Analysis of passing time in response to microenvironmental complexity.

<p>(A,B) Initial configurations of six normal glial cells (dotted circle) and a migratory glioma cell (double circles) when the turning angles are given as <i>θ</i> = 11.3° (A) and <i>θ</i> = 21.8° (B), respectively. Here, <i>θ</i> = angle between two vectors connecting centers of two static normal glial cells: one for cells in the first and third rows, and another for cells in the first and second rows. The distance between two cells in each row is fixed. (C) Time at which a migratory glioma cell travels given distances (x-axis) under various degrees of complexities of normal cells (<i>θ</i> = 11.3° (empty circle), 16.7° (triangle), 21.8° (square)).</p

Therapeutic strategies: inhibition of tumor infiltration using blebbistatin.

<p>(A) Time courses of blebbistatin level, concentrations of bound myosin II ([<i>m</i>_<i>b</i>]), and stiffening rate of nucleus (<i>r</i>_{[<i>m</i>_<i>b</i>]}) in response to blebbistatin injection with two different doses (<i>τ</i>_<i>B</i> = 2, <i>I</i>_<i>B</i> = 1 and <i>τ</i>_<i>B</i> = 2, <i>I</i>_<i>B</i> = 5). (B) Profile of a glioma cell in the presence of blebbistatin injection with <i>τ</i>_<i>B</i> = 2, <i>I</i>_<i>B</i> = 1 (blue solid curve) and <i>τ</i>_<i>B</i> = 2, <i>I</i>_<i>B</i> = 5 (red dotted curve). The relatively low dose of blebbistatin (<i>I</i>_<i>B</i> = 1) cannot sufficiently decrease the bound myosin II level and hence the stiffening rate of the nucleus is lowered, resulting in invasion of the glioma cell through the narrow gap. When the injection strength is increased (<i>I</i>_<i>B</i> = 5), the glioma cell cannot infiltrate the narrow intercellular space between two normal cells.</p

The role of myosin II in glioma invasion: A mathematical model

<div><p>Gliomas are malignant tumors that are commonly observed in primary brain cancer. Glioma cells migrate through a dense network of normal cells in microenvironment and spread long distances within brain. In this paper we present a two-dimensional multiscale model in which a glioma cell is surrounded by normal cells and its migration is controlled by cell-mechanical components in the microenvironment via the regulation of myosin II in response to chemoattractants. Our simulation results show that the myosin II plays a key role in the deformation of the cell nucleus as the glioma cell passes through the narrow intercellular space smaller than its nuclear diameter. We also demonstrate that the coordination of biochemical and mechanical components within the cell enables a glioma cell to take the mode of amoeboid migration. This study sheds lights on the understanding of glioma infiltration through the narrow intercellular spaces and may provide a potential approach for the development of anti-invasion strategies via the injection of chemoattractants for localization.</p></div

Experiments and simulation results using a mathematical model.

<p>(A-C) Experimental results of a GFP-expressing rat glioma cell. Time courses of the profiles of a moving glioma cell in (A) show the deformation of the cell body during cell translocation. Micrographs taken at 3-min intervals (<i>t</i> = 0, 3, 6, 9, 12, 15, 18, 21 <i>min</i>). Red arrowhead = a focal point between the cell body and the swelling in the leading edge. Micrographs of a section stained for GFP (green; moving glioma cell) and DAPI (blue; resident brain cells) show GFP-expressing glioma cells at distinct two phases of the migration in (B,C). While the nucleus (white arrow) is separated from a prominent dilatation at the front (yellow arrowhead) in the first step (<i>B</i> − <i>B</i>′′), a focal deformation of the nucleus (red arrow) and cell body is observed in the next step (<i>C</i> − <i>C</i>′′). Bars, 10<i>μm</i>. Reprinted from Beadle C, Assanah M, Monzo P, Vallee R, Rosenfield S, et al. (2008) The role of myosin II in glioma invasion of the brain. Mol Biol Cell 19: 3357-3368 [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0171312#pone.0171312.ref011" target="_blank">11</a>] under a CC BY license, with permission from American Society for Cell Biology, original copyright 2008. (D) Time courses of cell morphology as a glioma cell migrates through a narrow gap between two glial cells in the brain. Bars, 10<i>μm</i>. Profiles of a glioma cell with deforming nucleus (dark green) at <i>t</i> = 0, 3, 6, 9, 12, 15, 18, 21 <i>min</i> are shown in the presence of two normal cells (gray region with dotted line cell boundaries).</p

Optimal anti-invasion strategies of blebbistatin injection.

