Review Article

Review on Cell Mechanics: Experimental and Modeling Approaches

[+] Author and Article Information
Marita L. Rodriguez

Deptartment of Mechanical Engineering,
University of Washington,
Seattle, WA 98195
e-mail: maritar@uw.edu

Patrick J. McGarry

Deptartment of Mechanical
and Biomedical Engineering,
National University of Ireland,
Galway, Ireland
e-mail: patrick.mcgarry@nuigalway.ie

Nathan J. Sniadecki

Adjunct in Bioengineering,
Deptartment of Mechanical Engineering,
University of Washington,
Seattle, WA 98195
e-mail: nsniadec@uw.edu

Manuscript received December 21, 2012; final manuscript received September 3, 2013; published online October 15, 2013. Assoc. Editor: Francois Barthelat.

Appl. Mech. Rev 65(6), 060801 (Oct 15, 2013) (41 pages) Paper No: AMR-12-1063; doi: 10.1115/1.4025355 History: Received December 21, 2012; Revised September 03, 2013

The interplay between the mechanical properties of cells and the forces that they produce internally or that are externally applied to them play an important role in maintaining the normal function of cells. These forces also have a significant effect on the progression of mechanically related diseases. To study the mechanics of cells, a wide variety of tools have been adapted from the physical sciences. These tools have helped to elucidate the mechanical properties of cells, the nature of cellular forces, and mechanoresponses that cells have to external forces, i.e., mechanotransduction. Information gained from these studies has been utilized in computational models that address cell mechanics as a collection of biomechanical and biochemical processes. These models have been advantageous in explaining experimental observations by providing a framework of underlying cellular mechanisms. They have also enabled predictive, in silico studies, which would otherwise be difficult or impossible to perform with current experimental approaches. In this review, we discuss these novel, experimental approaches and accompanying computational models. We also outline future directions to advance the field of cell mechanics. In particular, we devote our attention to the use of microposts for experiments with cells and a bio-chemical-mechanical model for capturing their unique mechanobiological properties.

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Byfield, F. J., Reen, R. K., Shentu, T. P., Levitan, I., and Gooch, K. J., 2009, “Endothelial Actin and Cell Stiffness is Modulated by Substrate Stiffness in 2D and 3D,” J. Biomech., 42(8), pp. 1114–1119. [CrossRef] [PubMed]
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Ronan, W., Deshpande, V. S., McMeeking, R. M., and McGarry, J. P., 2013, “Cellular Contractility and Substrate Elasticity: A Numerical Investigation of the Actin Cytoskeleton and Cell Adhesion,” Biomech. Model. Mechanbiol., (in press).
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Lennon, A. B., 2011, Cellular and Biomolecular Mechanics and Mechanobiology, Springer, Heidelberg, Germany, pp. 297–329.


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Fig. 1

Major structural components of a cell. The cytoskeleton is composed of actin (parallel filaments), intermediate filaments (wavy filaments), and microtubules (thick filaments). The mechanics of a cell is also defined by its membrane (cell border), nucleus (oval), and cytoplasm (region between membrane and nucleus).

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Fig. 2

Three major protein filaments make up the cell cytoskeleton: microtubules (top), intermediate filaments (center), and actin filaments (bottom).

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Fig. 3

Stress fibers are the force-generating structures in a cell. Shown are F-actin (helical filaments), myosin (branched filaments), and α-actinin (ovals).

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Fig. 4

Mechanotransduction pathways and force-sensing structures at cell–cell and cell–ECM junctions

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Fig. 5

Force-application techniques described in Sec. 3.1

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Fig. 6

Force-sensing techniques described in the Sec. 3.2

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Fig. 7

Micropost array fabrication steps. (Reprinted from Ref. [394] with permission from Elsevier.)

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Fig. 8

Steps performed for micropost array functionalization. (Reprinted from Ref. [418] with permission from Elsevier.)

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Fig. 9

Force as a function of spread area for mouse embryo fibroblasts (MEF); human umbilical vein endothelial cells (HUVEC); human mammary epithelial cells (MCF10a); and bovine aortic smooth muscle cells (SMC) [422].

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Fig. 10

(a) Fluorescent images and traction forces for control (Ctrl), TNFα-treated (TNF), and monocyte transmigrating (TEM) monolayers of human pulmonary artery endothelial cells (HPAECs). Structures stained are: β-catenin (cell border), monocytes (light patch), nuclei (ovals), and microposts (dots). Scale bars indicate 10 μm; the white arrow bar indicates a vector traction force of 32 nN. (b) Bar graph indicating average tractions for these monolayers; where *p < 0.05 indicates comparison between TEM and Ctrl, and # p < 0.05 indicates comparison between TEM and TNF. (Reprinted from [427], with kind permission from Springer Science and Business Media.)

