# A thermodynamically motivated model for stress-fiber reorganization

- 681 Downloads
- 10 Citations

## Abstract

We present a model for stress-fiber reorganization and the associated contractility that includes both the kinetics of stress-fiber formation and dissociation as well as the kinetics of stress-fiber remodeling. These kinetics are motivated by considering the enthalpies of the actin/myosin functional units that constitute the stress fibers. The stress, strain and strain rate dependence of the stress-fiber dynamics are natural outcomes of the approach. The model is presented in a general 3D framework and includes the transport of the unbound stress-fiber proteins. Predictions of the model for a range of cyclic loadings are illustrated to rationalize hitherto apparently contrasting observations. These observations include: (1) For strain amplitudes around 10 % and cyclic frequencies of about 1 Hz, stress fibers align perpendicular to the straining direction in cells subjected to cyclic straining on a 2D substrate while the stress fibers align parallel with the straining direction in cells constrained in a 3D tissue. (2) At lower applied cyclic frequencies, stress fibers in cells on 2D substrates display no sensitivity to symmetric applied strain versus time waveforms but realign in response to applied loadings with a fast lengthening rate and slow shortening. (3) At very low applied cyclic frequencies (on the order of mHz) with symmetric strain versus time waveforms, cells on 2D substrates orient perpendicular to the direction of cyclic straining above a critical strain amplitude.

## Keywords

Mechano-sensitivity Actin/myosin contractility Stress fibers Cytoskeleton## Notes

### Acknowledgments

A.V. and V.S.D. acknowledge the Royal Society for supporting A.V. through a Newton International Fellowship. Insightful discussions with Prof. R. M. McMeeking (UCSB) are gratefully acknowledged.

