The Community for Technology Leaders
RSS Icon
Issue No.06 - Nov.-Dec. (2012 vol.9)
pp: 1607-1620
A. Abate , Delft Center for Syst. & Control, Delft Univ. of Technol., Delft, Netherlands
S. Vincent , Ecole Normale Super. de Lyon, Lyon, France
R. Dobbe , Delft Center for Syst. & Control, Delft Univ. of Technol., Delft, Netherlands
A. Silletti , Dept. of Inf. Eng., Univ. of Padova, Padua, Italy
N. Master , Dept. of Electr. Eng. & Comput. Sci., Univ. of California at Berkeley, Berkeley, CA, USA
J. D. Axelrod , Dept. of Pathology, Stanford Univ., Stanford, CA, USA
C. J. Tomlin , Dept. of Electr. Eng. & Comput. Sci., Univ. of California at Berkeley, Berkeley, CA, USA
Epithelia are sheets of connected cells that are essential across the animal kingdom. Experimental observations suggest that the dynamical behavior of many single-layered epithelial tissues has strong analogies with that of specific mechanical systems, namely large networks consisting of point masses connected through spring-damper elements and undergoing the influence of active and dissipating forces. Based on this analogy, this work develops a modeling framework to enable the study of the mechanical properties and of the dynamic behavior of large epithelial cellular networks. The model is built first by creating a network topology that is extracted from the actual cellular geometry as obtained from experiments, then by associating a mechanical structure and dynamics to the network via spring-damper elements. This scalable approach enables running simulations of large network dynamics: the derived modeling framework in particular is predisposed to be tailored to study general dynamics (for example, morphogenesis) of various classes of single-layered epithelial cellular networks. In this contribution, we test the model on a case study of the dorsal epithelium of the Drosophila melanogaster embryo during early dorsal closure (and, less conspicuously, germband retraction).
Cells (biology), Computational modeling, Finite element methods, Mechanical factors, Mathematical model, Biological system modeling,morphogenesis, Epithelium, cellular network, nonlinear dynamical model, spring-damper system, discrete element method, early dorsal closure
A. Abate, S. Vincent, R. Dobbe, A. Silletti, N. Master, J. D. Axelrod, C. J. Tomlin, "A Mathematical Model to Study the Dynamics of Epithelial Cellular Networks", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.9, no. 6, pp. 1607-1620, Nov.-Dec. 2012, doi:10.1109/TCBB.2012.126
[1] D. Boal, Mechanics of the Cell. Cambridge Univ. Press, 2011.
[2] Single-Cell-Based Models in Biology and Medicine, R. Alexander, M. Anderson, Chaplain, and K.R. eds. Springer Verlag, 2007.
[3] X. Peralta, Y. Toyama, M. Hutson, R. Montague, S. Venakides, D. Kiehart, and G. Edwards, “Upregulation of Forces and Morphogenic Asymmetries in Dorsal Closure During Drosophila Development,” Biophysical J., vol. 92, no. 7, pp. 2583-2596, 2007.
[4] J. Solon, A. Kaya-Copur, J. Colombelli, and D. Brunner, “Pulsed Forces Timed by a Ratchet-Like Mechanism Drive Directed Tissue Movement During Dorsal Closure,” Cell, vol. 137, no. 7, pp. 1331-1342, 2009.
[5] A. Layton, Y.T. Y, G. Yang, G. Edwards, D. Kiehart, and S. Venakides, “Drosophila Morphogenesis: Tissue Force Laws and the Modeling of Dorsal Closure,” HFSP J., vol. 3, no. 6, pp. 441-460, 2009.
[6] S. Vincent, N. Perrimon, and J. Axelrod, “Hedgehog and Wingless Stabilize but Do Not Induce Cell Fate during Drosophila Dorsal Embryonic Epidermal Patterning,” Development, vol. 135, pp. 2767-2775, 2008.
