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The original TIFF images recorded in the experiments and used for the analysis are available at datadryad.org ( https://doi.org/10./dryad.1rn8pk0qc ). All simulation and visualization codes are written in Matlab. The codes and resulting data for each figure are available at GitHub ( https://github.com/zzyustcrice/csgA-pilC-wt-matlab ).
Result of aggregation rate after increasing the threshold for detecting aggregate in the experiment (A) and simulation (B). The results are very similar to , suggesting that our results are robust regarding the threshold selection. Download FIG S6, PDF file, 0.9 MB .
Identification of key cell behaviors that drive mutant strain aggregation. Simulation results of pilC (A and D), csgA (B and E), and WT (C and F) based on the experimental data [quantified as P(t), equation 1 ] (on y axis). Blue line and shaded areas are the simulation results under normal conditions. Black lines represent simulations without any dependence, i.e., data are randomly chosen (A to C), or simulation where run duration does not depend on time (D to F). Shaded areas show standard deviations. Download FIG S2, PDF file, 0.3 MB .
Self-organization into spatial patterns is evident in many multicellular phenomena. Even for the best-studied systems, our ability to dissect the mechanisms driving coordinated cell movement is limited. While genetic approaches can identify mutations perturbing multicellular patterns, the diverse nature of the signaling cues coupled to significant heterogeneity of individual cell behavior impedes our ability to mechanistically connect genes with phenotype. Small differences in the behaviors of mutant strains could be irrelevant or could sometimes lead to large differences in the emergent patterns. Here, we investigate rescue of multicellular aggregation in two mutant strains of Myxococcus xanthus mixed with wild-type cells. The results demonstrate how careful quantification of cell behavior coupled to data-driven modeling can identify specific motility features responsible for cell aggregation and thereby reveal important synergies and compensatory mechanisms. Notably, mutant cells do not need to precisely recreate wild-type behaviors to achieve complete aggregation.
IMPORTANCE Self-organization into spatial patterns is evident in many multicellular phenomena. Even for the best-studied systems, our ability to dissect the mechanisms driving coordinated cell movement is limited. While genetic approaches can identify mutations perturbing multicellular patterns, the diverse nature of the signaling cues coupled to significant heterogeneity of individual cell behavior impedes our ability to mechanistically connect genes with phenotype. Small differences in the behaviors of mutant strains could be irrelevant or could sometimes lead to large differences in the emergent patterns. Here, we investigate rescue of multicellular aggregation in two mutant strains of Myxococcus xanthus mixed with wild-type cells. The results demonstrate how careful quantification of cell behavior coupled to data-driven modeling can identify specific motility features responsible for cell aggregation and thereby reveal important synergies and compensatory mechanisms. Notably, mutant cells do not need to precisely recreate wild-type behaviors to achieve complete aggregation.
Single mutations frequently alter several aspects of cell behavior but rarely reveal whether a particular statistically significant change is biologically significant. To determine which behavioral changes are most important for multicellular self-organization, we devised a new methodology using Myxococcus xanthus as a model system. During development, myxobacteria coordinate their movement to aggregate into spore-filled fruiting bodies. We investigate how aggregation is restored in two mutants, csgA and pilC, that cannot aggregate unless mixed with wild-type (WT) cells. To this end, we use cell tracking to follow the movement of fluorescently labeled cells in combination with data-driven agent-based modeling. The results indicate that just like WT cells, both mutants bias their movement toward aggregates and reduce motility inside aggregates. However, several aspects of mutant behavior remain uncorrected by WT, demonstrating that perfect recreation of WT behavior is unnecessary. In fact, synergies between errant behaviors can make aggregation robust.
To identify motility behaviors affecting mutant cell aggregation, we extended our previously developed approach that combines individual cell tracking with simulations driven by the accumulated cell behavior data ( 14 ). Directly applying experimental cell data to simulations allowed us to fully investigate the effect of each change in the mutant motility behavior on their aggregation. The results demonstrate that the WT developmental field is robust enough to nearly completely restore csgA development. By comparison, the pilC mutant has two striking sensory deficits that diminish its ability to accumulate inside the fruiting bodies. By exchanging particular aspects of cell behavior between WT and mutant cells, our agent-based modeling was able to pinpoint specific differences in cell behavior that are most biologically significant.
