence of inducer, i.e. when I = 0, we have h(I) = 1. Hence in the absence of inducer, the synthesis rate of protein x 1 is (1 + L 1 ) −1 in the absence of the quorum sensing signal, and 1 + (1−r)N x2 θ1 n1 + L 1 −1 when the quorum sensing signal is present.
We assume that the total quorum sensing signal produced by strain 2 is proportional to the overall protein concentration in strain 2, i.e. (1 − r)N x 2 , and the proportionality constant is absorbed in the parameter θ 1 . The parameters n i and θ i parametrize the Hill function that represents the effect of the quorum sensing signal on the protein synthesis rate in strain i (i = 1, 2). We assume that the inducer can overwhelm the effects of leakiness and the quorum sensing signal. Precisely, as I gets large, h(I) tends to zero, and the protein synthesis rate in strain 1 tends to its maximum, α 0 .
We model protein synthesis rate in strain 2 in an equivalent way. Since the two strains use similar promoters, we assume that the maximal production rate is the same in both strains. We opted not to model the effect of inducer on strain 2 because doing so would add no new information due to the symmetry of the system.
The parameter values we used in Supplementary Equations (1)-(5) are given in Table 1. As we were only interested in getting insight about the dynamical behavior of the consortium, we did not use a systematic fitting technique to infer parameter values from experimental data. Rather, we chose biologically feasible values that lead to dynamics that closely followed those we observed experimentally. In particular, we chose the values of λ and C in Supplementary Equation (1) in a way that the cell growth dynamics closely mimics the OD data given in Supplementary Figure 3    We developed a similar mathematical model for the minority wins pattern that is shown in Figure 5a in the main text. As in the model for the majority wins consortium, we have one equation for the cell population dynamics while other equations model protein dynamics. However, note that in the minority wins circuit the synthase and the fluorescent protein dynamics are not directly linked. Unlike the majority wins circuit, the corresponding promoters are different, and are regulated differently by the quorum sensing signal. To capture this in our model, we use separate equations for the synthase and the fluorescent proteins in each strain. Therefore, the mathematical model for the minority wins pattern has the forṁ Supplementary Equation (6) describes the cell population dynamics, as in the earlier model. Supplementary Equations (7) and (9) describe the synthase dynamics, while Supplementary Equations (8) and (10) describe the dynamics of the fluorescent protein. In particular, x 1 , x 2 , p 1 , and p 2 are cellular concentrations of rhlI, cinI, sfYFP, and sfCFP, respectively. The parameters α 1 and α 2 are the synthesis rates of the corresponding synthases and α p1 and α p2 are the synthesis rates of the fluorescent proteins. The parameters n i , θ i , i = 1, 2, are the Hill function parameters that represent the inhibition of the synthase production by quorum sensing signal and m i , Z i , i = 1, 2, are the Hill function parameters that represent the activation of the fluorescent protein production by quorum sensing signal. Note that the quorum sensing signal is proportional to the total amount of the synthase proteins in each strain. For example, the quorum sensing signal from strain 2 to strain 1 is proportional to (1 − r)N x 2 . As in the case of the majority wins circuit, we included dilution terms and enzymatic degradation terms. However, in the case of the minority wins circuit we do not model the effect of leakiness, as it had only a minor effect on the behavior of the model.
In addition, we did not incorporate the effect of inducer in the model. Such effects could be easily included.
We used the parameter values given in Table 2 for the minority wins model.
Supplementary Table 2: Parameters in the model described by Supplementary Equations (6)-(10). In both graphs, the fluorescence was ON in the blank media, but to a lesser extent than in the inducing media. This is due to slight leaky expression of the repressors in both strains. The presence of the opposite strain's QS molecule in the repressing media reduced fluorescence significantly. This is as expected for the majority wins strains The repressing media was media in which the opposite strain was previously grown in then we spun down the cells to only carry over the media and QS molecule. n=3 biological replicates shown as black dots. Results were obtained using 10% increments starting with 100% cyan strain and ending with 100% yellow strain. To compare fluorescence intensities with a maximum, they are normalized to the values measured in wells containing a single strain of the respective color (100% wells). Fluorescence intensity still correlates with strain fraction in a majority wins pattern at this larger volume. Same symbols with different colors represents the yellow and cyan intensities from the same well of the same replicate experiment. Right graph shows fluorescence intensity of the minority wins consortium in larger, 2ml volumes grown in a 24 deep well plate (n=4). 200 microliter samples were taken from the deep well plate to measure in the plate reader at the same OD as all other experiments in the main text. Results were obtained using 10% increments starting with 100% cyan strain and ending with 100% yellow strain. Data is normalized to strain fraction to account for any change in fluorescence due to the decrease in the number of cells containing the fluorescence gene. Fluorescence intensity still correlates with strain fraction in a minority wins pattern at this larger volume. Same symbols with different colors represents the yellow and cyan intensities from the same well of the same replicate experiment.

Minority wins
Supplementary Figure 5: Measuring strain ratios. To confirm that actual strain ratios were the same as the mixed strain ratios, cultures were serially diluted and plated. Cyan and yellow colonies were counted to determine strain fractions. Graphs show counted versus mixed yellow strain fractions for a subset of replicates from each of the experiments from the main text. For each graph, n=4 biological replicates with the mean shown as dots and error bars displaying standard deviation. Linear fit lines are displayed with R-squared values given. In all cases, the measured strain ratios very closely match the mixed strain ratios.  Fig. 6. For the majority wins consortium, the fluorescence patterns follows the strain ratio patterns, and for the minority wins consortium, the fluorescence pattern are opposite of the strain ratio patterns. Top to bottom represent data from Supplemental videos 3-5 (left) and Supplemental Videos 6-8 (right).