Fig 1.
Clustering behavior of non-reversing flexible agents in simulations.
(A-D) Snapshots of the simulation region at 180 min of simulation time for different cell densities, η. (A) η = 0.08, (B) η = 0.16, (C) η = 0.24, (D) η = 0.32. Flexible agents formed aligned clusters at moderate to high cell densities (η ≥ 0.16). (E) Mean cluster sizes, 〈m〉, from simulation as a function of cell density, η. The error bars indicate the standard deviation in the data. The results are averaged over 5 independent simulation runs. The mean cluster sizes increased with increases in cell density. (F) Orientation correlation 〈cos 2Δθr〉 among cells as a function of neighbor cell distance, r. Δθr is the angle deviation between orientations (θ) of a pair of neighbor cells separated by a distance r. Orientation correlation (cos 2Δθr) values from all cell pairs are binned based on r (bin width = 1 μm) and averaged. Dashed and solid lines represent orientation correlation values at 1 min and 180 min of simulation time, respectively. Agents in clusters showed higher neighbor alignment at larger distances compared to the initial randomly oriented cells. Furthermore, the alignment increases with increases in cell density.
Fig 2.
Clustering behavior of periodically reversing agents in simulations.
(A) Snapshot of the simulation with periodically reversing agents (η = 0.24) at 180 min of simulation time. Reversing agents did not show significant clustering. (B) Mean cluster sizes, 〈m〉, in simulation as a function of cell density, η, for agents following slime trails (green line) and agents without slime trails (black line). Agents following slime trails showed a significant increase in mean cluster size compared to agents without slime-trail-following. (C) Snapshot of the simulation for periodically reversing cells with the slime-trail-following mechanism (η = 0.24, Ls = 11 μm, εs = 1.0, refer to Methods for details) at 180 min of simulation time. Agents show improved clustering compared to those without the slime-trail-following mechanism. (D) Orientation correlation 〈cos 2Δθr〉 among agents for reversing cells (black) and reversing cells with the slime-trail-following mechanism (green). Dashed and solid lines are orientation correlation values at 1 min and 180 min of simulation time, respectively. Orientation correlation with neighbors improved for larger neighbor distances with the slime-trail-following mechanism.
Fig 3.
Robustness of the slime-trail-following mechanism for cell clustering.
(A-D) Snapshots of simulations showing agent clustering behavior (η = 0.24) for variation in the slime effectiveness value and slime trail length at 180 min of simulation time. Only agents with high slime-trail-following efficiency and long slime trails show significant clustering behavior (D). Inset figures show the slime distribution in the simulation region. The mean cluster sizes in the simulations (E) as a function of the slime effectiveness factor, εs for different slime trail lengths and (F) as a function of the slime trail length, Ls, for different slime effectiveness factor values. Cell clustering improved with increases in the slime effectiveness factor (E), provided the slime trails are sufficiently long, and with increases in the slime trail length (F).
Fig 4.
Comparison of cell clustering behavior in simulations with experiments.
(A-B) Comparison of cluster size distributions (CSD) from simulations (lines) with experimental data (symbols, digitized from Starruẞ et al. [16]) for non-reversing (A) and reversing (B) cells. Probability, p(m), of finding a cell in a cluster is plotted as a function of the cluster size m. We use different sets of slime-trail-following mechanism parameters for non-reversing (Ls = 0.6 μm, εs = 0.5) and reversing (Ls = 11 μm, εs = 0.2) agents. CSD results from simulations show a similar trend to that of the experimental data. (A) Non-reversing cells show a power-law-like CSD, whereas reversing cells show a monotonically decreasing CSD (B). (C-D) Heat maps of cell visit frequencies over the simulation region for 2 consecutive hours (η = 0.24). The color bar represents the number of cell visits per hour at a particular location. Non-reversing cells show a dynamic cluster pattern with changes in cell traces (C), whereas reversing cells show a static cluster pattern with the pattern of cell traces remaining approximately the same over time (D). (E) Probability of cell visits, p(N), as a function of visit frequency, N, for non-reversing (red) and reversing cells (green) over a 1-hr simulation time (120–180 min). Reversing cells show a large fraction of sites with high visit frequencies compared to non-reversing cells.
Fig 5.
(A) Hypothetical mechanism of cell clustering through slime-trail-following in reversing M. xanthus cells. (B) Circular cell aggregates observed in simulation for non-reversing agents with the slime-trail-following mechanism (η = 0.24, Ls = 11 μm, εs = 1.0).