The extent of WT rescue of two mutants is examined in this work. The first of these contains a mutation in the pilC gene. PilC is an inner membrane protein located at the base of the pilus where it interacts with PilB and PilM to mediate pilus assembly ( 16 , 17 ). This mutation interrupts pilus production ( 18 ) and consequently S-motility, one of the two motility systems in M. xanthus ( 19 , 20 ). Aggregation can occur with the help of the A-motility system, which uses a novel molecular motor and focal adhesion complexes ( 21 , 22 ). However, most S-system mutants fail to develop because they cannot produce an extracellular matrix (ECM) that is both essential for S-motility and vital for development. The ECM is required for some types of chemotaxis ( 23 , 24 ) as well as for cell cohesion, which could inhibit motility inside the aggregate ( 25 , 26 ). As shown in this work, pilC mutants cannot aggregate on their own but marginally improve when mixed with wild-type cells. The second mutation is a deletion of the csgA gene, which inhibits the production of one or more intercellular signals that are required for aggregation and sporulation ( 27 ). While CsgA signaling exerts control over most of development, the precise nature of the signals and their sensory pathways is only beginning to be revealed ( 28 ). csgA cells do not form fruiting bodies on their own ( 7 ) and respond much more completely to a WT cell developmental field than pilC ( 29 ). Although much is known about M. xanthus aggregation ( 7 , 29 , &#; 31 ), few quantitative data sets describe mutant cell movement during aggregation and the mechanism of their rescue ( 32 ).
In this work, we examined reciprocal interactions between wild-type (WT) cells mixed with nondeveloping mutants. More so than other bacteria, M. xanthus cell growth and development depend on neighboring cells, diffusing molecules, and the surrounding biotic and abiotic environment. To determine the factors that contribute to developmental robustness, we employed conditional mutants that were unable to develop on their own but will develop when mixed with WT cells. It is expected that the mutants respond to at least some of the conditions established by WT cells in the field of developing cells. The extent of the response is expected to reveal signaling and sensory transduction pathways that are essential for WT development and are defective in the mutants.
Myxococcus xanthus is a rod-shaped member of the Deltaproteobacteria with a life cycle centered around surface motility of cells in a biofilm. M. xanthus has evolved multiple social mechanisms such as S-motility ( 2 ) and C-signaling ( 3 , &#; 5 ) to achieve coordinated group behaviors such as predation ( 6 ), rippling ( 7 , &#; 9 ), and development ( 7 , 10 , 43 ). Upon amino acid limitation, M. xanthus cells move into three-dimensional aggregates called fruiting bodies where they sporulate ( 11 , &#; 13 ). Recent studies based on cell tracking have provided unprecedented detail of cell movement during development ( 14 ). In combination with mathematical modeling, these data sets unambiguously identified individual cell behaviors that are essential for aggregation ( 14 , 15 ). These behaviors include reduced movement inside the aggregate and bias in the directed movement toward the aggregation centers, likely via chemotaxis ( 15 ). This methodology provides an unprecedented window into developmental behavior that is presently difficult to realize in larger organisms with thicker tissues or longer cell migration routes, such as the vertebrate neural crest, or in disease states such as tumor metastases.
Development is one example of multiscale emergent behavior in which molecular interactions between cells allow self-organization into multicellular patterns. One of the most remarkable features of all types of development is how robust it is in the face of genetic and environmental perturbations, suggesting that backup systems are in place ( 1 ). While molecular genetics has identified mutations that impede multicellular development, even single mutations create downstream effects that influence multiple aspects of cell behavior and physiology. It is frequently difficult to ascertain which of the behavioral changes are deleterious to development and which can be tolerated. Here, we develop a new approach that leverages data-driven modeling to determine whether a statistically significant trend in cell behavior results in a biologically significant alteration of the multicellular program. We demonstrate this approach by focusing on the full or partial rescue of the mutants during the multicellular development of Myxococcus xanthus biofilms.
