Broadcasting of amplitude- and frequency-modulated c-di-GMP signals facilitates cooperative surface commitment in bacterial lineages

Abstract

Work on surface sensing in bacterial biofilms has focused on how cells transduce sensory input into cyclic diguanylate (c-di-GMP) signaling, low and high levels of which generally correlate with high-motility planktonic cells and low-motility biofilm cells, respectively. Using Granger causal inference methods, however, we find that single-cell c-di-GMP increases are not sufficient to imply surface commitment. Tracking entire lineages of cells from the progenitor cell onward reveals that c-di-GMP levels can exhibit increases but also undergo oscillations that can propagate across 10 to 20 generations, thereby encoding more complex instructions for community behavior. Principal component and factor analysis of lineage c-di-GMP data shows that surface commitment behavior correlates with three statistically independent composite features, which roughly correspond to mean c-di-GMP levels, c-di-GMP oscillation period, and surface motility. Surface commitment in young biofilms does not correlate to c-di-GMP increases alone but also to the emergence of high-frequency and small-amplitude modulation of elevated c-di-GMP signal along a lineage of cells. Using this framework, we dissect how increasing or decreasing signal transduction from wild-type levels, by varying the interaction strength between PilO, a component of a principal surface sensing appendage system, and SadC, a key hub diguanylate cyclase that synthesizes c-di-GMP, impacts frequency and amplitude modulation of c-di-GMP signals and cooperative surface commitment.

Keywords: Pseudomonas aeruginosa; bacteria biofilms; cyclic-di-GMP; motility; surface sensing.

Fig. 1.

Cells can persist or detach with either high or low c-di-GMP levels. Events where (A) a cell detaches (note the white arrow and circle) with low c-di-GMP and (B) a cell persists with high c-di-GMP are common. However, the other cases where (C) a cell detaches with high c-di-GMP and (D) a cell persists with low c-di-GMP are not rare. All four combinations are readily observable in the dataset. (E) Quantification of the last observed c-di-GMP levels at the time of the “detach” or “persist” event. In these violin plots, the points represent individual data points, the circles represent the median, and the lines represent the IQR (25th to 75th percentiles). Bootstrap sampling of the medians of the two distributions shows that they are statistically significantly different (P < 1e-3). However, the difference between the medians (0.15) is smaller than the IQR (0.58 for “persist” and 0.51 for “detach”), suggesting that this difference is difficult to observe due to having an effect size that is not large. For “detach” events, it is very common for cells to detach after dividing but before the fluorescence imaging interval of 15 min, so in these cases the last known c-di-GMP level of the mother cell is used.

Fig. 2.

By tracking c-di-GMP levels for longer periods of time in lineages we find that c-di-GMP levels have oscillatory behavior over several division generations. (A–F) Shown are six different lineages tracked over the indicated time. Gray lines in the bottom left corner of the plots denote the mean division time in a lineage (∼1 h). Black points and lines denote the lineage trace data for c-di-GMP, where each point represents one time point and multiple cells in a lineage present at a single time point are averaged together. This time-series data are then fit, via two different methods, to a sine function $C\left(t\right)=A_0+A_1\sin \left(\frac{2\pi t}{T}-T_0\right)$, where $A_0$ is the mean, $A_1$ is the amplitude, $T$ is the period, and $T_0$ is the phase of the sine function. The blue lines represent the first fit method, where the fit is performed to find all the coefficients $\left[A_0, A_1, T, T_0\right]$. The red lines represent the second fit method, where certain coefficients are substituted with values calculated from the time-series data before performing the fit: $A_0$ is substituted with the mean of the time-series data; $A_1$ is substituted with a multiple of the variance of the time series data (so $A_1=A*\mathit{var}$); and $T$ is substituted with the period of the time-series data, which is calculated as follows. The power spectral density (via Lomb–Scargle periodogram) estimate is calculated from the time series, which provides weights to each frequency (or 1/period), which is then used to calculate a weighted average period. After substituting the previously described values, the fit is then performed to find the coefficients $\left[A, T_0\right]$. Both fit methods provide similar results but have different degrees of freedom. Each plot in A–F is a different strain, summarized along with the fit coefficients in SI Appendix, Table S1. For each plot, the scale is set such that the oscillatory shape of the curve is easily visible. The same plots using a unified scale is shown in SI Appendix, Fig. S3.

