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First published online 13 February 2007
doi: 10.1242/jcs.03395

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Sheet migration by wounded monolayers as an emergent property of single-cell dynamics

Department of Biomedical Engineering, University of Rochester, Rochester, NY 14450, USA

View larger version (21K): [in this window] [in a new window]   Fig. 1. Histograms of speed and persistence times for real and simulated cells. (A) Underlying speeds from 272 real cell trajectories. Median is 0.76 µm/minute. (B) Persistence times from same trajectories as A. Median is 12.3 minutes. (C) Underlying speeds for 407 simulated cell trajectories. Median is 0.75 µm/minute. (D) Persistence times for same simulated trajectories as C. Median is 14.0 minutes. In all histograms, large outliers (less than 0.5% of the data) are not shown to better show the bulk of the data, however these outliers were not excluded from the median calculations.

View larger version (33K): [in this window] [in a new window]   Fig. 2. Cell crowding and division. (A) Cell density saturates with time. The thick black line is the average of three growth experiments. The red and green curves are transformations of the fits performed in panel B. (B) Per capita division rate falls with crowding. The thick black line is a transformation of the experimental data in panel A. A linear fit was performed the two growth regions (spacing<60 µm, red line; and 100 µm<spacing<200 µm, green line). The red and green fits and the boundary line are transformed back into density vs. time space and shown in panel A. (C) Schematic of model cell. Cells are considered to have an incompressible core corresponding to the spacing at which cell division ceases, and compressible zone extending to the distance at which division begins to be sensitive to contact. This allows a calculation of the spacing-dependent division rate on a cell-by-cell basis. (D) Simulation per capita division rates. Several cell culture growth simulations were run with incompressible diameter 47 µm and different compressible zone thicknesses: 9 µm (red), 2 µm (blue), 0 µm (yellow), 50 µm (pink). The experimental data (black) is the same as in panel B.

View larger version (36K): [in this window] [in a new window]   Fig. 3. Real and simulated wound healing curves and rates. (A) L1 fibroblast wound healing wound edge advancement vs time is shown for three independent experiments. Each curve is labeled with its initial wound width and its average division density. (B) Parameter effects on wound healing all curves in this panel are labeled according to their deviation from the following parameters: sensing radius 4 µm, division radius 4 µm, underlying speed 0.76 µm/minute, maximal division rate 0.04 divisions/cell/hour. x/y means sensing radius x and division radius y. (C) Speed variation, simple cohesion, and 80% efficiency. Real wound underlying cell speeds are assumed to be the speeds of sparse fibroblasts in identical conditions: 0.76 µm/minute for untreated wounds (black circle) and 0.49 µm/minute for mitomycin-C-treated wounds (black square). Error bars are standard deviations. Four simulation speed variation series are plotted: 100% efficient obstacle guidance with division (solid grey line with circles), 80% efficient obstacle guidance with (dashed line with circles) and without (dashed line with squares) division, and simple cohesion between cells (dash dot with circles). The thin dashed line is the theoretical maximum wound healing rate (healing rate=underlying speed). Inset shows an example experimental wound (dashed line) compared with a 100% efficient simulation (thick black line), an 80% efficient simulation (thin black line) and a model with simple cohesion (dash dot). All inset curves include division.

View larger version (31K): [in this window] [in a new window]   Fig. 4. Factors influencing the duration of linear monolayer expansion in wound healing. (A) Duration of linear expansion varies with monolayer depth and division. All curves in this panel are derived from simulations with cells carrying 4 µm sensing and 4 µm division radii. Without division, the duration of the collective phase increases with increased monolayer depth (the distance from the wound edge to the back wall of the simulation). Monolayer depths are noted in the figure. The thin dashed curve repeats the 1200 µm simulation with cell division turned on. In this case the healing curve never becomes nonlinear. We term the transition to non-linearity `breaking'. (B) Duration of linear expansion also depends on sensing radius. Simulations employed a 600 µm monolayer without division and a 2, 4 or 9 µm sensing radius. As in panel A, the healing curves break owing to the limited capacity of the monolayer for expansion, but the duration of linear expansion increases with the increased sensing radius. Division radii are not specified for the breaking curves because division does not occur and so the value is meaningless in simulations. (C,D) Breaking occurs with division if the sensing radius is smaller than the division radius. All simulation in panels C and D include division. By either holding the sensing radius constant at 2 µm and lowering the division radius (panel C), or holding the division radius constant at 9 µm and increasing the sensing radius (panel D) we see that breaking occurs when the sensing radius is smaller than the division radius. In these cases, inhibition of division is not relieved before cells crawl out of the range over which they influence each other's movements.

View larger version (128K): [in this window] [in a new window]   Fig. 5. Direct comparison between real and simulated wounds. (A) 0 hours after wounding. (B) 8 hours. Arrows indicate dividing/recently divided cells deep in the monolayer in the simulation and the real wound. (C) 16 hours. (D) 22.5 hours. The overlaid box is to scale and the line through the box shows the initial wound edge in the simulation and the real wound for reference. The colors of the cells are primarily to help with contrast, but the newest cells are the darkest red. The full movie sequences are available as supplementary material Movie 4.