Mechanical cell-matrix feedback explains pairwise and collective endothelial cell behavior in vitro

In vitro cultures of endothelial cells are a widely used model system of the collective behavior of endothelial cells during vasculogenesis and angiogenesis. When seeded in an extracellular matrix, endothelial cells can form blood vessel-like structures, including vascular networks and sprouts. Endothelial morphogenesis depends on a large number of chemical and mechanical factors, including the compliancy of the extracellular matrix, the available growth factors, the adhesion of cells to the extracellular matrix, cell-cell signaling, etc. Although various computational models have been proposed to explain the role of each of these biochemical and biomechanical effects, the understanding of the mechanisms underlying in vitro angiogenesis is still incomplete. Most explanations focus on predicting the whole vascular network or sprout from the underlying cell behavior, and do not check if the same model also correctly captures the intermediate scale: the pairwise cell-cell interactions or single cell responses to ECM mechanics. Here we show, using a hybrid cellular Potts and finite element computational model, that a single set of biologically plausible rules describing (a) the contractile forces that endothelial cells exert on the ECM, (b) the resulting strains in the extracellular matrix, and (c) the cellular response to the strains, suffices for reproducing the behavior of individual endothelial cells and the interactions of endothelial cell pairs in compliant matrices. With the same set of rules, the model also reproduces network formation from scattered cells, and sprouting from endothelial spheroids. Combining the present mechanical model with aspects of previously proposed mechanical and chemical models may lead to a more complete understanding of in vitro angiogenesis.Comment: 25 pages, 6 figures, accepted for publication in PLoS Computational Biolog

Clinical doses of radiation reduce collagen matrix stiffness

Cells receive mechanical cues from their extracellular matrix (ECM), which direct migration, differentiation, apoptosis, and in some cases, the transition to a cancerous phenotype. As a result, there has been significant research to develop methods to tune the mechanical properties of the ECM and understand cell-ECM dynamics more deeply. Here, we show that ionizing radiation can reduce the stiffness of an ex vivo tumor and an in vitro collagen matrix. When non-irradiated cancer cells were seeded in the irradiated matrix, adhesion, spreading, and migration were reduced. These data have ramifications for both in vitro and in vivo systems. In vitro, these data suggest that irradiation may be a method that could be used to create matrices with tailored mechanical properties. In vivo, these suggest that therapeutic doses of radiation may alter tissue mechanics directly

Clinical doses of radiation reduce collagen matrix stiffness

Cells receive mechanical cues from their extracellular matrix (ECM), which direct migration, differentiation, apoptosis, and in some cases, the transition to a cancerous phenotype. As a result, there has been significant research to develop methods to tune the mechanical properties of the ECM and understand cell-ECM dynamics more deeply. Here, we show that ionizing radiation can reduce the stiffness of an ex vivo tumor and an in vitro collagen matrix. When non-irradiated cancer cells were seeded in the irradiated matrix, adhesion, spreading, and migration were reduced. These data have ramifications for both in vitro and in vivo systems. In vitro, these data suggest that irradiation may be a method that could be used to create matrices with tailored mechanical properties. In vivo, these suggest that therapeutic doses of radiation may alter tissue mechanics directly

Simulated cellular responses to static strains.

<p>Cells do not generate traction forces in this figure. (<i>A</i>) Cell length as a function of the durotaxis parameter, , on a substrate stretched along the vertical axis. (<i>B</i>) Cell orientation as a function of the stretch orientation (simulated with ). Error bars show standard deviation for . Insets show five simulations per value tested.</p

Visualization of simulated traction forces (<i>black arrows</i>) and resulting matrix strains (<i>blue line segments</i>) generated in the proposed hybrid cellular Potts and finite element simulation model.

<p>Visualization of simulated traction forces (<i>black arrows</i>) and resulting matrix strains (<i>blue line segments</i>) generated in the proposed hybrid cellular Potts and finite element simulation model.</p

Simulated individual cell responses to mechanical cell-ECM feedback.

<p>(<i>A</i>) Single cells on substrates of varying stiffness after 100 MCS. Line pieces indicate strain magnitude and orientation. (<i>B</i>) cell area () of cells; (<i>C</i>) cell length (length of major axis if the cell is seen as an ellipse) as a function of substrate stiffness (<i>D</i>) cell eccentricity (, with and the lengths of the cell's major and minor semi-axes) as a function of stiffness. Mean and standard deviation shown for in panels B-D. (<i>E</i>) Dispersion coefficients of individual, simulated cells, derived from a linear fit on the mean square displacements (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003774#pcbi.1003774.s002" target="_blank">Figure S2</a>); . Error bars indicate 95% confidence intervals of linear fits.</p

Simulated network formation assay.

<p>(<i>A</i>) Simulated collective cell behavior on substrates of varying stiffness, with a uniformly distributed initiated configuration of cells. (<i>B</i>) Time lapse showing the development of a polygonal network on a 10kPa substrate (time in MCS). Panels <i>A</i> and <i>B</i> represent a 0.75×0.75 area ( pixels) initiated with 450 cells. (<i>C</i>) Close-up of simulated network formation on a 10 kPa substrate, showing the reconnection of two sprouts. Time in MCS. (<i>D</i>) Time lapse imaging of bovine aortic endothelial cells seeded onto a 2.5 kPa polyacrylamide gel functionalized with RGD-peptide. Arrows indicate cells that join together and elongate into a network. Time scale is in hours. Scale bar is 50<i> µ</i>m.</p

Simulated cell-cell interactions on substrates of varying stiffnesses.

<p>(<i>A</i>) Visualization of cell shapes and substrate strains in absence of external strain. Line pieces indicate strain magnitude and orientation. (<i>B-D</i>) Mean square displacement of individual cells (<i>blue errorbars</i>) and cell pairs (<i>red errorbars</i>) on simulated substrates. (<i>B</i>) 4 kPa; (<i>C</i>) 12 kPa; (<i>D</i>) 32 kPa. Error bars in panels B to D indicate standard deviation for . (<i>E</i>) Number of cell-cell contacts made over 500 MCS between two simulated cells initiated at a distance of fourteen lattice sites from each other. Error bars show standard deviation over simulations (<i>F</i>) Quantification of head-to-tail alignment of cells. An obtuse angle between the two cells' long axes indicates that cells are oriented head-to-tail. Plotted is the fraction of Monte Carlo steps over MCS 20-500 that the two cells are aligned head-to-tail. Shown are means and standard deviations over 100 independent simulations on a field of 0.25×0.25 (100×100 pixels). Insets: examples of acute (left) and obtuse (right) cell configurations.</p