Clonal population derived from a human primary myoblast.

<p><b>A</b>: The cells were fixed and immunostained with an anti-desmin antibody. A series of 55 pictures were obtained and compiled into a single picture showing the whole population. The variation in the intensity of desmin immunostain is higher at the periphery of the growing population. The left panel shows 4 high resolution images of different parts of the population pointed by the blue arrows. <b>B</b>: Colour coded image of the same population as on the A panel. The colour code is based on the intensity of the pixels (red: low, green: high intensity). On the left are shown 2 high resolution images with the same color code. In the upper left, a region of interest is indicated in white with the corresponding pixel histogram shown beneath. Two additional histograms show the pixel intensities of two regions of interest: high-(green) and a low-desmin expressing cells (red). Note that the low desmin expressing cells are more frequent at the periphery of the culture.</p

The “extrinsic” model.

<p><b>A</b>: Simulations with the “extrinsic” model using increasing values of N_ex. Note the increasing proportion and clustering of type A (red) cells with increasing N_ex. In all simulations N_{max death} = 40 was used. <b>B</b>: Analysis of type A cell distribution as a function of average migration velocity and varying N_ex using the standardized nearest neighbour distance. Type A cells were clustered (<i>w</i><1) at all but small average velocity values at all N_ex values analysed.</p

The “hybrid extrinsic-intrinsic” model.

<p><b>A.</b> Cells migrate, divide and die under the same conditions as in the “extrinsic” and “intrinsic” models. The phenotypic switch of each cell is dependent on the local cell density as in the “extrinsic” model, but the cells encountering a favourable microenvironment undergo phenotypic change with probabilities p_AtoB and p_BtoA. B: Results of a typical simulation of the “hybrid” model during the growth phase and at equilibrium. Note the simultaneous presence of small clusters and dispersed single type A cells. p_AtoB = 0.7 and p_BtoA = 0.4. C: The distribution of the number of neighbours around the A and B cells (left and right respectively) in the hybrid model. The average number of neighbours and the standard deviation are indicated for each panel. Note the more dispersed distribution of type A cell neighbours. D: Analysis of the spatial distribution randomness of SP and MP cells using Ripley's L statistics. The upper panel shows the type A cell L-function (red line) with values larger than 0 and outside the range defined by the upper-and lower-envelope functions (black line) (this indicates significant clustering of type A cells at small R distances). The type B cells (green line) are randomly distributed, because the L(h) values are close to 0 at all scales (R).</p

Results of a typical simulations.

<p><b>A</b>: Results of a typical run at the exponential growth phase and at equilibrium (type A cells are red and type B cells are green). Left panels: “intrinsic” phenotypic switch; right panels: “extrinsic” phenotypic switch.. In all simulations N_{max death} = 40 was used. <b>B</b>: The distribution of the number of neighbours around the A and B cells (upper and lower panels, respectively) in the “extrinsic” (left) and “intrinsic” (right) models. The average number of neighbours and the standard deviation is indicated for each panel. <b>C</b>: Analysis of the spatial randomness of cell distribution at equilibrium using Ripley's L statistics. Ripley's L a point pattern with those generated by a homogeneous Poisson process. The plot shows the estimate of L(h) for various values of R ( = radius of a circle around the cell), and compares them to the line y = 0 (expected in a homogeneous Poisson process). An envelope defining the confidence interval is obtained from the maximum and minimum L(h) estimates of a large number of Monte Carlo simulations. The point set is significantly clustered in the range of scales where the estimated L(h) values are larger than 0 and lay outside the region defined by the envelope. This is the case for type A cells when considering small distances in the “extrinsic” model (red line). However, there is no significant clustering of type A cells (red line) in the “intrinsic” model and no clustering of type B cells (green line) in any of the two models, because all L(h) values are close to 0 and lay inside the region defined by the envelope (black lines).</p

The “intrinsic” model.

<p><b>A</b>: Results of the “intrinsic” model simulations for large values for p_BtoA. Note corresponding increase in proportion of type A cells (in red) and their random distribution. <b>B</b>: Analysis of type A (left panel) and type B (right panel) cell distributions in the “intrinsic” model as a function of average migration velocity using the standardized nearest neighbour distance (<i>w</i>). If <i>w</i> = 1, the cells are randomly distributed. Small standardized nearest neighbour distances (<i>w</i><1) indicate clustering; this is only observed for B cells with very low average migration velocities (<0.2). In these examples p_AtoB = 0.7 and p_BtoA = 0.02, but similar results were obtained for other values of p.</p

The basic parameters in the model.

<p><b>A</b>: Multiagent computer simulation of the “extrinsic” and “intrinsic” mechanisms. Cells migrate and divide in the same way in the two models, and cell death is a function of the local cell density. The phenotypic switch of each cell is either dependent on the local cell density in the “extrinsic” (left) or a fixed probability in the “intrinsic” (right) model.” N” is the number of neighbours in the circle with a radius “R”; “p_d” is the probability of division; p₁ and p₂ are the probabilities of the A and B type cells to change their phenotype in the “intrinsic” model; N_ex is the threshold, given by the number of neighbours. <b>B</b>: Characteristics of the cell migration in the computer model and <i>in vitro</i>, as observed in the cultures of the C2C12 cell line. The trajectories of a single cell simulated <i>in silico</i> (left) and its <i>in vitro</i> counterpart (right, determined by video microscopy), are shown. <b>C</b>: The exponential distribution of the cumulative velocity magnitudes in the simulation (left) and <i>in vitro</i>, as determined experimentally (right).</p

Localization of the SP cells in the growing population of C2C12 cells.

<p><b>A</b>: The SP cells were identified on the basis of their capacity to exclude the fluorescent dye Hoechst 33342. Four representative images (<i>a, b, c</i> and <i>d</i>) are shown from regions with different cell densities. The nuclei are shown in false color (red for SP cells and green for MP cells). <b>B</b>: The frequency distribution of the number of neighbours is significantly different for SP and MP cells (upper and lower panel). The average number of neighbours is shown on the left side of each panel. Note the bimodal distribution for SP cells. The number of neighbours for each cell in a circle of R = 15 µm was calculated on the basis of the digitalized images. The two distributions were found to be significantly different (p<0.001) as analysed by the non-parametric Wilcoxon-Rank-Sum test. <b>C</b>: Analysis of the spatial randomness of SP cell distribution using Ripley's L statistics of the four images shown in Fig. 5A. The red lines indicate the L-functions for the SP cells over a range of <i>r = </i>100. The black lines show the upper and lower limits of the envelope functions for the images analysed. The <i>c</i> and <i>d</i> patterns are significantly different from a random pattern, because the values of the observed L-function are larger than the upper envelope function while the two other L-functions (panels a and b) indicate homogeneously distributed SP cells on the corresponding images.</p