Fig 1.
Overview of aggregate formation experiment.
(A) Sketch of experimental setup. (B) Image of a 100x100 mm2 subregion of the experimental plate before and after aggregate formation. (C) Zoomed in 20x20 mm2 region showing the aggregates at 22.5 h. (D) Number of aggregates on the plate versus time for the duration of the 44 hour experiment. The number of spot aggregates peaks at 22.5 hours, marked by the vertical line.
Fig 2.
Spatial structure of aggregate formation.
A-D) Spatial analysis of the aggregate pattern at 22.5 h for a subregion of the plate. (A) The aggregate area distribution is depicted, with a mean of 1.01 mm2 and standard deviation of 0.25 mm2. (B) Histogram of the nearest neighbor distance distributions of the aggregate pattern and a random point pattern for comparison. For the bacterial aggregates, a pronounced single peak shows the existence of small-scale structure in the pattern. The average is 3.33 mm, with standard deviation of 2.33 mm. The distribution of the random pattern had an average of 3.35 mm, with standard deviation of 3.00 mm and it was found to be statistically different from that of the aggregate pattern, with a two-sided Kolmogorov-Smirnov test distance 0.15 and a p-value of p = 3.69e-155. (C) Structure factor versus wavenumber. The structure factor saturates to 1 at 3 mm-1, suggesting absence of long-range order. The dotted horizontal line represents the structure factor of a random point pattern for large system size. (D) Radial pair correlation function. The pair correlation is zero for distances less than 1.7 average aggregate diameters, as no other spots are detected in that proximity. The pair correlation peaks at 3.37 mm, exhibiting short range order, and saturates to one at 7 mm, consistent with disorder at longer distances. The dotted horizontal line represents the pair correlation factor of a random point pattern for large system size.
Fig 3.
(A) Snapshots of a subregion of the plate at T = 14.5 h and T = 37.3 h. The aggregates are depicted along with the trajectory identified by the tracking algorithm. (B) Distribution of the average speed of all aggregates (n = 495). (C) Distribution of path deflection, quantified as the ratio of distance to displacement (n = 495). The path taken by the aggregates slightly deviates from a straight line. D) Log-log plot of mean square displacement versus time. The fit yields a coefficient of 1.54 indicating that the trajectories are, on average, superdiffusive. Brownian motion, corresponding to diffusion, yields a coefficient of 1.0.
Fig 4.
Single cell motility and aggregate movement.
High magnification imaging of cells in an aggregate. Aggregates were formed within a coverslip bottom chamber to enable 100X imaging of cells within the aggregate. (A) Motile cells exist in the vicinity of the aggregate and a subset consolidates with the aggregate and becomes immotile. Representative trajectories of individual cells that are motile at t = 0. Yellow lines denote cells that swim towards the spot and become immotile within 0.24 s. Green lines denote cells that remain motile for 0.24 s. (B) Immotile cells within the aggregate. Shown in blue are representative cells within the aggregate that do not change position over 10 seconds. In A and B, trajectories are labeled with respective cellular velocities in μm/sec, and the scale bar is 40 μm. (C) Aggregate movement on the microscale. Progression of the boundary of a typical aggregate over 80 mins. The yellow solid line marks the periphery of the spot in real time, whereas the cyan solid line indicates the position of the spot front at t = 0 mins. Direction of the spot movement is shown with the white arrow. (D) Distribution of aggregate front speeds. By tracking the position of an aggregate boundary over time, the front speed is calculated for n = 40 aggregates. The histogram shows the measured distribution of front speeds with an average value of 0.023 mm/hr.
Fig 5.
(A) Snapshots of a 10 mm x 9mm subregion of the plates at T = 17.5 h and T = 31.5 h. Two instances of two-aggregate merging events are highlighted in the boxed regions. The trajectories are plotted in blue for non-merging aggregates and in red for mergers of two aggregates. (B) Relative distance vs. time for all merging processes, color coded with total aggregate area. (C) The acceleration is positively correlated with the total aggregate area (spearman’s rho 0.30 and p-value 0.040). (D) Distribution of aggregate speed for two-spot mergers and non-merging spots. The average (shown with a dashed line) illustrates that aggregates that eventually merge, on average, move faster. (E) Distribution of trajectory distance divided by displacement for two-spot mergers and non-merging spots. On average, the path taken by aggregates that eventually merge is more direct.
Fig 6.
Computational Model: Spatial Structure and Merging.
A)- D) Spatial Structure of Aggregates. (A) The simulated spot area distribution has an average of 0.97mm2and a standard deviation of 0.38 mm2. (B) The simulated nearest neighbor distribution has an average of 3.30mm and a standard deviation of 2.49 mm. (C) The spatial correlation function of the simulated aggregates mirrors the saturation of the experimental structure, with saturation to 1 at 3.50 mm. (D) Snapshots before (T = 5.0 h) and after (T = 46.5 h) the merging of two segmented aggregates (see Materials and Methods for segmentation details). E)-H) Merging dynamics in the simulations. (E) Relative distance vs. time for all merging processes, color coded with total aggregate area. (F) The acceleration is not found to be correlated with aggregate size (spearman’s rho 0.01 and a p-value of 0.962). (G) Distribution of aggregate speed for two-spot mergers and non-merging spots. The average (shown by a dashed line) illustrates that mergers, on average, move faster. The speeds of the simulated aggregates are on the same order of magnitude as found in the experiments. (H) Distribution of the ratio of trajectory distance divided by displacement for two-spot mergers and non-merging spots. On average, the paths taken by spots that merge are more direct. Non-merging spots follow a less direct path as compared to the experiments.
Fig 7.
Merging at the scale of agents in the simulation.
A-C) Three frames of the same region at different times in the simulation. The two aggregates, both consisting of motile (blue) and immotile cells (red), eventually merge. (D) The number of cells in a 2 mm x 2 mm square region encompassing the initial position of the bottom aggregate from A) vs. time. The aggregate gradually loses both motile and immotile cells until the chemoattractant concentration drops below the threshold at 11.8 hours (arrow). Then, all cells regain motility and collectively move towards the proximal aggregate. (E) The number of cells in a 2 mm x 2 mm square region positioned on the initial position of the upper aggregate from (A) vs. time. The aggregate experiences fluctuations in the number of cells and eventually receives the motile cells from the proximal aggregate.