Fluorescence microscopy was used to quantify the behavior of mutant cells at both single-cell and population levels. A small fraction of cells expressing the fluorescent protein tdTomato were mixed with cells expressing eYFP. Each cell expressing tdTomato is bright enough to be segmented and tracked, allowing quantification of their behaviors, whereas the weaker eYFP signal was used to quantify cell density during aggregate growth (14).
When either pilC or csgA cells are mixed with differentially labeled cells of their genotype, no aggregates are observed and the distribution of cells is nearly uniform at the final time point, i.e., at T&#;=&#;5 h ( and ). Application of the 2-D Kolmogorov-Smirnov test (33) to cell positions shows that the null hypothesis of the uniform distribution of labeled cells cannot be rejected (P value&#;>&#;0.95). Conversely, when tdTomato-labeled csgA cells are mixed with eYFP-labeled wild-type (WT) cells, csgA cells are overrepresented in the aggregates ( ). The distribution of the cells is clearly nonuniform (P value < 0.05). For pilC cells mixed with WT cells, the rescue is less pronounced ( ) and there is not sufficient evidence to reject the null hypothesis of uniform distribution of labeled cells (P value&#;=&#;0.64). Below we describe a more sensitive metric to quantify aggregation rescue of mutant cells. As a comparison, Fig. S1 in the supplemental material shows the aggregation result of WT cells.
Open in a separate windowAggregation result of WT cells from reference 14. (A) Beginning frame of WT experiment. (B) Ending frame of WT experiment. Blue circles are labeled cells; red circles are aggregates. Download FIG S1, PDF file, 0.5 MB.
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Copyright © Zhang et al.To quantify aggregate positions, densities, and sizes, we filtered out the tdTomato signal and then used the eYFP intensity to estimate cell density. These data were used to segment the aggregates and detect their boundaries and positions. For segmentation of the images in which aggregation was observed (mutant strains mixed with a majority of WT cells), we determined a threshold intensity that separates aggregates from the background using K-means clustering on the light intensity of each pixel in the final frame of the experimental movies. Dividing the light intensity of pixels into two clusters gives the threshold of light intensity for aggregates. Applying the same threshold throughout the sequence of time-lapse imaging, we can compare aggregate growth for different experiments. To compare the aggregation rate across different sets of experiments, we use the average aggregate size fraction, Fagg(t), i.e., the total area of aggregates in each frame corresponding to time (t) divided by the field of view area. The results ( ) indicate that aggregation of WT mixed with pilC cells is slightly slower than WT aggregation (data set from reference 14). On the other hand, WT cells mixed with csgA show faster aggregation. However, at the final time point, data sets lead to approximately the same area covered by aggregates, Fagg(tfinal). Given that WT cells represent the overwhelming majority (>99.9%) of the cells, it is unlikely the observed differences are directly attributable to the presence of mutant cells. Instead, these differences are likely due to a slight variation of experimental conditions. Indeed, different biological repeats of the mixture experiments show differences in the aggregation dynamics ( and ). Therefore, previously used metrics to characterize aggregation such as the fraction of cells within the current area of aggregates could be overly sensitive to this variability.
Open in a separate windowTo quantify the distribution of the tracked cells relative to the aggregates in a way that is robust to the variability of aggregation rate, we decided to focus on the fraction of cells accumulated inside the final-frame boundaries of the aggregates. If the tracked cells were uniformly distributed, we would expect that fraction to be equal to the fraction of area covered by aggregates, i.e., Fagg(tfinal). Therefore, to see if labeled cells are overrepresented, we focus on
P(t)=Nin(t)Ntot&#;Fagg(tfinal)
(1)
Here, Nin is the number of tracked cells inside the final aggregate area and Ntot is the total number of tracked cells over the total field of view area. We do this calculation for each frame (at time t) and use it to quantify the aggregation rate of labeled cells.
