Research Papers

Myofibrils in Cardiomyocytes Tend to Assemble Along the Maximal Principle Stress Directions

[+] Author and Article Information
Hongyan Yuan

Department of Mechanical, Industrial
and Systems Engineering,
University of Rhode Island,
Kingston, RI 02881
e-mail: hongyan_yuan@uri.edu

Bahador Marzban

Department of Mechanical, Industrial
and Systems Engineering,
University of Rhode Island,
Kingston, RI 02881

Kevin Kit Parker

Disease Biophysics Group,
Wyss Institute for Biologically
Inspired Engineering,
School of Engineering and Applied Sciences,
Harvard University,
Cambridge, MA 02138
e-mail: kkparker@seas.harvard.edu

1Corresponding authors.

Manuscript received June 2, 2017; final manuscript received August 27, 2017; published online September 28, 2017. Assoc. Editor: Carlijn V. C Bouten.

J Biomech Eng 139(12), 121010 (Sep 28, 2017) (8 pages) Paper No: BIO-17-1240; doi: 10.1115/1.4037795 History: Received June 02, 2017; Revised August 27, 2017

The mechanisms underlying the spatial organization of self-assembled myofibrils in cardiac tissues remain incompletely understood. By modeling cells as elastic solids under active cytoskeletal contraction, we found a good correlation between the predicted maximal principal stress directions and the in vitro myofibril orientations in individual cardiomyocytes. This implies that actomyosin fibers tend to assemble along the maximal tensile stress (MTS) directions. By considering the dynamics of focal adhesion and myofibril formation in the model, we showed that different patterns of myofibril organizations in mature versus immature cardiomyocytes can be explained as the consequence of the different levels of force-dependent remodeling of focal adhesions. Further, we applied the mechanics model to cell pairs and showed that the myofibril organizations can be regulated by a combination of multiple factors including cell shape, cell–substrate adhesions, and cell–cell adhesions. This mechanics model can guide the rational design in cardiac tissue engineering where recapitulating in vivo myofibril organizations is crucial to the contractile function of the heart.

Copyright © 2017 by ASME
Topics: Adhesion , Fibers , Stress , Shapes
Your Session has timed out. Please sign back in to continue.