[7] M. Gibson, R. Nagpal, and N. Perrimon, “The Emergence of Geometric Order in Proliferating Metazoan Epithelia,” Nature, pp. 1038-1041, 2006.
[8] G. Blanchard, S. Murugesu, R. Adams, A. Martinez-Arias, and N. Gorfinkiel, “Cytoskeletal Dynamics and Supracellular Organisation of Cell Shape Fluctuations During Dorsal Closure,” Development, vol. 137, no. 16, pp. 2743-2752, 2010.
[9] D. Stamenovic, “Models of Cytoskeletal Mechanics Based on Tensegrity,” Cytoskeletal Mechanics, M.R. Kazempur-Mofrad and R.D. Kamm, eds., Cambridge Univ. Press, pp. 103-128, 2006.
[10] T. Cickovski, C. Huang, R. Chaturvedi, T. Glimm, H. Hentschel, M. Alber, J. Glazier, S. Newman, and J. Izaguirre, “A Framework for Three-Dimensional Simulation of Morphogenesis,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 2, no. 4, pp. 273-288, Oct.-Dec. 2005.
[11] H. Chen and G. Brodland, “Cell-Level Finite Element Studies of Viscous Cells in Planar Aggregates,” J. Biomechanical Eng., vol. 122, pp. 394-401, 2000.
[12] G. Brodland, D. Viens, and J. Veldhuis, “A New Cell-Based fe Model for the Mechanics of Embryonic Epithelia,” Computer Methods in Biomechanics and Biomedical Eng., vol. 10, no. 2, pp. 121-128, Apr. 2007.
[13] G. Brodland, “Computational Modeling of Cell Sorting, Tissue Engulfment, and Related Phenomena: A Review,” Applied Mechanics Rev., vol. 57, no. 1, pp. 47-76, 2004.
[14] G. Karp, Cell and Molecular Biology: Concepts and Experiments. Wiley, 2004.
[15] K. Kasza, A. Rowat, J. Liu, T. Angelini, C. Brangwynne, G. Koenderink, and D. Weitz, “The Cell as a Material,” Current Opinion in Cell Biology, vol. 19, pp. 101-107, 2007.
[16] D. Discher, P. Janmey, and Y. Wang, “Tissue Cells Feel and Respond to the Stiffness of Their Substrate,” Science, vol. 310, pp. 1139-1143, 2005.
[17] D. Pesen and J. Hoh, “Micromechanical Architecture of the Endothelial Cell Cortex,” Biophysical J., vol. 88, pp. 670-679, 2005.
[18] U. Potard, J. Butler, and N. Wang, “Cytoskeletal Mechanics in Confluent Epithelial Cells Probed through Integrins and E-Cadherins,” Am. J. Physiology, vol. 272, no. 41, pp. 1654-1663, 1997.
[19] S. Hu, J. Chen, B. Fabry, Y. Numaguchi, A. Gouldstone, D. Ingber, J. Fredberg, J. Butler, and N. Wang, “Intracellular Stress Tomography Reveals Stress Focusing and Structural Anisotropy in Cytoskeleton of Living Cells,” Am. J. Physiology Cell Physiology, vol. 285, pp. C1082-C1090, 2003.
[20] S. Kumar, I. Maxwell, A. Heisterkamp, T. Polte, T. Lele, M. Salanga, E. Mazur, and D. Ingber, “Viscoelastic Retraction of Single Living Stress Fibers and Its Impact on Cell Shape, Cytoskeletal Organization, and Extracellular Matrix Mechanics,” Biophysical J., vol. 90, pp. 3762-3773, May 2006.
[21] C. Wiebe and G. Brodland, “Tensile Properties of Embryonic Epithelia Measured Using a Novel Instrument,” J. Biomechanics, vol. 38, pp. 2087-2094, 2005.