The results for P(t) quantification for aggregation of csgA mixed with WT (red) and pilC mixed with WT (black) cells are shown in . To compare it with WT-only aggregation, we use a data set from reference 14 to compute the same quantity ( , blue line). The result shows that csgA has a similar aggregation rate to WT cells. In the final frame, cells inside aggregates are overrepresented by 50% of the total cell number, P(tfinal) ~ 0.5. In contrast, pilC cells show much weaker aggregation, P(tfinal) ~ 0.1. To test if overrepresentation of pilC mutants inside the aggregate is statistically significant, we performed a z-test. The null hypothesis is that the pilC cells are randomly distributed, and therefore the mean of P(tfinal) is 0. The P value for accepting the null hypothesis is 0.002, indicating that the pilC mutant is partially rescued by WT cells.
Open in a separate windowTo quantify single-cell behaviors, the cell trajectories were discretized into segments using the same method as in reference 14. The resulting segmented trajectories were then quantified as either persistent or nonpersistent run vectors. Persistent runs are interpreted as cells moving along their major axis using one or both motility systems whereas nonpersistent runs correspond to &#;stops&#; (or pauses) in progressive movements, during which cells can perhaps be pushed around by other cells. A run vector begins at a change of state (persistent to either nonpersistent or reversal) and ends at the next change of state. The properties of the resulting run vectors, such as duration (time between state changes) and speed (Euclidean distance over time), were used to quantify single-cell behavior during aggregation. The run vectors were also labeled with the distance to the nearest aggregate boundary and moving direction relative to the nearest aggregate center. Previous work has shown that WT cells have longer run durations when running toward an aggregate (bias effect), and cells decrease their motility inside aggregates (&#;traffic jam&#; effect) (14, 34). These effects have been shown to be important for aggregation (14, 15, 30). To quantify traffic jam and bias effects, we focus on the relationship between run vector properties and their distance and direction relative to aggregates.
To study the relationship between the run vector properties and the distance to aggregates, we divided the run vectors into 2 groups: those inside aggregates and those outside. Then we calculated the mean duration and speed for the persistent and nonpersistent state in each group ( ). We find that both WT and mutant cells mixed with WT cells display a traffic jam effect since they all have shorter persistent run durations and longer nonpersistent run durations inside aggregates ( and ). To quantify the bias in run duration, we divided the run vectors into 2 groups: those running toward aggregates and those running away. Then we define the bias ratio by
B=dto&#;dawaydall,
(2)
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where dto is the average run duration of cells going toward aggregates, daway is the average run duration of cells going away from aggregates, and dall is the average run duration of all cells. shows that each mutant mixed with WT cells has a bias ratio greater than 0, though both are less than WT.
Open in a separate windowTo compare the traffic jam effect of pilC cells mixed with WT cells, we compared the speed and state durations of pilC and WT cells. In general, pilC cells exhibit longer stop durations, more frequent stops, and slower speeds, suggesting that loss of S-motility has compromised their overall mobility. Unlike WT cells, pilC cells show less than a 5% speed reduction inside aggregates during the persistent state ( ) and show only 7% shorter persistent run durations ( ). Furthermore, pilC cells show less bias in their run duration ( ). Compared with WT and csgA, smaller differences between cell behaviors inside and outside aggregates may reduce the traffic jam effect, thereby impeding aggregation of pilC cells. On the other hand, pilC cells show a longer nonpersistent duration and a higher probability of transitioning to the nonpersistent state. However, the difference in the transitioning probability between inside and outside aggregates is smaller ( and ).
Similarly, we compared the traffic jam and bias effects of a csgA-WT mixture with WT cells. While csgA speed is &#;20% faster than WT cells inside aggregates, csgA cells show proportional speed reduction inside aggregates ( ). Similar to WT cells, csgA cells also have shorter persistent durations inside aggregates ( ), and longer nonpersistent durations ( ). Moreover, csgA cells increase their probability of transitioning to the nonpersistent state when inside the aggregates. However, the difference of this probability between inside and outside the aggregates of csgA cells is smaller than that of WT cells ( ). All of the above behaviors reduce the motility of csgA cells inside the aggregates, likely creating a WT-like traffic jam effect.