Chien, K. R. , Domian, I. J. , and Parker, K. K. , 2008, “ Cardiogenesis and the Complex Biology of Regenerative Cardiovascular Medicine,” Science, 322(5907), pp. 1494–1497. [CrossRef] [PubMed]
Pasqualini, F. S. , Sheehy, S. P. , Agarwal, A. , Aratyn-Schaus, Y. , and Parker, K. K. , 2015, “ Structural Phenotyping of Stem Cell-Derived Cardiomyocytes,” Stem Cell Rep., 4(3), pp. 340–347. [CrossRef]
Gerdes, A. M. , and Capasso, J. M. , 1995, “ Structural Remodeling and Mechanical Dysfunction of Cardiac Myocytes in Heart Failure,” J. Mol. Cell Cardiol., 27(3), pp. 849–856. [CrossRef] [PubMed]
Aratyn-Schaus, Y. , Pasqualini, F. S. , Yuan, H. , McCain, M. L. , Ye, G. J. C. , Sheehy, S. P. , Campbell, P. H. , and Parker, K. K. , 2016, “ Coupling Primary and Stem Cell-Derived Cardiomyocytes in an In Vitro Model of Cardiac Cell Therapy,” J. Cell Biol., 212(4), pp. 389–397.
Wang, G. , McCain, M. L. , Yang, L. , He, A. , Pasqualini, F. S. , Agarwal, A. , Yuan, H. , Jiang, D. , Zhang, D. , Zangi, L. , Geva, J. , Roberts, A. E. , Ma, Q. , Ding, J. , Chen, J. , Wang, D.-Z. , Li, K. , Wang, J. , Wanders, R. J. A. , Kulik, W. , Vaz, F. M. , Laflamme, M. A. , Murry, C. E. , Chien, K. R. , Kelley, R. I. , Church, G. M. , Parker, K. K. , and Pu, W. T. , 2014, “ Modeling the Mitochondrial Cardiomyopathy of Barth Syndrome With Induced Pluripotent Stem Cell and Heart-on-Chip Technologies,” Nat. Med., 20(6), pp. 616–623. [CrossRef] [PubMed]
Sheehy, S. P. , Grosberg, A. , and Parker, K. K. , 2012, “ The Contribution of Cellular Mechanotransduction to Cardiomyocyte Form and Function,” Biomech. Model. Mechanobiol., 11(8), pp. 1227–1239. [CrossRef] [PubMed]
Feinberg, A. W. , Feigel, A. , Shevkoplyas, S. S. , Sheehy, S. , Whitesides, G. M. , and Parker, K. K. , 2007, “ Muscular Thin Films for Building Actuators and Powering Devices,” Science, 317(5843), pp. 1366–1370. [CrossRef] [PubMed]
Ribeiro, A. J. S. , Ang, Y.-S. , Fu, J.-D. , Rivas, R. N. , Mohamed, T. M. A. , Higgs, G. C. , Srivastava, D. , and Pruitt, B. L. , 2015, “ Contractility of Single Cardiomyocytes Differentiated From Pluripotent Stem Cells Depends on Physiological Shape and Substrate Stiffness,” Proc. Natl. Acad. Sci. U.S A., 112(41), pp. 12705–12710. [CrossRef] [PubMed]
Parker, K. K. , Tan, J. , Chen, C. S. , and Tung, L. , 2008, “ Myofibrillar Architecture in Engineered Cardiac Myocytes,” Circ. Res., 103(4), pp. 340–342. [CrossRef] [PubMed]
Du, A. , Sanger, J. M. , and Sanger, J. W. , 2008, “ Cardiac Myofibrillogenesis Inside Intact Embryonic Hearts,” Dev. Biol., 318(2), pp. 236–246. [CrossRef] [PubMed]
Sparrow, J. C. , and Schock, F. , 2009, “ The Initial Steps of Myofibril Assembly: Integrins Pave the Way,” Nat. Rev. Mol. Cell Biol., 10(4), pp. 293–298. [CrossRef] [PubMed]
Dlugosz, A. A. , Antin, P. B. , and Nachmias, V. T. , 1984, “ The Relationship Between Stress Fiber-Like Structures and Nascent Myofibrils in Cultured Cardiac Myocytes,” J. Cell Biol., 99(6), pp. 2268–2270. [CrossRef] [PubMed]
Rhee, D. , Sanger, J. M. , and Sanger, J. W. , 1994, “ The Premyofibril: Evidence for Its Role in Myofibrillogenesis,” Cell Motil. Cytoskeleton, 28(1), pp. 1–24. [CrossRef] [PubMed]
Bray, M. A. , Sheehy, S. P. , and Parker, K. K. , 2008, “ Sarcomere Alignment Is Regulated by Myocyte Shape,” Cell Motil. Cytoskeleton, 65(8), pp. 641–651. [CrossRef] [PubMed]
Grosberg, A. , Kuo, P.-L. , Guo, C.-L. , Geisse, N. A. , Bray, M. A. , Adams, W. J. , Sheehy, S. P. , and Parker, K. K. , 2011, “ Self-Organization of Muscle Cell Structure and Function,” PLoS Comput. Biol., 7(2), p. e1001088. [CrossRef] [PubMed]