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Fig. 11

Contractile velocity (A) and power (B) of cardiomyocytes from newborn Fischer 344 rats on substrates of different stiffnesses: 3 kPa (diamonds), 8 kPa (squares), 10 kPa (triangles), and 15 kPa (circles). (Reprinted from [428], with permission from Elsevier.)

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Fig. 12

Top: Tugging forces (arrows) exerted by human pulmonary artery endothelial cells (HPAECs); where adherens junctions are fluorescently stained with anti-α-catenin (cell-cell boundary). Bottom: Relationship between tugging force and junction size, as well as traction force and junction size. (Reprinted from [432], with permission from the National Academy of Sciences.)

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Fig. 13

(c) Traction force vector map of a representative NIH 3T3 cell, with the cell perimeter shown in red. (d) Immunofluorescence images of fibronectin (white). Scale bar represents 20 mm. (Reprinted from Ref. [433] with permission from Elsevier.)

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Fig. 14

(a) Average traction force vector for monolayer of by Madin–Darby canine kidney epithelial cells on a micropillar array. Scale bar = 20 μm (b) Average reaction force vector for each individual cell [435]. (Reproduced by permission of IOP Publishing.)

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Fig. 15

Traction forces exerted by a human platelet aggregate [436]

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Fig. 16

Measuring the contraction of cardiac microtissues with the μTUG system. (Reprinted from Ref. [437] with permission from the National Academy of Sciences.)

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Fig. 17

Average traction force of (a) MDCK and (b) fibroblasts as a function of substrate stiffness [444]. (Reproduced by permission of The Royal Society of Chemistry.)

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Fig. 18

Brightfield micrographs and corresponding traction force maps for micropatterned single human mesenchymal stem cells (hMSCs) exposed to (top) osteogenic differentiation medium (OM) or (bottom) adipogenic differentiation medium (AM). Scale bars, 50 μm. (Reprinted by permission from Macmillan Publishers Ltd: Nature Methods [446].)

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Fig. 19

(A) Immunofluorescent staining of cell A, force-stimulated with a magnetic post, and cell B, unstimulated control. Stained structures are: actin (cell cytoskeleton), nuclei (ovals), and PDMS (dots). (B) Plot of displacement and force versus time for all posts for cell A. Onset of force stimulation is indicated by dashed line (t = 0). (Reprinted from [450], National Academy of Sciences, U.S.A.)

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Fig. 20

Top row: vector maps of traction forces measured from microposts for static (left), laminar (center), and disturbed (right) monolayers. Bottom row: β-catenin staining for monolayers on flat substrates exposed to static (A), laminar (B), or disturbed flow (C). Scale bar 20 μm [452].

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Fig. 21

Comparison between experimental (dots) and computational (line) results for the micropipette aspiration of neutrophils. Top: data for an aspiration pressure of 1 kPa, and Bottom: data for an aspiration pressure of 2 kPa. The viscosities in panels on the left were determined using a slope-matching technique, while those in the panels on the right were determined using a best fit between the computed and experimental data [461].

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Fig. 22

Recovery curves for whole cell and nucleus aspiration length versus recovery time for lymphocytes. Solid and dashed lines represent computed recovery lengths for the cell and nucleus, respectively. Open circles and asterisks correspond to the experimental data for the cell and nucleus, respectively. (Reprinted from Ref. [464], with permission from Springer Science and Business Media.)

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Fig. 23

Comparison between the shear thinning model and experimental results for a neutrophil entering a 4 μm diameter pipette. Where dark circles indicate the experimental results, dashes indicate the model results, and small dots indicate model results when the cell is given an initial cell projection length. (Reprinted from Ref. [466] with permission from Elsevier.)

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Fig. 24

Comparison of leukocyte displacements during micropipette aspiration to series (dashed) and FEA (solid) solutions of the Maxwell liquid drop model [469]

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Fig. 25

Comparison between experimental and computational results for bovine articular chondrocytes subject to creep indentation [106]

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Fig. 26

Strain distribution in four confocal image-derived models of osteocytes (a)–(d) and idealized osteocytes without ECM projections (e), and with ECM projections included (f) under global loading of 3000 με. (Figure adapted from Ref. [478] with permission from The Royal Society.)

