Primary Phenomenon in the Network Formation of Endothelial Cells: Effect of Charge
<p>(<b>a</b>) Network formation of vascular endothelial cells at 6 h after dispersion of cells. When the areal fraction of cells was sufficiently high to distribute throughout the system (above the percolation threshold [<a href="#B8-ijms-16-26149" class="html-bibr">8</a>]), the cells first shrunk and then formed networks; (<b>b</b>) As a primary phenomenon of network formation, chain-type clusters were formed before cells adhered to the substrate. When the number of these increased, the chains formed percolated networks, as shown in (<b>a</b>); (<b>c</b>) In the case of increased cell density, cells still tended to form chains, and the coarsening seems to be stopping for a while. These photos are taken by Matsunaga [<a href="#B14-ijms-16-26149" class="html-bibr">14</a>]. Both of the photos, (<b>b</b>,<b>c</b>), are taken at 10 min after cells were dispersed into the medium. All of the experiments above were conducted with the culture in the absence of VEGF (vascular endothelial growth factor). All scale bars indicate 200 μm.</p> "> Figure 2
<p>Morphogenesis of vascular endothelial cells. White spheres indicate cells, and the color shows the sum of concentration of ions ρ<sub>tot</sub>: (<b>a</b>) without salt (only the counter ions of cells are considered) and (<b>b</b>) with salt (Cα = 20 μM). This corresponds to the early stage of vascular network formation; (<b>c</b>) Expanded View of a chain composed by three cells. Cells are surrounded by ions denoted by the color field which is the same as (<b>b</b>).</p> "> Figure 3
<p>Effects of hydrodynamic interactions: (<b>a</b>–<b>c</b>) Langevin dynamics simulation (without hydrodynamic interactions); and (<b>d</b>–<b>f</b>) fluid particle dynamics simulation (including the effects of long-range hydrodynamic interactions); (<b>g</b>) Schematic showing the deceleration of chain folding. To form the spherical cluster, it is necessary to squeeze the fluid surrounding cells, which slows the dynamics of the interactions. This dynamic selection supports the chain-like nature of clusters, despite the observation that the most stable structure is the spherical cluster.</p> "> Figure 4
<p>Chain-like cluster formation. (<b>a</b>) Schematic explanation of an effective potential acting on cells. The blue and red lines show the electrostatic repulsion and integrated van der Waals attractions, respectively; (<b>b</b>) The long-range nature of repulsive Coulomb interactions stabilized the chain by preventing the clusters from folding; (<b>c</b>) Ionic clouds surrounding cells may also play an important role in making the chain-like structure rigid.</p> "> Figure 5
<p>Observation of charged colloids. Charged colloids are used as a model system, and are observed using confocal microscope. (<b>a</b>) Colloids are dispersed in the medium without salt. Colloids do not form chain-like clusters, and this phase corresponds to <a href="#ijms-16-26149-f002" class="html-fig">Figure 2</a>a; (<b>b</b>) Chain-like structure in a simple system. The colloidal dispersion, including salts, which screened the interactions of charged colloids (diameter: 2.6 μm), also exhibited the same configuration as cells, indicating that this structure formed without the assumptions of interactions and chemical reactants. Scale bars show 25 μm.</p> "> Figure 6
<p>The interparticle potential (<b>blue line</b>) and the force (<b>red line</b>) acting on cells. There exists a soft repulsive force close to the cell wall. The <b>yellow line</b> is plotted according to Equation (4), and this potential could effectively describe the medium-ranged nature of the attractive potential.</p> "> Figure 7
<p>(<b>a</b>) Brownian motion of charged cells from the calculation of the mean square displacement of cells. The Brownian motion of cells exhibited a continuous change from ballistic (below <span class="html-italic">τ</span><sub>B</sub>) to diffusive motion (above <span class="html-italic">τ</span><sub>B</sub>). The horizontal axis indicates time scaled by the Brownian time, and the vertical axis indicates the MSD scaled by the radius of cells. The red and blue solid lines represent the ballistic motion and diffusional motion, which are characterized by <math display="inline"> <semantics> <mrow> <mrow> <mo>(</mo> <mrow> <mrow> <mrow> <mn>3</mn> <msub> <mi>k</mi> <mi>B</mi> </msub> <mi>T</mi> </mrow> <mo>/</mo> <mi>m</mi> </mrow> </mrow> <mo>)</mo> </mrow> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> </semantics> </math> and 6Dt, respectively; (<b>b</b>) The concentration distribution of ions surrounding charged cells: (<b>b-1</b>) two-dimensional profile of counter ion concentration and (<b>b-2</b>) concentration profile of counter ions surrounding a cell. This shows the artificially introduced potential <math display="inline"> <semantics> <mrow> <msub> <mi>k</mi> <mi>B</mi> </msub> <mi>T</mi> <mi mathvariant="sans-serif">χ</mi> </mrow> </semantics> </math> prevents ions from penetrating into the cell; (<b>c</b>) Electrostatic potential of charged cells. Screened-coulomb or Yukawa potential allowed us to fit the profile. All of the results in this figure were obtained from three-dimensional simulations with box sizes of 128 × 128 × 128.</p> ">
Abstract
:1. Introduction
Network Formations of Endothelial Cells
2. Results and Discussion
- (1)
- Cellular Potts model
- (2)
- Continuous model
- (3)
- Lattice free particle dynamics
2.1. Results of FPD Simulation Including the Effect of Surface Charge of Cells
2.2. Effects of Hydrodynamic Interactions on the Formation of the Chain-Like Structure
2.3. Effects of Charge on the Formation of Chain-Like Structures
2.4. Other Systems for Chain Formation
3. Materials and Methods
3.1. Simulation of Charged Particles
3.2. Dynamics of a Single Cell
3.3. Distribution of Ions and Electrostatic Behavior
3.4. Langevin Dynamics Simulation
4. Conclusions
Supplementary Materials
Acknowledgments
Conflicts of Interest
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Arai, S. Primary Phenomenon in the Network Formation of Endothelial Cells: Effect of Charge. Int. J. Mol. Sci. 2015, 16, 29148-29160. https://doi.org/10.3390/ijms161226149
Arai S. Primary Phenomenon in the Network Formation of Endothelial Cells: Effect of Charge. International Journal of Molecular Sciences. 2015; 16(12):29148-29160. https://doi.org/10.3390/ijms161226149
Chicago/Turabian StyleArai, Shunto. 2015. "Primary Phenomenon in the Network Formation of Endothelial Cells: Effect of Charge" International Journal of Molecular Sciences 16, no. 12: 29148-29160. https://doi.org/10.3390/ijms161226149