Cell migration along the planar surface of fibronectin.

<p>A) Simulated trajectories of cell migrations on fibronectin coated substrates under five different ligand surface densities of 19.4, 192, 568, 1140 and 1522 molecules/µm². The black lines indicate trajectories of nuclei for the first three hours, B) comparison of average cell migration speeds: the simulation model vs. experiment data by Palecek <i>et al.</i> <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002926#pcbi.1002926-Palecek1" target="_blank">[17]</a>. Average speed and standard error of mean (N = 5) are shown for the five different ligand surface densities, and C). linear regression (R² = 0.767) of simulated migration speed vs. experimental migration speed.</p

Contour plots of traction (or FA) force on ventral cell surfaces.

<p>Spreading cells on three fibronectin coated micropatterns of A) disk, B) pacman and C) crossbow shapes. Plots also reveal distributions of oriented ventral SFs and SFs connected to the nucleus (red lines). <b>N</b> indicates a nucleus and scale bar is 10 µm. D) Temporal variations of total traction stress per a cell on three different micropatterns, and E) time-averaged total traction stress of the cell for one hour is high in the order of the crossbow, pacman and disk shapes.</p

Improved DFT Potential Energy Surfaces via Improved Densities

Density-corrected DFT is a method that cures several failures of self-consistent semilocal DFT calculations by using a more accurate density instead. A novel procedure employs the Hartree–Fock density to bonds that are more severely stretched than ever before. This substantially increases the range of accurate potential energy surfaces obtainable from semilocal DFT for many heteronuclear molecules. We show that this works for both neutral and charged molecules. We explain why and explore more difficult cases, for example, CH⁺, where density-corrected DFT results are even better than sophisticated methods like CCSD. We give a simple criterion for when DC-DFT should be more accurate than self-consistent DFT that can be applied for most cases

Optimal condition of cell migration.

<p>A) Trajectories and morphologies of simulated cell migrations along the planar surface of fibronectin surface density of 1140 molecules/µm2 for three hours under nine different cases of polymerization times with 60, 180, and 300 s (rows) and depolymerization times with 1, 10, and 30 s (columns), and B) bar graphs showing time-averaged cell migration speeds and error bars indicate standard deviations for nine different cases in A). Scale bar is 10 µm.</p

Dynamic model of cell migration.

<p>A) Integrated cell migration model consisting of the cytoskeleton, the nucleus, <i>N</i> integrin nodes on the surface of cytoskeleton, <i>N</i> nuclear nodes on the surface of nucleus, and two types of actin SFs which connect the integrin node to the nuclear node and between integrin nodes; a top view of the model showing triangular mesh network of double membranes of cytoskeleton and nucleus. B) the free body diagram of the i-th integrin node in the circle marked in A) where five external forces are acting. Note that, while shown in 2-D, the force balance exists in 3-D.</p

Ligand surface density (Fibronectin).

<p>Ligand surface density (Fibronectin).</p

List of simulation parameters.

<p>List of simulation parameters.</p

Experimental observations of filopodia state changes during penetration.

<p><b>A</b>) 3-D confocal images showing filopodia protrusive, tugging, and contractile motions in GFP-transfected HUVECs, and remodeling of collagen fiber network at time points of 0, 2, 4, 6, 8 and 10 minutes. <b>B</b>) 3D collapsed images showing the crawling behavior of filopodial tip at time points 0, 2, 4, 6, 8 and 10 minutes. Blue sphere indicates a monitored location on the ECM, which was shown to be mechanically linked to the filopodial tip. Yellow arrows indicate directions of displacements of the blue sphere and the filopodial tip. Red arrows and red dots indicate filopodial tips and roots, respectively. <b>C</b>) Graph showing temporal variations of speeds at the tip of filopodium (Filo A in <b>A</b>) and blue sphere in <b>B</b>). <b>D</b>) Graphs showing filopodial length changes in Filo A and B over time. Graphs in <b>E)</b> and <b>F)</b> showing temporal variations in speedsn at both tip and root of the two filopodia: Filo A in <b>E</b>) and Filo B <b>F</b>). Note that plus and minus signs represent forward and backward movements of filopodium, respectively, and blue arrows in <b>E</b>) indicate fast oscillatory ‘load-and-fail’ traction dynamics during the retractile phase. <i>T</i>, <i>C</i>, and <i>R</i> in <b>E</b>) and <b>F</b>) indicate tugging, contractile, and retractile phases, respectively.</p

List of simulation parameters.

<p>List of simulation parameters.</p

Filopodial tugging phase during the simulation.

<p><b>A</b>) One instant during the simulation of a filopodium interacting with an ECM fiber network model; blue dotted lines represent fibers and spheres represents two kinds of ECM nodes (fiber node and crosslink node); colours of spheres indicate magnitudes of stress at ECM nodes; yellow arrows indicate directions of FC movements. <b>B)</b>, <b>C)</b>, and <b>D)</b> indicate timeframe shots of filopodial tugging phase showing movements of two FCs (tiny blue bars; ‘a’ in <b>B</b>) at the <i>k</i>-th filopodial tip along two different fibers (thick red lines) and substantial pulling ECM fibers towards the filopodial tip at t+190, t+200 and t+210 seconds, respectively. Note, <b>B)</b>, <b>C)</b>, and <b>D)</b> are magnified views in the circle marked in <b>A)</b>, and scale bars indicate 500 nm.</p