<p>Passing time of the glioma cell through the intercellular space between two glial cells for various dose schedules (<i>τ</i>_<i>B</i> = 1, 2, 3, 4, 5 <i>hours</i>) and injection strength (<i>I</i>_<i>B</i> = 1, 5, 10, 20, 30). *Blue = non-invasive glioma cell, red = the glioma cell in the process of infiltration through the gap, yellow = complete infiltration of the cell.</p

Patterns of glioma infiltration in different intra- and extra-cellular microenvironment.

<p>(A) Different patterns of two migratory glioma cells at final time t = 60 <i>min</i> for various distances between two astrocytes (<i>d</i> = 3, 4, 5, 6 <i>μm</i>) and different nuclear stiffness (fold) of a glioma cell located in the center. The default parameter value of the elastic stiffness of nucleus is . (B,C) A migration profile and stiffening rate (<i>r</i>_{[<i>m</i>_<i>b</i>]}) of two migratory glioma cells at time <i>t</i> = 0, 20, 40, 60 mins when <i>d</i> = 4<i>μm</i> and nuclear stiffness is a fold-change of 1 for the migratory glioma cell in the center. The default parameter value was used for the glioma cell on the left.</p

Patterns of glioma infiltration under perturbation of actin-myosin reactions and different microenvironment.

<p>(A) Different patterns of two migratory glioma cells at final time t = 60 <i>min</i> for various distances between two astrocytes (<i>d</i> = 3, 4, 5, 6 <i>μm</i>) and acto-myosin association rates (<i>k</i>₁ = 0.0004, 0.001, 0.002, 0.004, 0.01 <i>μM</i>⁻¹ <i>s</i>⁻¹). (B) Distribution of the bound myosin II level ([<i>m</i>_<i>b</i>]) of the glioma cell for different <i>k</i>₁ and various distances <i>d</i> = 3, 4, 5, 6 <i>μm</i> simulated in (A). Each color indicates the change in concentration of the bound myosin II for 20 minutes.</p

Dynamics of elongation and retraction of a infiltrating glioma cell in a narrow intercellular gap (IS) between normal glial cells.

<p>(A) Cell deformation and velocity field (red arrows) near a moving glioma cell (double blue solid curves) and normal glial cells (dashed circles) during the elongation steps at <i>t</i> = 21, 81 <i>min</i> and retraction steps at <i>t</i> = 23, 83 <i>min</i>. (B) Spatial distribution of pressure along the cell membrane at <i>t</i> = 30, 60, 90, 120 <i>min</i> as it pushes through a narrow gap.</p

Experimental observation on cell infiltration in glioma models.

<p>(Left) Invasive Human glioma xenografts. Tumor has spread across the corpus callosum (CC) to the contralateral white matter located between straiatum (Str) and cortex (CX). Green = staining for human nuclear antigen to illustrate the location of human tumor cells in the rat background. White arrow = the location of the site of tumor inoculation. Reprinted from Beadle C, Assanah M, Monzo P, Vallee R, Rosenfield S, et al. (2008) The role of myosin II in glioma invasion of the brain. Mol Biol Cell 19: 3357-3368 [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0171312#pone.0171312.ref011" target="_blank">11</a>] under a CC BY license, with permission from American Society for Cell Biology, original copyright 2008. (See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0171312#pone.0171312.s001" target="_blank">S1 File</a>) (Right) A schematic representation of diffuse infiltration of glioma cells. Arrowhead = blood vessels, asterisk = active tumor growth, arrow = tumor cells migrating along white matter tracks.</p

Therapeutic strategies (Localization of the glioma cells).

<p>(A-C) Effect of the different strength of the chemotactic source on migration patterns of a glioma cell (wild type; blue curves) at the final time <i>t</i> = 392 <i>min</i>: = 0.14 (A), 0.82 (B), 1.64 (C). Red star (*) = a chemotactic source, red circles = the initial configuration of a glioma cell. (D-F) Profiles of the chemoattractant at the final time for the corresponding three cases in (A-C). (G) Anti-invasion treatment efficacy for those three cases in (A-C).</p