Gaddiel Yonathan Ouaknin, Pinhas Zvi Bar-Yoseph Biophysical Journal

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Stochastic Collective Movement of Cells and Fingering Morphology: No Maverick Cells Gaddiel Yonathan Ouaknin, Pinhas Zvi Bar-Yoseph Biophysical Journal Volume 97, Issue 7, Pages 1811-1821 (October 2009) DOI: 10.1016/j.bpj.2009.05.064 Copyright © 2009 Biophysical Society Terms and Conditions

Figure 1 Sequence of images of one strip of biological cells moving forward. (First row) Cell state. (Second row) Chemical field. D = 0.005; γ = 50. The fingering morphology is well seen in both the cell state and the chemical state. (a) 0 MCS, (b) 600 MCS, (c) 900 MCS, and (d) 1800 MCS. Biophysical Journal 2009 97, 1811-1821DOI: (10.1016/j.bpj.2009.05.064) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 2 Sequence of images of one strip of biological cells moving forward. (First row) Cell state. (Second row) Chemical field. D = 0.005; γ = 10. The fingering morphology is well seen also in this case in both the cell state and the chemical state. (a) 0 MCS, (b) 600 MCS, (c) 900 MCS, and (d) 1800 MCS. Biophysical Journal 2009 97, 1811-1821DOI: (10.1016/j.bpj.2009.05.064) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 3 (a) c(x) for y = 0.35: concentration of the chemical as function of x at the front. (b) c(y) for x = 0.45: concentration of the chemical for a constant x, t = 1800 MCS. D = 0.005; γ = 10. Biophysical Journal 2009 97, 1811-1821DOI: (10.1016/j.bpj.2009.05.064) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 4 Displacement for different initial rows (left) 〈x〉 versus time: displacement parallel to the front; and (right) 〈y〉 versus time: displacement perpendicular to the front. D = 0.005; γ = 50. Biophysical Journal 2009 97, 1811-1821DOI: (10.1016/j.bpj.2009.05.064) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 5 Progression of the leaders for four independent fingers. Leaders progress mostly perpendicularly to the initial edge at a constant velocity. D = 0.005; γ = 50. Biophysical Journal 2009 97, 1811-1821DOI: (10.1016/j.bpj.2009.05.064) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 6 Fingering morphology for different D and γ. t = 1200 MCS. The diffusion coefficient and the decay rate clearly influence on the fingering morphology: the upper triangular matrix exhibits a fingering morphology, but the rest do not. Biophysical Journal 2009 97, 1811-1821DOI: (10.1016/j.bpj.2009.05.064) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 7 Stochastic front behavior: for the same biophysical parameters and the same initial conditions, the cell dynamics and the final fingering morphology are different. t = 1800 MCS; D = 0.005; decay rate = 50. Biophysical Journal 2009 97, 1811-1821DOI: (10.1016/j.bpj.2009.05.064) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 8 Correlation between two front points with distance Δx: no general pattern can be deduced as the results are stochastic. D = 0.005; decay rate = 50. Biophysical Journal 2009 97, 1811-1821DOI: (10.1016/j.bpj.2009.05.064) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 9 Front-front interaction as function of time: two fronts attract each other via chemical signals. The interaction is higher for higher diffusion coefficients and lower decay rates. Biophysical Journal 2009 97, 1811-1821DOI: (10.1016/j.bpj.2009.05.064) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 10 During wound healing, two fronts that attract each other and are correlated as fingers send chemical signals and meet. D = 0.02, decay rate = 0. (a) 0 MCS; (b) 160 MCS; (c) 320 MCS; and (d) 480 MCS. Biophysical Journal 2009 97, 1811-1821DOI: (10.1016/j.bpj.2009.05.064) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 11 Stochastic cells flow: It starts at t = 0 MCS and it advances by steps of 300 MCS. Leader cells generate fingers and compete to pull the cells of the submarginal layers. Many cells belong to a particular finger but some are pulled by more than one finger and do not know where to go, and thus simply turn around. Biophysical Journal 2009 97, 1811-1821DOI: (10.1016/j.bpj.2009.05.064) Copyright © 2009 Biophysical Society Terms and Conditions