Kuo, P. L. , Lee, H. , Bray, M. A. , Geisse, N. A. , Huang, Y. T. , Adams, W. J. , Sheehy, S. P. , and Parker, K. K. , 2012, “ Myocyte Shape Regulates Lateral Registry of Sarcomeres and Contractility,” Am. J. Pathol., 181(6), pp. 2030–2037. [CrossRef] [PubMed]
Parker, K. K. , Brock, A. L. , Brangwynne, C. , Mannix, R. J. , Wang, N. , Ostuni, E. , Geisse, N. A. , Adams, J. C. , Whitesides, G. M. , and Ingber, D. E. , 2002, “ Directional Control of Lamellipodia Extension by Constraining Cell Shape and Orienting Cell Tractional Forces,” FASEB J., 16(10), pp. 1195–1204. [CrossRef] [PubMed]
Kresh, J. Y. , and Chopra, A. , 2011, “ Intercellular and Extracellular Mechanotransduction in Cardiac Myocytes,” Pflugers Arch. 462(1):75-87, pp. 75–87. [CrossRef] [PubMed]
McCain, M. L. , Yuan, H. , Pasqualini, F. S. , Campbell, P. H. , and Parker, K. K. , 2014, “ Matrix Elasticity Regulates the Optimal Cardiac Myocyte Shape for Contractility,” Am. J. Physiol. Heart Circ. Physiol., 306(11), pp. H1525–H1539. [CrossRef] [PubMed]
Pathak, A. , Deshpande, V. S. , McMeeking, R. M. , and Evans, A. G. , 2008, “ The Simulation of Stress Fibre and Focal Adhesion Development in Cells on Patterned Substrates,” J. R. Soc. Interface, 5(22), pp. 507–524. [CrossRef] [PubMed]
Deshpande, V. S. , McMeeking, R. M. , and Evans, A. G. , 2006, “ A Bio-Chemo-Mechanical Model for Cell Contractility,” Proc. Natl. Acad. Sci. U.S.A., 103(38), pp. 14015–14020. [CrossRef] [PubMed]
Pe, A. , Thery, M. , Pepin, A. , Dressaire, E. , Chen, Y. , and Bornens, M. , 2006, “ Cell Distribution of Stress Fibres in Response to the Geometry of the Adhesive Environment,” Cell Motil. Cytoskeleton, 63(6), pp. 341–355. [CrossRef] [PubMed]
Vernerey, F. J. , and Farsad, M. , 2011, “ A Constrained Mixture Approach to Mechano-Sensing and Force Generation in Contractile Cells,” J. Mech. Behav. Biomed. Mater., 4(8), pp. 1683–1699. [CrossRef] [PubMed]
Geisse, N. A. , Sheehy, S. P. , and Parker, K. K. , 2009, “ Control of Myocyte Remodeling In Vitro With Engineered Substrates,” In Vitro Cell. Dev. Biol., 45(7), pp. 343–350. [CrossRef]
Zemel, A. , Rehfeldt, F. , Brown, A. E. X. , Discher, D. E. , and Safran, S. A. , 2010, “ Optimal Matrix Rigidity for Stress-Fibre Polarization in Stem Cells,” Nat. Phys., 6(6), pp. 468–473. [CrossRef] [PubMed]
Kang, J. , Steward, R. L. , Kim, Y. T. , Schwartz, R. S. , LeDuc, P. R. , and Puskar, K. M. , 2011, “ Response of an Actin Filament Network Model Under Cyclic Stretching Through a Coarse Grained Monte Carl Approach,” J. Theor. Biol., 274(1), pp. 109–119. [CrossRef] [PubMed]
Walcott, S. , and Sun, S. X. , 2010, “ A Mechanical Model of Actin Stress Fiber Formation and Substrate Elasticity Sensing in Adherent Cells,” Proc. Natl. Acad. Sci. U.S.A., 107(17), pp. 7757–7762. [CrossRef] [PubMed]
Burridge, K. , and Wittchen, E. S. , 2013, “ The Tension Mounts: Stress Fibers as Force-Generating Mechanotransducers,” J. Cell Biol., 200(1), pp. 9–19. [CrossRef] [PubMed]
Volk, T. , Fessler, L. I. , and Fessler, J. H. , 1990, “ A Role for Integrin in the Formation of Sarcomeric Cytoarchitecture,” Cell, 63(3), pp. 525–536. [CrossRef] [PubMed]
Sadd, M. , 2014, Elasticity: Theory, Applications, and Numerics, Academic Press, Cambridge, MA.
Banerjee, S. , and Marchetti, M. C. , 2012, “ Contractile Stresses in Cohesive Cell Layers on Finite-Thickness Substrates,” Phys. Rev. Lett., 109(10), pp. 1–5. [CrossRef]