In comparison with pilC cells, csgA cells likely have a stronger traffic jam effect due to a more pronounced reduction in speed ( ) and persistent run duration ( ) inside the aggregates. On the other hand, their traffic jam effect is expected to be weaker than WT due to reduced differences in nonpersistent duration ( ) and probability between inside and outside ( ). The csgA cells also have a weaker bias than WT cells ( ). It remains to be seen why, despite a somewhat weaker bias and traffic jam effect, about the same proportion of csgA cells accumulate in the aggregate as WT cells ( ).
To more stringently test the effect of cell behaviors on aggregation, we extended the data-driven model approach used in our previous work (14) to model experiments with mixtures of two strains. To this end, we introduce a population of two agents corresponding to WT and mutant (either pilC or csgA) cells. Agent behaviors are chosen from the experimental data using K-nearest neighbor (KNN) sampling based on simulation time and the agents&#; distance and moving direction relative to the nearest aggregate. Given that the overwhelming majority of cells in the experiments are WT, we use only WT agent density to detect aggregates. This way, WT agents affect the behavior of mutant agents but not vice versa. At each time step, the WT density profile is estimated from the WT agent positions by kernel density estimation (KDE) (35), and the aggregates are then detected from the density profile. Thereafter, we pick agent behaviors and move agents accordingly. Each simulation was run for 5&#;h, after which we calculated the aggregation rate P(t) as we did for the experiment. Simulations containing csgA agents mixed with WT agents display an aggregation rate similar to that of WT agents, whereas simulations with pilC agents exhibit much weaker aggregation ( ). Comparing the results of these simulations to the experimental measurements ( ), we concluded that the model can reproduce the aggregation dynamics for WT and each mutant cell mixture with WT. In other words, dependencies (correlations) included in the sampling of agent behavior contain sufficient information to recapture observed aggregation dynamics.
As a control for the previous simulations, we performed simulations where we removed all dependencies such that agent behavior was randomly chosen from the whole data set. As expected, we did not see any aggregation for mutant mixtures or WT agents (Fig. S2A to C). This result shows that some combination of cell behavior dependence on time, distance, and direction to nearest aggregate is essential for aggregation. Since there are many cell behavior dependencies in this model, our next step is to find which dependencies are more important for aggregation.
Identification of key cell behaviors that drive mutant strain aggregation. Simulation results of pilC (A and D), csgA (B and E), and WT (C and F) based on the experimental data [quantified as P(t), equation 1] (on y axis). Blue line and shaded areas are the simulation results under normal conditions. Black lines represent simulations without any dependence, i.e., data are randomly chosen (A to C), or simulation where run duration does not depend on time (D to F). Shaded areas show standard deviations. Download FIG S2, PDF file, 0.3 MB.
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Copyright © Zhang et al.Previous work on WT aggregation has shown that cell behaviors are different at different times during development, and this time dependence of cell behaviors affects aggregation dynamics (14). To determine whether time dependence is important for mutant cell aggregation, we performed simulations where agent behavior does not depend on time. Removing time dependence for WT aggregation causes P(tfinal) to drop from &#;0.45 to &#;0.35 (Fig. S2F), which confirms our previous result (14) that time dependence helps WT aggregation. However, removing time dependence for mutant agents (while keeping it for WT agents) does not affect aggregation dynamics for either pilC (Fig. S2D) or csgA (Fig. S2E). This shows that behavior dependence on time is not important for mutant cell aggregation.
To further illuminate differences between WT, cgsA, and pilC strains, we used our simulations to quantify the fraction of cells that enter and exit aggregates as a function of time ( ). The results indicate notable differences. Comparing WT and cgsA, we can see that, although more cgsA cells reach the aggregates (red line in versus ), a larger fraction of these cells leave (green line in versus ). Therefore, we can hypothesize that reduced traffic jamming of cgsA cells is compensated by increase in motility. On the other hand, for pilC cells, the motility defects make them less likely to reach aggregates and slightly less likely to stay, leading to only weak aggregation. In what follows, we aim to test these hypotheses and relate these observations with the trends in cell behaviors quantified in .
