Vascular networks due to dynamically arrested crystalline ordering of elongated cells

Recent experimental and theoretical studies suggest that crystallization and glass-like solidification are useful analogies for understanding cell ordering in confluent biological tissues. It remains unexplored how cellular ordering contributes to pattern formation during morphogenesis. With a computational model we show that a system of elongated, cohering biological cells can get dynamically arrested in a network pattern. Our model provides a new explanation for the formation of cellular networks in culture systems that exclude intercellular interaction via chemotaxis or mechanical traction.Comment: 11 pages, 4 figures. Published as: Palm and Merks (2013) Physical Review E 87, 012725. The present version includes a correction in the calculation of the nematic order parameter. Erratum submitted to PRE on Jun 5th 2013. The correction does not affect the conclusion

Computational Screening of Tip and Stalk Cell Behavior Proposes a Role for Apelin Signaling in Sprout Progression

Angiogenesis involves the formation of new blood vessels by sprouting or splitting of existing blood vessels. During sprouting, a highly motile type of endothelial cell, called the tip cell, migrates from the blood vessels followed by stalk cells, an endothelial cell type that forms the body of the sprout. To get more insight into how tip cells contribute to angiogenesis, we extended an existing computational model of vascular network formation based on the cellular Potts model with tip and stalk differentiation, without making a priori assumptions about the differences between tip cells and stalk cells. To predict potential differences, we looked for parameter values that make tip cells (a) move to the sprout tip, and (b) change the morphology of the angiogenic networks. The screening predicted that if tip cells respond less effectively to an endothelial chemoattractant than stalk cells, they move to the tips of the sprouts, which impacts the morphology of the networks. A comparison of this model prediction with genes expressed differentially in tip and stalk cells revealed that the endothelial chemoattractant Apelin and its receptor APJ may match the model prediction. To test the model prediction we inhibited Apelin signaling in our model and in an \emph{in vitro} model of angiogenic sprouting, and found that in both cases inhibition of Apelin or of its receptor APJ reduces sprouting. Based on the prediction of the computational model, we propose that the differential expression of Apelin and APJ yields a "self-generated" gradient mechanisms that accelerates the extension of the sprout.Comment: 48 pages, 10 figures, 8 supplementary figures. Accepted for publication in PLoS ON

Heritable tumor cell division rate heterogeneity induces clonal dominance

<div><p>Tumors consist of a hierarchical population of cells that differ in their phenotype and genotype. This hierarchical organization of cells means that a few clones (i.e., cells and several generations of offspring) are abundant while most are rare, which is called <i>clonal dominance</i>. Such dominance also occurred in published <i>in vitro</i> iterated growth and passage experiments with tumor cells in which genetic barcodes were used for lineage tracing. A potential source for such heterogeneity is that dominant clones derive from cancer stem cells with an unlimited self-renewal capacity. Furthermore, ongoing evolution and selection within the growing population may also induce clonal dominance. To understand how clonal dominance developed in the iterated growth and passage experiments, we built a computational model that accurately simulates these experiments. The model simulations reproduced the clonal dominance that developed in <i>in vitro</i> iterated growth and passage experiments when the division rates vary between cells, due to a combination of initial variation and of ongoing mutational processes. In contrast, the experimental results can neither be reproduced with a model that considers random growth and passage, nor with a model based on cancer stem cells. Altogether, our model suggests that <i>in vitro</i> clonal dominance develops due to selection of fast-dividing clones.</p></div

Parameters of the stochastic growth and passage models.

<p>Parameters of the stochastic growth and passage models.</p

ABM simulations match the limited clonal dominance development for the monoclonal K562 cell line.

<p><b>A</b>–<b>B</b> Maximum Likelihood estimator (<i>ℓ</i>) based on clone loss (<b>A</b>) or Gini coefficient (<b>B</b>), for a range of initial division rate SDs () and mutation SDs (). <b>C</b>–<b>D</b> Clone loss (<b>C</b>) and clonal dominance (<b>D</b>) in simulations, with the parameters from the red rectangle in <b>B</b>, and in the experiments with monoclonal K562 cells. All simulation results are the mean of 10 runs and the results for the monoclonal K562 cells are the mean of 3 replicates, with the error bars representing the SD.</p

ABM simulations describing evolution of division rate variability match results for polyclonal K562 cell line.

