3D rendering of an oblate ellipsoidal tumor.

<p>The 3D rendering, created using images taken with a light sheet fluorescence microscope, is rotated about the vertical axis in this sequence of images. Blue: Hoechst-stained nuclei; Red: E-cadherin. Scale bar is 90 µm.</p

Elastic free energy landscapes of the tumor-gel system.

<p>The landscapes are plotted <i>versus</i> the tumor's ellipsoidal axes ratios and . The origin has been shifted, so that the maximum energy is zero in each case: (<b>a</b>) For . The oblate shapes ( =  = 3) are the low energy states. This surface has been generated from 576 separate nonlinear elasticity computations of tumors of aspect ratios and varying between 1 and 3, growing in a gel. (<b>b</b>) The same as (a), but for . Note the flatness of the landscape relative to (<b>a</b>). Spherical shapes are not penalized strongly for , but are strongly penalized for .</p

Elastic Free Energy Drives the Shape of Prevascular Solid Tumors

<div><p>It is well established that the mechanical environment influences cell functions in health and disease. Here, we address how the mechanical environment influences tumor growth, in particular, the shape of solid tumors. In an <i>in vitro</i> tumor model, which isolates mechanical interactions between cancer tumor cells and a hydrogel, we find that tumors grow as ellipsoids, resembling the same, oft-reported observation of <i>in vivo</i> tumors. Specifically, an oblate ellipsoidal tumor shape robustly occurs when the tumors grow in hydrogels that are stiffer than the tumors, but when they grow in more compliant hydrogels they remain closer to spherical in shape. Using large scale, nonlinear elasticity computations we show that the oblate ellipsoidal shape minimizes the elastic free energy of the tumor-hydrogel system. Having eliminated a number of other candidate explanations, we hypothesize that minimization of the elastic free energy is the reason for predominance of the experimentally observed ellipsoidal shape. This result may hold significance for explaining the shape progression of early solid tumors <i>in vivo</i> and is an important step in understanding the processes underlying solid tumor growth.</p></div

Cyclic Tensile Strain Controls Cell Shape and Directs Actin Stress Fiber Formation and Focal Adhesion Alignment in Spreading Cells

<div><p>The actin cytoskeleton plays a crucial role for the spreading of cells, but is also a key element for the structural integrity and internal tension in cells. In fact, adhesive cells and their actin stress fiber–adhesion system show a remarkable reorganization and adaptation when subjected to external mechanical forces. Less is known about how mechanical forces alter the spreading of cells and the development of the actin–cell-matrix adhesion apparatus. We investigated these processes in fibroblasts, exposed to uniaxial cyclic tensile strain (CTS) and demonstrate that initial cell spreading is stretch-independent while it is directed by the mechanical signals in a later phase. The total temporal spreading characteristic was not changed and cell protrusions are initially formed uniformly around the cells. Analyzing the actin network, we observed that during the first phase the cells developed a circumferential arc-like actin network, not affected by the CTS. In the following orientation phase the cells elongated perpendicular to the stretch direction. This occurred simultaneously with the <i>de novo</i> formation of perpendicular mainly ventral actin stress fibers and concurrent realignment of cell-matrix adhesions during their maturation. The stretch-induced perpendicular cell elongation is microtubule-independent but myosin II-dependent. In summary, a CTS-induced cell orientation of spreading cells correlates temporary with the development of the acto-myosin system as well as contact to the underlying substrate by cell-matrix adhesions.</p></div

Overview of cell spreading and orientation under cyclic stretch conditions.

<p>Spreading of fibroblasts upon CTS application occurs in two phases. In the first phase (“Spreading”) the initial cell attachment is generated. Then a circular lamellipodia and dot-like cell-matrix adhesion sites are visible. The cell reaches its critical adhesive area. In the beginning of the second phase (“Polarization/Orientation”) the cell adhesive area reaches its maximum and cell elongation is initiated. The cell develops with increasing time of stretching pronounced actin stress fibers and cell-matrix adhesions which become with time perpendicularly oriented with respect to the stretch axis. In the spreading phase the formation of actin bundles in parallel to the stretch axis is observed while cell-matrix adhesions emerged homogenously distributed along the cell edges independently of the stretch direction. Cell-matrix adhesions sites reoriented into a perpendicular alignment and the parallel actin fibers realign into a perpendicular orientation and partially disassemble as the stretching force continues to act on the cell.</p

The initial cell spreading phase is stretch-independent while minimum stretching forces are necessary for cell orientation in the later phase of cell spreading.

<p>(<b>A</b>) NIH3T3 fibroblasts were freshly seeded on fibronectin-coated membranes and cyclically stretched in uniaxial direction (double-headed arrow) with an amplitude of 8% at a frequency of 3 Hz. Cell spreading was monitored via time-lapse phase contrast microscopy. The cell contour of one exemplary cell is outlined in black. (Scale bar: 10 µm) (<b>B</b>) Kinetics of the mean cell adhesive area of initially non-adherent NIH3T3 fibroblasts at indicated stretch frequencies (control = non-stretched static condition). Time t = 0 indicates the time point at which cells were seeded onto the substrate. The data set can be divided into two groups depending on the applied frequencies (group I: low frequencies; group II: high frequencies) (ANOVA; group I compared to control: ^‡p>0.05; group II compared to control: *p<0.05). (<b>C</b>) The mean cell orientation at indicated stretch frequencies over time. A mean value of 1 for the orientation parameter indicates a perfectly-parallel, −1 a perfectly-perpendicular mean cell orientation with respect to the stretch axis. (ANOVA; group I compared to control: ^‡p>0.05; group II compared to control: *p<0.05) (<b>D</b>) Cell elongation over time at indicated conditions. A value of 1 would describe a perfectly round cell, a value of 0 would be a perfect thin line. (ANOVA; group I and II compared to control: ^‡p>0.05) (control, n = 89 cells; 0.1 Hz, n = 110 cells; 0.05 Hz, n = 80 cells; 1 Hz, n = 120 cells; 3 Hz, n = 117 cells; each from four independent experiments).</p

The stress field created by tumor growth when

<p><b>.</b> The growth volume ratio . All normal stress components, (——), are equal in a spherical tumor of initial radius 50 µm. The maximum compressive stress is −1300 Pa. However, in an ellipsoidal tumor with axes µm, the () component, has a maximum compressive stress of −1200 Pa, and the () component has a maximum compressive stress of −1180 Pa.</p

Oblate ellipsoidal tumors have a similar distribution of orientations regardless of viewing direction.

<p><b>a</b>. The relationship between tumor rotation angle, , and projected aspect ratio, , as an oblate ellipsoid with maximum aspect ratio of 3 (  =  3) is rotated about its () axis. <b>b</b>. The tumor rotation angle was calculated from the projected aspect ratio (part <b>a</b>) for tumors grown in 1% agarose for 30 days. Top image: observation perpendicular to the plane of the cell-culture well, Bottom image: side view perpendicular to a physical cross-section of the gel made with a scalpel blade (out-of-focus cut marks are visible in the gel) Scale bars are 200 µm.</p

Amplitude of steady state force oscillation in a homogeneously activated stress fiber as a function of the cyclic stretching frequency.

<p>Note the saturation of force variation beyond the intrinsic clock frequency . Similar behavior would occur in a locally activated stress fiber with the lower intrinsic clock frequency where is the total number of sarcomere units in the stress fiber.</p

A sarcomere unit of SF with passive viscosity anchored on a substrate under high frequency cyclic stretch.

<p>At low cyclic frequencies, the distributed anchoring points are released so that the sarcomere unit should be replaced by the entire SF anchored on two FAs.</p