Mertz, A. F. , Che, Y. , Banerjee, S. , Goldstein, J. M. , Rosowski, K. A. , and Revilla, S. F. , 2013, “ Cadherin-Based Intercellular Adhesions Organize Epithelial Cell–Matrix Traction Forces,” Proc. Natl. Acad. Sci. U.S.A., 110(3), pp. 842–847. [CrossRef] [PubMed]
Riveline, D. , Zamir, E. , Balaban, N. Q. , Schwarz, U. S. , Ishizaki, T. , Narumiya, S. , Kam, Z. , Geiger, B. , and Bershadsky, A. D. , 2001, “ Focal Contacts as Mechanosensors: Externally Applied Local Mechanical Force Induces Growth of Focal Contacts by an mDia1-Dependent and ROCK-Independent Mechanism,” J. Cell Biol., 153(6), pp. 1175–1185. [CrossRef] [PubMed]
Sato, Y. , Nakajima, S. , Shiraga, N. , Atsumi, H. , Yoshida, S. , Koller, T. , Gerig, G. , and Kikinis, R. , 1998, “ Three-Dimensional Multi-Scale Line Filter for Segmentation and Visualization of Curvilinear Structures in Medical Images,” Med. Image Anal., 2(2), pp. 143–168. [CrossRef] [PubMed]
Schindelin, J. , Arganda-Carreras, I. , Frise, E. , Kaynig, V. , Longair, M. , Pietzsch, T. , Preibisch, S. , Rueden, C. , Saalfeld, S. , Schmid, B. , Tinevez, J.-Y. , White, D. J. , Hartenstein, V. , Eliceiri, K. , Tomancak, P. , and Cardona, A. , 2012, “ Fiji: An Open-Source Platform for Biological-Image Analysis,” Nat. Methods, 9(7), pp. 676–682. [CrossRef] [PubMed]
Nelson, C. M. , Jean, R. P. , Tan, J. L. , Liu, W. F. , Sniadecki, N. J. , Spector, A. A. , and Chen, C. S. , 2005, “ Emergent Patterns of Growth Controlled by Multicellular Form and Mechanics,” Proc. Natl. Acad. Sci. U.S.A., 102(33), pp. 11594–11599. [CrossRef] [PubMed]
McCain, M. L. , Lee, H. , Aratyn-Schaus, Y. , Kléber, A. G. , and Parker, K. K. , 2012, “ Cooperative Coupling of Cell-Matrix and Cell–Cell Adhesions in Cardiac Muscle,” Proc. Natl. Acad. Sci. U.S.A., 109(25), pp. 9881–9886. [CrossRef] [PubMed]
Dabiri, G. A. , Turnacioglu, K. K. , Sanger, J. M. , and Sanger, J. W. , 1997, “ Myofibrillogenesis Visualized in Living Embryonic Cardiomyocytes,” Proc. Natl. Acad. Sci. U.S.A., 94(17), pp. 9493–9498. [CrossRef] [PubMed]
Chopra, A. , Tabdanov, E. , Patel, H. , Janmey, P. A. , and Kresh, J. Y. , 2011, “ Cardiac Myocyte Remodeling Mediated by N-Cadherin-Dependent Mechanosensing,” Am. J. Physiol. Heart Circ. Physiol., 300(4), pp. H1252–H1266. [CrossRef] [PubMed]
Sim, J. Y. , Moeller, J. , Hart, K. C. , Ramallo, D. , Vogel, V. , Dunn, A. R. , Nelson, W. J. , and Pruitt, B. L. , 2015, “ Spatial Distribution of Cell-Cell and Cell-ECM Adhesions Regulates Force Balance While Main Taining E-Cadherin Molecular Tension in Cell Pairs,” Mol. Biol. Cell, 26(13), pp. 2456–2465. [CrossRef] [PubMed]
Fyhrie, D. P. , and Carter, D. R. , 1986, “ A Unifying Principle Relating Stress to Trabecular Bone Morphology,” J. Orthop. Res., 4(3), pp. 304–317. [CrossRef] [PubMed]
Hamant, O. , Heisler, M. G. , Jönsson, H. , Krupinski, P. , Uyttewaal, M. , Bokov, P. , Corson, F. , Sahlin, P. , Boudaoud, A. , Meyerowitz, E. M. , Couder, Y. , and Traas, J. , 2008, “ Developmental Patterning by Mechanical Signals in Arabidopsis,” Science, 322(5908), pp. 1650–1655. [CrossRef] [PubMed]
Lee, L. C. , Kassab, G. S. , and Guccione, J. M. , 2016, “ Mathematical Modeling of Cardiac Growth and Remodeling,” Wiley Interdiscip. Rev.: Syst. Biol. Med., 8(3), pp. 211–226. [CrossRef] [PubMed]
Engler, A. J. , Carag-Krieger, C. , Johnson, C. P. , Raab, M. , Tang, H.-Y. , Speicher, D. W. , Sanger, J. W. , Sanger, J. M. , and Discher, D. E. , 2008, “ Embryonic Cardiomyocytes Beat Best on a Matrix With Heart-Like Elasticity: Scar-Like Rigidity Inhibits Beating,” J. Cell Sci., 121(Pt. 22), pp. 3794–3802. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