## References

- Aref A, Horvath R, Ramsden JJ (2010) Spreading kinetics for quantifying cell state during stem cell differentiation. J Biol Phys Chem 10:145–151CrossRefGoogle Scholar
- Buck RC (1980) Reorientation response of cells to repeated stretch and recoil of the substratum. Exp Cell Res 127(2):470–474MathSciNetCrossRefGoogle Scholar
- Burridge K, Chrzanowska-Wodnicka M (1996) Focal adhesions, contractility and signaling. Annu Rev Cell Dev Biol 12:463–469CrossRefGoogle Scholar
- Byers HR, Fujiwara K (1982) Stress fibers in cells in situ: immunofluorescence visualization with antiactin, antimyosin and anti-alpha-actinin. J Cell Biol 93:804–811CrossRefGoogle Scholar
- Chen CS, Alonso JL, Ostuni E, Whitesides GM, Ingber DE (2003) Cell shape provides global control of focal adhesion assembly. Biochem Biophys Res Commun 307:355–361CrossRefGoogle Scholar
- De Bruyn PPH, Cho Y (1974) Contractile structures in endothelial cells of splenic sinusoids. J Ultrastruct Res 49:24–33CrossRefGoogle Scholar
- Deshpande VS, McMeeking RM, Evans AG (2006) A bio-chemo-mechanical model for cell contractility. Proc Natl Acad Sci USA 103:14015–14020CrossRefGoogle Scholar
- Discher DE, Janmey P, Wang YL (2005) Tissue cells feel and respond to the stiffness of their substrate. Science 310:1139–1143CrossRefGoogle Scholar
- Eisenberg E, Hill TL, Yi-Der Chen (1980) Cross-bridge model for muscle contraction. Biophys J 29:195–227CrossRefGoogle Scholar
- Evans E, Ritchie K (1997) Dynamic strength of molecular adhesion bonds. Biophys J 72:1541–1555CrossRefGoogle Scholar
- Faust U, Hampe N, Rubner W, Kirchgessner N, Safran S, Hoffmann B, Merkel R (2011) Cyclic stress at mHz frequencies aligns fibroblasts in direction of zero strain. PLoS One 6(12):e28963CrossRefGoogle Scholar
- Foolen J, Deshpande VS, Kanters FMW, Baaijens FPT (2012) The influence of matrix integrity on stress-fiber remodeling in 3D. Biomaterials 33:7508–7518CrossRefGoogle Scholar
- Gauvin R, Parenteau-Bareil R, Larouche D, Marcoux H, Bisson F, Bonnet A, Auger FA, Bolduc S, Germain L (2011) Dynamic mechanical stimulations induce anisotropy and improve the tensile properties of engineered tissues produced without exogenous scaffolding. Acta Biomater 7(9):3294–3301CrossRefGoogle Scholar
- Gordon SR, Essner E, Rothstein H (1982) In situ demonstration of actin in normal and injured ocular tissues using 7-nitrobenz-2-oxa-1,3-diazole phallacidin. Cell Motil Cytoskelet 4:343–354CrossRefGoogle Scholar
- Guterl KA, Haggart CR, Janssen PM, Holmes JW (2007) Isometric contraction induces rapid myocyte remodeling in rat right ventricular papillary muscles. Am J Heart Circ Physiol 293:H3706–H3712CrossRefGoogle Scholar
- Hill AV (1938) The heat of shortening and the dynamic constants of muscle. Proc R Soc B 126:136–195CrossRefGoogle Scholar
- Howard J (2001) Mechanics of motor proteins and the cytoskeleton. Sinauer Associated Inc., SunderlandGoogle Scholar
- Hunter P (1995) Myocardial constitutive laws for continuum mechanics models of the heart. In: Sideman S, Beyar R (eds) Molecular and subcellular cardiology. Springer, New York, pp 303–318CrossRefGoogle Scholar
- Jungbauer S, Gao H, Spatz JP, Kemkemer R (2008) Two characteristic regimes in frequency-dependent dynamic reorientation of fibroblasts on cyclically stretched substrates. Biophys J 95(7):3470–3478CrossRefGoogle Scholar
- Kaunas R, Nguyen P, Usami S, Chien S (2005) Cooperative effects of Rho and mechanical stretch on stress-fiber organization. Proc Natl Acad Sci USA 102(44):15895–15900CrossRefGoogle Scholar
- Kolega J (1986) Effects of mechanical tension on protrusive activity and microfilament and intermediate filament organization in an epidermal epithelium moving in culture. J Cell Biol 102:1400–1411CrossRefGoogle Scholar
- Langanger G, Moeremans M, Daneels G, Sobieszek A, De Brabander M, De Mey J (1986) The molecular organisation of myosin in stress-fiber of cultured cells. J Cell Biol 102:200–209CrossRefGoogle Scholar
- Lucas SM, Ruff RL, Binder MD (1995) Specific tension measurements in single soleus and medial gastrocnemius muscle fibers of the cat. Exp Neurol 95:142–154CrossRefGoogle Scholar
- McGarry JP, Fu J, Yang MT, Chen CS, McMeeking RM, Evans AG, Deshpande VS (2009) Simulation of the contractile response of cells on an array of micro-posts. Philos Trans R Soc A 367(1902):3477–3497MathSciNetCrossRefzbMATHGoogle Scholar
- McGrath JL, Tardy Y, Dewey CF, Meister JJ, Hartwig JH (1998) Simultaneous measurements of actin filament turnover, filament fraction and monomer diffusion in endothelial cells. Biophys J 75:2070–2078CrossRefGoogle Scholar
- McMahon TA (1984) Muscles, reflexes and locomotion. Princeton University Press, PrincetonGoogle Scholar
- Mochitate K, Pawelek P, Grinnell F (1991) Stress relaxation of contracted collagen gels: disruption of actin filament bundles, release of cell surface fibronectin, and down-regulation of DNA and protein synthesis. Exp Cell Res 193:198–207CrossRefGoogle Scholar
- Neidlinger-Wilke C, Grood ES, Wang JH-C, Brand RA, Claes L (2001) Cell alignment is induced by cyclic changes in cell length: studies of cells grown in cyclically stretched substrates. J Orthop Res 19(2):286–293CrossRefGoogle Scholar
- Nieponice A, Maul TM, Cumer JM, Soletti L, Vorp DA (2007) Mechanical stimulation induces morphological and phenotypic changes in bone marrow-derived progenitor cells within a three-dimensional fibrin matrix. J Biomed Mater Res A 81(3):523–530CrossRefGoogle Scholar
- Obbink-Huizer C, Oomens CWJ, Loerakker S, Foolen J, Bouten CVC, Baaijens FPT (2014) Computational model predicts cell orientation in response to a range of mechanical stimuli. Biomech Model Mechanobiol 13:227–236CrossRefGoogle Scholar
- Parker KK, Brock AL, Brangwynne C, Mannix RJ, Wang N, Ostuni E, Geisse NA, Adams JC, Whitesides GM, Ingber DE (2002) Directional control of lamellipodia extension by constraining cell shape and orienting cell tractional forces. FASEB J 16:1195–1204Google Scholar
- Pathak A, McMeeking RM, Evans AG, Deshpande VS (2011) An analysis of the co-operative mechano-sensitive feedback between intracellular signaling, focal adhesion developed and stress-fiber contractility. ASME J Appl Mech 78:041001-1Google Scholar
- Ronan W, Deshpande VS, McMeeking RM, McGarry JP (2012) Numerical investigation of the active role of the actin cytoskeleton in the compression resistance of cells. J Mech Behav Biomed Mater 14:143–157CrossRefGoogle Scholar
- Tan JL, Tien J, Pirone DM, Gray DS, Bhadriraju K, Chen CS (2003) Cells lying on a bed of microneedles: an approach to isolate mechanical force. Proc Natl Acad Sci USA 100:1484–1489CrossRefGoogle Scholar
- Thavandiran N, Dubois N, Mikryukov A, Massé S, Beca B, Simmons CB, Deshpande VS, McGarry JP, Chen CS, Nanthakumar K, Keller K, Radisic M, Zandstra PW (2013) Design criteria-guided formulation of pluripotent stem cell-derived cardiac microtissues. Proc Natl Acad Sci USA 110:E4698–E4707CrossRefGoogle Scholar
- Thomopoulos S, Fomovsky GM, Holmes JW (2005) The development of structural and mechanical anisotropy in fibroblast populated collagen gels. J Biomech Eng ASME 127:742–750CrossRefGoogle Scholar
- Tondon A, Hui-Ju H, Kaunas R (2012) Dependence of cyclic stretch-induced stress-fiber reorientation on stretch waveform. J Biomech 45:728–735CrossRefGoogle Scholar
- Vernerey FJ, Farsad M (2011) A constrained mixture approach to mechano-sensing and force generation in contractile cells. J Mech Behav Biomed Mater 4(8):1683–1699CrossRefGoogle Scholar
- Vigliotti A, McMeeking RM, Deshpande VS (2015) Simulation of the cytoskeletal response of cells on grooved or patterned substrates. J R Soc Interface 12:20141320CrossRefGoogle Scholar
- Wang JH, Thampatty BP (2006) An introductory review of cell mechanobiology. Biomech Model Mechanobiol 5:1–16CrossRefGoogle Scholar
- Wei Z, Deshpande VS, McMeeking RM, Evans AG (2008) Analysis and interpretation of stress-fiber organization in cells subject to cyclic stretch. J Biomech Eng ASME 130:031009-1Google Scholar