Open in a separate windowGiven that the increase of nonpersistent state duration increases the time that cells spend inside aggregates, we hypothesized that this effect is an essential component of the traffic jam effect and aids the aggregation of mutant cells. To test this hypothesis, we performed simulations where the nonpersistent state duration for agents is not conditional on their position relative to the aggregate. Surprisingly, removing this dependence does not have an obvious effect on pilC ( ) or csgA ( ) and leads to only a modest decrease in WT aggregation [&#;0.05 or &#;10% drop in P(tfinal); ]. This result shows that longer &#;stops&#; inside aggregates are not the main reason for successful aggregation.
Open in a separate windowTo assess the effects of a higher probability of &#;stops&#; (i.e., nonpersistent runs) inside the aggregates, we performed simulations where the probability of transitioning to a nonpersistent state is independent of the agents&#; position (i.e., sampled from the same distribution inside and outside an aggregate). We discovered that removing this dependence does not affect aggregation for pilC ( ) or csgA ( ) and leads to only an &#;0.07 (&#;15%) drop in P(tfinal) for WT ( ). It appears that longer nonpersistent state durations and a higher probability of transitioning to the nonpersistent state are not the main reasons for cell accumulation in aggregates. In summary, the difference in stopping probability and duration between inside and outside the aggregates is not critical for the traffic jam effect or can be compensated by other mechanisms.
To test which persistent state behaviors are important for aggregation, we first removed the bias toward aggregates, which is the dependence of run duration on the angle between the moving cell and the closest aggregate. This leads to an &#;0.03&#;drop in P(tfinal) for pilC ( ). For csgA ( ) and WT ( ), P(tfinal) drops to the 0.15 to 0.2 range. This result shows that bias in run duration is essential, more so for csgA and WT aggregation than pilC aggregation. This also agrees with where we showed that csgA and WT cells have larger bias ratios than pilC cells. However, given the overall poor aggregation of pilC, the decrease associated with lack of bias is still important and in relative terms is just slightly weaker than that of the other strains [30% reduction of final P(tfinal) for pilC versus 40% for csgA and 45% for WT].
Open in a separate windowNext, we attempt to make the cells behave the same way inside and outside the aggregate to remove the traffic jam effect but maintain the bias. First, we removed persistent state speed and duration dependence on the agents&#; distance to the nearest aggregate while keeping the dependence of run duration on the angle between the moving cell and the closest aggregate. The results show that removing the distance dependence decreases aggregation for all types of cells: P(tfinal) drops &#;0.03 for pilC ( ) and drops &#;0.25 for csgA ( ) and WT ( ) cells. Therefore, the reduction of speed and duration inside aggregates is important for aggregation. Interestingly, the reduction of speed and duration can also be considered a traffic jam effect. Comparing the traffic jam effects in the nonpersistent state, i.e., longer duration and higher probability of nonpersistent state inside aggregates, traffic jam effects in the persistent state appear to be more important. Notably, removing persistent speed and duration dependence on distance decreases aggregation more in csgA and WT cells than in pilC cells. Even considering the poor aggregation of pilC, the relative decrease in aggregation is still weaker for pilC [30% reduction of final P(tfinal) for pilC versus 55% for csgA and 55% for WT]. This shows that csgA and WT cells have a stronger traffic jam effect than pilC, in agreement with and .
The results thus far match the observed behaviors of mutant cells with their observed aggregation dynamics. Next, we try to determine which mutant cell behaviors are responsible for the different aggregation rates compared with WT. To this end, we introduce a new &#;hybrid&#; simulation technique in which certain aspects of mutant and WT agent behaviors are swapped with one another or scaled to match the mean of another. For example, the experimental data show that pilC mutants switch to the nonpersistent state more frequently and stay in the nonpersistent state longer ( and ). To determine whether these behaviors contribute to weaker aggregation, we performed simulations where we swap some of the pilC motility behaviors with WT behaviors ( ). When agents use the pilC probability of transitioning to the nonpersistent state and WT data for other behaviors, aggregation drops [P(tfinal) drops &#;0.2] ( ). On the other hand, agents&#; use of WT probability of transitioning to the nonpersistent state with pilC data for other behaviors does not improve pilC aggregation ( ). To further confirm that the decrease in aggregation is due to longer stops or a higher stopping frequency rather than some other feature of the pilC data, we performed simulations of WT cells where we increased only the nonpersistent duration or nonpersistent probability to match the average data of pilC cells (Fig. S3). The aggregation rate is decreased compared to WT aggregation, suggesting that frequent stops are one of the major impediments to pilC aggregation.