Fig. 3.

Factor analysis (FA) reveals three orthogonal dimensions of data: c-di-GMP mean, c-di-GMP period, and surface motility. Each dimension contributes independently to surface commitment and is named by the variable that has the largest factor loading in that dimension. Tree symmetry is one quantitative indicator of surface commitment (e.g., a larger tree symmetry value corresponds to a larger portion of a lineage committing to the surface), so the factor loading of tree symmetry (red bars) in each dimension can indicate how that dimension contributes to surface commitment. Analysis is applied to lineage data in A–C as well as individual branch data in D–F. (A and D) This dimension corresponds to c-di-GMP mean (and c-di-GMP amplitude) and explains ∼31 to 32% of the variance in the data for both lineages and branches. Tree symmetry has a positive factor loading in this dimension for both lineages and branches, which suggests that this dimension has a positive correlation with surface commitment (i.e., larger c-di-GMP mean correlates with higher surface commitment). (B and E) This dimension corresponds to c-di-GMP period and explains ∼18 to 23% of the variance in the data for both lineages and branches. At the lineage level, tree symmetry has a negative factor loading, which suggests that this dimension has a negative correlation with surface commitment (i.e., shorter c-di-GMP period correlates with higher surface commitment). However, at the branch level, tree symmetry has a negative factor loading with a smaller magnitude, which suggests that there is reduced correlation with surface commitment. (C and F) This dimension corresponds to surface motility (MSD slope and radius of gyration) and explains ∼16% and ∼21% of the variance in the data for lineages and branches, respectively. At the lineage level, tree symmetry has a negative factor loading, which suggests that this dimension has a negative correlation with surface commitment (i.e., lower surface motility correlates with higher surface commitment). However, at the branch level, tree symmetry has a factor loading close to zero, which suggests that there is little correlation with surface commitment.

Fig. 4.

Lineages that persist tend to have a larger c-di-GMP mean, less surface motility, and a shorter c-di-GMP period compared with lineages that detach. Lineage end fate is where a lineage either persists or detaches, while branch end fate is where an individual branch either persists or detaches. These end fates are also indicators of surface commitment, as they directly relate to whether a cell or lineage will commit to the surface or not. Each data point in A–C corresponds to one lineage, while each data point in D–I corresponds to one branch in the lineage. Differences in persisting vs. detaching for each dimension are greatest when using lineage data and reduced when using branch data, suggesting that surface commitment depends more on the long-term, collective behavior of the lineage rather than on the behavior of individual members.

Fig. 5.

PilO–SadC interaction strength is optimized for surface commitment. High interaction strength mutants (HI) are PilO(VxxxL) and SadC(T83A), low interaction strength mutant (LO) is SadC(L172Q), and WT is the baseline strain for comparison. (A and D) Compared with WT, HI mutants have smaller c-di-GMP mean, while LO mutants have larger c-di-GMP mean. In this dimension, having increased interaction strength correlates with higher surface commitment, and vice versa. (B and E) Compared with WT, all mutants have longer c-di-GMP periods. In this dimension, having a modified interaction strength in any direction correlates with lower surface commitment. (C and F) Compared with WT, HI mutants have less surface motility, while LO mutants have more surface motility. In this dimension, having increased interaction strength correlates with higher surface commitment, and vice versa. Here, lineages and branches have slightly different trends, with branches having a more apparent correlation. Taken together, these results show that WT has the highest tendency to be surface committed across all dimensions, and either interaction strength mutant is correlated with lower surface commitment in at least one dimension.

Fig. 6.

(A–F) SadC null mutants show unexpected c-di-GMP trends. The single-null mutant $\text{Δ}\mathit{sadC}$ (NM1) has counterintuitive results of elevated c-di-GMP levels, large oscillation amplitudes, long oscillation periods, and high surface motility. This mutant behaves very similarly to the LO mutant. The double-null mutant $\text{Δ}\mathit{roeA} \text{Δ}\mathit{sadC}$ (NM2) has the expected behavior of a null mutant lacking DGCs, with low c-di-GMP levels, small oscillation amplitudes, short oscillation periods, and low surface motility. WT data are repeated from Fig. 5 for easier comparisons.