<p><b>A</b>–<b>B</b> Maximum Likelihood estimator (<i>ℓ</i>) based on the percentage of clones lost (<b>A</b>), on the Gini coefficient (<b>B</b>), and on both metrics (<b>C</b>) for a range of initial division rate SDs () and mutation SDs (). Note that we plot −<i>ℓ</i> in these plots and thus its minimum value is sought. <b>D</b>–<b>E</b> comparison of clone loss (<b>D</b>) and clonal dominance (<b>E</b>) observed in simulations with the best fitting parameter values for the Gini coefficient (red rectangle in <b>B</b>) and in the experiments with polyclonal K562 cells. <b>F</b> Comparison of the number of major clones, i.e. clones representing more than 1% of the population, developing in simulations with the parameter set highlighted by the red rectangle in <b>B</b> and in the experiments with polyclonal K562 cells. <b>G</b> Evolution of the mean division rate with the best fitting parameter values for the Gini coefficient. All simulation results are the mean of 10 simulations and the results for the polyclonal K562 cells are the mean of 3 replicates, with the error bars or colored areas representing the SD.</p

Simulations with CSC model result in massive clone loss and no development of clonal dominance.

<p><b>A</b> Scheme illustrating the divisions and cell death in the CSC growth model. <b>B</b> Heatmap showing the difference between <i>in vitro</i> and simulated population doubling time (19 hours) depending on the maximum number of DC divisions (<i>M</i>) and DC division rates (<i>r</i>_DC) in the CSC growth model. The white cross denotes the default model settings and the black crosses depict several alternative parameter sets that result in a similar population doubling time. <b>C</b>–<b>D</b> Clone loss (<b>C</b>) and Gini coefficient (<b>D</b>) for the parameter sets highlighted in <b>B</b> and all other parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005954#pcbi.1005954.t001" target="_blank">Table 1</a>. <b>E</b>–<b>F</b> Effect of symmetric CSC division probability (<i>p₁</i>) and initial CSC percentage (CSC₀) on clone loss (<b>E</b>) and Gini coefficient (<b>F</b>), with all other parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005954#pcbi.1005954.t001" target="_blank">Table 1</a>. All values are the mean of 10 simulation replicates with the error bars depicting the SD.</p

The ABM that describes evolution of division rate variability induces clone loss and clonal dominance.

<p><b>A</b>–<b>B</b> Clone loss (<b>A</b>) and Gini coefficient (<b>B</b>) for a range of initial division rate SDs () and mutation SDs (), with all other parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005954#pcbi.1005954.t001" target="_blank">Table 1</a> and all data points representing the mean for 10 simulations.</p

Clonal dominance does not develop during passaging of cells that divide at a fixed rate.

<p><b>A</b>–<b>B</b> Clone loss (<b>A</b>) and Gini coefficient (<b>B</b>) during iterated growth and passage with either deterministic or stochastic growth and initialized either with a uniform clone size distribution or the initial distribution for polyclonal K562 cells. All values are the mean of 10 simulations and the error bars represent the SD. <b>C</b> histogram of the initial clone sizes of polyclonal K562 cells.</p

Setup and results of the <i>in vitro</i> iterated growth and passage experiment previously described by Porter <i>et al</i>. [13].

<p><b>A</b> Experimental setup. <b>B</b>–<b>E</b> Development of the clone size distribution of polyclonal K562 cells, as obtained from our own analysis of the FASTQ files published by Porter <i>et al</i>. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005954#pcbi.1005954.ref013" target="_blank">13</a>]. Shown are the percentage of clones that remain after each passage (<b>B</b>), the percentage of clones versus the percentage of the population taken up by those clones (<b>C</b>, mean ± SD and 3 biological replicates shown) and the Gini coefficient (<b>E</b>; ratio of areas X and Y in <b>D</b>). <b>F</b> Clone loss (left) and Gini coefficient (right) for the <i>in vitro</i> experiments with the monoclonal K562 cell line. <b>G</b> Clone loss (left) and Gini coefficient (right) for the <i>in vitro</i> experiments with HeLa cells. All error bars depict the SD of the 3 replicates.</p