Open in a separate windowSimulation of WT agents with longer nonpersistent duration (red) or higher nonpersistent probability (black) impedes aggregation rate (equation 1) compared to simulations with unperturbed behaviors (blue). Shaded areas show standard deviations. Download FIG S3, PDF file, 0.7 MB.
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Copyright © Zhang et al.To learn how pilC persistent behaviors affect aggregation, we performed simulations where agents use the WT persistent duration data combined with other pilC cell data and vice versa ( ). Agents using pilC persistent duration combined with other WT data have reduced aggregation compared with WT [P(tfinal) drops &#;0.25]. Agents using WT persistent duration combined with other pilC data show improved aggregation over pilC [P(tfinal) increases &#;0.02]. This is not surprising since WT cells have a much stronger persistent duration bias, and stronger bias leads to more complete aggregation. Finally, agents using pilC persistent speed combined with other WT data have reduced aggregation compared with WT [P(tfinal) drops &#;0.2] whereas WT persistent speed combined with other pilC data improves pilC aggregation [P(tfinal) increases &#;0.02] ( ). This is because pilC cells have similar speeds inside and outside aggregates whereas WT cells have slower speeds inside aggregates and this slowdown improves aggregation. Overall, our results show that weak aggregation of pilC is due to slow speed, longer nonpersistent durations, and a higher probability of transitioning to the nonpersistent state.
For csgA mutants, shows that the difference for stopping probabilities and durations inside and outside aggregates is less pronounced than WT. To test whether these behaviors decrease aggregation, we performed a simulation where agents use WT data for probability of transitioning into the nonpersistent state and csgA data for other behaviors. This simulation does not improve csgA aggregation ( ). But agents using csgA probability to transition to the nonpersistent state and WT data for other behaviors cause P(tfinal) to drop &#;0.05 compared with WT aggregation. Moreover, in , agents using csgA nonpersistent duration and WT data for other behaviors show a slight decrease in aggregation compared with WT aggregation [P(tfinal) drops &#;0.05]. On the other hand, agents using WT nonpersistent duration and csgA data for other behaviors show a slight increase in aggregation compared with csgA aggregation [P(tfinal) increases &#;0.02]. These results show that the differences in nonpersistent state switching and duration between WT and csgA do not affect aggregation much.
Open in a separate windowTo learn how csgA persistent behaviors affect aggregation, we performed a simulation where agents use persistent duration of WT cells and other behaviors of csgA cells ( ). This leads to a slightly better aggregation compared with csgA cells [P(tfinal) increases &#;0.05]. Agents using csgA persistent duration and other WT cell behavior show a slightly lower aggregation compared with WT cells [P(tfinal) drops &#;0.07]. Note that WT persistent duration has a bigger bias but shorter duration. To learn whether a shorter duration will decrease csgA aggregation, we performed a simulation where agents use csgA data but scale the persistent duration to match the average duration of WT cells. This led to a lower aggregation (Fig. S4). These results show that the csgA weaker bias is partially compensated by the longer persistent duration.
Model demonstrates that longer persistent run duration helps csgA. Scaling persistent duration of csgA agents to WT persistent duration (black line) impedes their aggregation compared to simulations using unscaled data (blue line). Shaded areas show standard deviations. Download FIG S4, PDF file, 0.5 MB.
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Copyright © Zhang et al.Finally, to find whether the faster speed of csgA cells in the persistent state helps aggregation, we performed simulations where agents use csgA persistent speed and other WT behaviors ( ). This leads to faster aggregation, but P(tfinal) remains the same compared with WT. Moreover, agents using WT persistent speed and other csgA behaviors have a slightly lower aggregation rate compared with csgA. This result shows that csgA cells&#; faster speed compensates for the weaker (compared with WT cells) bias in persistent duration and explains why csgA and WT cells show similar aggregation rates. Therefore, the rescue of collective behaviors can occur even without the complete rescue of the underlying single-cell behaviors.
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