Myofibril organization in shape-constrained cardiomyocytes (F-actin staining in (a)–(f) and α-actinin staining in (c)) (Reprinted with permission from Parker et al. [9]. Copyright 2002 by National Institutes of Health; Reprinted with permission from Bray et al. [14]. Copyright 2008 by Wiley; Reprinted with permission from Grosberg et al. [15]. Copyright 2011 by Public Library of Science; and Reprinted with permission from Geisse et al. [24]. Copyright 2009 by Springer.)

Grahic Jump Location
Fig. 2

Different myofibril organizations observed in (a) and (b) immature (stem-cell derived) versus (c) and (d) mature (neonatal) cardiomyocytes for the same cell shapes. (Reprinted with permission from Sheehy et al. [6]. Copyright 2012 by Springer.)

Grahic Jump Location
Fig. 3

Schematics of the elasticity model of the cell: (a) cell–substrate and cell–cell adhesions (side view), (b) (top view) at the stress-free boundary the MTS direction is always parallel to the edge irrespective of the overall cell shape, and (c) mechanobiochemical feedback loops between the mechanical stresses and the remodeling of FA and myofibrils

Grahic Jump Location
Fig. 4

Myofibrils tend to assemble along the maximal principal stress directions. (a) and (d) Myofibril organizations in single cardiomyocytes (Reprinted with permission from Geisse et al. [24]. Copyright 2009 by Springer and Reprinted with permission from Bray et al. [14]. Copyright 2008 by Wiley.). (b) and (e) Model predictions of stress ellipses and MTS directions. (c) and (f) Predicted traction stress distributions. Parameter values: μ = 3.8 kPa, λ = 5.8 kPa, h = 3 μm, k0 = 0.18 kPa/μm, σc0 = 1 kPa, and cell area = 2000 μm2 (these values are used in the latter simulations unless specifically mentioned). Note that the spatial patterns of MTS and traction stress are robust for a range of parameter values.

Grahic Jump Location
Fig. 5

Predicted maximal principal stress directions for irregular shapes and rectangular shapes. Myofibril images on the top row were acquired using the same protocol as in Ref. [37].

Grahic Jump Location
Fig. 6

Disparate myofibril organizations in immature and mature cardiomyocytes. The first column shows the initial condition of FA distribution. The second to fourth columns show the steady-state FA distribution, traction stress, and stress ellipse, respectively. Parameter values: Konρ = 0.07, Kfbρ = 0.08, T0 = 0.36 kPa, n = 2, ρa = 0.5, Koffρ = 0.1, kcsmax = 0.6 kPa/μm, ρ0 = 0.3, KonS = 0.03, σm = 4 kPa, KoffS = 0.03, σcf = 4 kPa, and KTρ value is listed in the figure. (These values are used in the latter simulations unless specifically mentioned.)

Grahic Jump Location
Fig. 7

Cell pairs composed of two cardiomyocytes confined in a rectangle area. First column: two mature cells without cell–cell adhesion. Second column: two mature cells with cell–cell adhesion. Third column: an immature cell (on the left) and a mature cell (on the right) with cell–cell adhesion. (a) Myofibril organization in a cell-pair with the cell–cell adhesion not formed yet. (b) Myofibril organization in a cell-pair with mature cell–cell adhesion (Reprinted with permission from McCain et al. [37]. Copyright 2012 by United States National Academy of Sciences.). (c) Myofibril organization in a cell-pair, the left cell is an immature cardiomyocyte (Reprinted with permission from Aratyn-Schaus et al. [4]. Copyright 2016 by Rockefeller University Press). Parameter values: kcc = 1 kPa/μm; in scenario III, for the cell on the left: KTρ = 0.5 and σcf = 2 kPa and for the cell on the right: KTρ = 0.8 and  σcf = 4 kPa.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In