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Fig. 27

G′ and G″ versus f in HASM cells under control conditions (black square); and after 10 min treatment with the contractile agonist histamine (white diamond), the relaxing agonist DBcAMP (black diamond) and the actin-disrupting drug cytochalasin D (white square). (Figure reprinted with permission from Ref. [468] by the American Physical Society.)

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Fig. 28

Comparison between equilibrium (a) and creep (b) responses of osteoarthritic and nonosteoarthritic chondrons subject to aspiration pressure ΔP, to the biphasic model. (Reprinted from Ref. [487] with permission from Elsevier.)

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Fig. 29

Comparison between model predictions of elastic (G′) and frictional (G″) moduli dependence on frequency (ω) for a heterogeneous tensegrity structure and experimental results from human airway smooth muscle cells. Circles represent experimental data replotted from Fabry et al. [481]; lines indicate data generated by the tensegrity model. (Reprinted from Ref. [507] with permission from Springer Science and Business Media.)

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Fig. 30

The shear modulus G' of actin networks as a function of concentration; based upon the semiflexible chain model. (Figure reprinted with permission from Ref. [521] by the American Physical Society.)

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Fig. 31

Modulation of cell spreading area with matrix rigidity. The main panel shows a quantitative fit of the dipole polymerization model to experimentally measured values for human mesenchymal stem cells [524]. (Reproduced by permission of IOP Publishing).

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Fig. 32

Speed of the polymerization ratchet v driven by a single actin filament as a function of dimensionless load force ω. The solid line represents the ratchet speed when depolymerization is negligible, while the dashed line is valid when polymerization is much slower than diffusion. (Reprinted from Ref. [526] with permission from Elsevier.)

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Fig. 33

Comparison between the model prediction [529] and the experimental data [528] for normalized ratchet speed V versus load force F. (Figure reprinted with permission from Ref. [529] by the American Physical Society.)

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Fig. 34

Predicted (solid lines) and experimentally reported [536] (symbols) response to equibiaxial stretch (10% strain at 1 Hz - triangles) and uniaxial stretch (10% strain at 1 Hz - circles; 10% strain at 0.5 Hz - squares). (Reprinted from [535] with permission from Elsevier.)

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Fig. 35

W (θ), the distribution of angles versus angle (in radians) of cells controlled by stress (a) and strain (b). The dashed curves are for Ts = 0.001 (scaled temperature) and scaled frequencies ω = 10, 0.5, 0.001 (uppermost right, lower right, and left, respectively). The solid curves are for Ts = 0.1 with ω = 10, 0.5 (upper right and lower right, respectively); for the solid curves, we show 5 W (θ) for clarity. The distributions are normalized to unity in the physical interval from θ = 0 to θ = π/2. (Figure reprinted with permission from Ref. [538] by the American Physical Society.)

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Fig. 36

Steady-state contractile force as a function of support stiffness predicted with the constrained mixture model. The steady-state morphology and corresponding stress fiber distributions are shown for select values of substrate stiffness. For comparison, experimental results from Ghibaudo et al. [444] are also reported. (Reprinted from Ref. [539] with permission from Elsevier.)

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Fig. 37

Experimental (left) and computationally predicted (right) concentrations of stress fiber assembly for a square cell attached to posts at its corners [455]

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Fig. 38

Comparison experimental and simulated stress fiber alignment in response to applied uniaxial strain of varying magnitudes [546]

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Fig. 39

Spatial mapping of simulated one-dimensional cellular traction forces for a migrating cell [551]

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Fig. 40

Comparison of experimental (rows 1 and 2) and simulated (rows 3 and 4) stress fiber and focal adhesion assembly for cells of various shapes. (Figure adapted from Ref. [553] with permission from The Royal Society.)

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Fig. 41

Relationship between the contractility model, signaling model, and focal adhesion model within the bio-chemo-mechanical modeling framework [555]

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Fig. 42

Role of contractility on the compression resistance of cells. (a) Relationship between cell contractility and compression resistance; (c) aligned axial stress fibers in 3D polarized cell. (Reprinted from Ref. [558] with permission from Elsevier.)

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Fig. 43

Prediction of active modeling framework for the shear resistance of untreated contractile cells, capturing a distinctive yield behavior. In contrast, the linear response predicted by passive hyperelastic material modeling is appropriate only for cells in which the actin cytoskeleton has been removed. (Reprinted from Ref. [562] with permission from Elsevier.)

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Fig. 44

Stress distribution in cartilage tissue due to physiological loading and chondrocyte contractility. (Reprinted from Ref. [562] with permission from Elsevier.)



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