[22] G. Brodland, D. Chen, and J. Veldhuis, “A Cell-Based Constitutive Model for Embryonic Epithelia and Other Planar Aggregates of Biological Cells,” Int'l J. Plasticity, vol. 22, pp. 965-995, 2006.
[23] R. Kamm and M. Mofrad, Cytoskeletal Mechanics: Models and Measurements, first ed. Cambridge Univ. Press, 2006.
[24] D. Ingber, “Tensegrity I. Cell Structure and Hierarchical Systems Biology,” J. Cell Science, vol. 116, pp. 1157-1173, 2003.
[25] D. Stamenovic, M. Mijailovich, I. Tolic-Nørrelykke, J. Chen, and N. Wang, “Cell Prestress. II. Contribution of Microtubules,” Am. J. Physiology, vol. 282, pp. 617-624, 2002.
[26] X. Chen and G. Brodland, “Mechanical Determinants of Epithelium Thickness in Early-Stage Embryos,” J. Mechanical Behavior of Biomedical Materials, vol. 2, pp. 494-501, 2009.
[27] R. Zaidel-Bar, M. Cohen, L. Addadi, and B. Geiger, “Hierarchical Assembly of Cell-Matrix Adhesion Complexes,” Biochemical Soc. Transactions, vol. 32, no. 3, pp. 416-420, 2004.
[28] F. Beer, E. Johnston, J. Dewolf, and D. Mazurek, Mechanics of the Cell. McGraw Hil, 2009.
[29] N. Wang, I. Tolic-Nørrelykke, J. Chen, S. Mijailovich, J. Butler, J. Fredberg, and D. Stamenovic, “Cell Prestress. I. Stiffness and Prestress are Closely Associated in Adherent Contractile Cells,” Am. J. Physiology, vol. 282, pp. 606-616, 2002.
[30] Y. Fung, Biomechanics: Mechanical Properties of Living Tissues, second ed. Springer-Verlag, 1993.
[31] V. Vasioukhin and E. Fuchs, “Actin Dynamics and Cell-Cell Adhesion in Epithelia,” Current Opinion in Cell Biology, vol. 13, pp. 76-84, 2001.
[32] Y. Luo, X. Xu, T. Lele, S. Kumar, and D. Ingber, “A Multi-Modular Tensegrity Model of an Actin Stress Fiber,” J. Biomechanics, vol. 41, pp. 2379-2387, 2008.
[33] A. Munjiza, The Combined Finite-Discrete Element Method. Wiley, 2004.
[34] W. Mollemans, F. Schutyser, J. Van Cleynenbreugel, and P. Suetens, “Tetrahedral Mass Spring Model for Fast Soft Tissue Deformation,” Proc. Int'l Conf. Surgery Simulation and Soft Tissue Modeling, N. Ayache and H. Delingette, eds., pp. 145-154, 2003.
[35] G. Odell, G. Oster, B. Burnside, and P. Alberch, “A Mechanical Model for Epithelial Morphogenesis,” J. Math. Biology, vol. 9, pp. 291-295, 1980.
[36] D. Terzopoulos and K. Waters, “Physically-Based Facial Modeling, Analysis, and Animation,” J. Visualization and Computer Animation, vol. 1, no. 2, pp. 73-80, 1990.
[37] L. Cooper and S. Maddock, “Preventing Collapse within Mass-Spring-Damper Models of Deformable Objects,” Proc. Fifth Int'l Conf. in Central Europe on Computer Graphics and Visualization, pp. 196-204, 1997.
[38] M. Arcak and E. Sontag, “A Passivity-Based Stability Criterion for a Class of Biochemical Reaction Networks,” J. Math. Biosciences and Eng., vol. 5, no. 1, pp. 1-19, 2008.
[39] A. Nealen, M. Müller, R. Keiser, E. Boxerman, and M. Carlson, “Physically Based Deformable Models in Computer Graphics,” Computer Graphics Forum, vol. 25, no. 4, pp. 809-836, 2005.
[40] D. Chen and B. Paden, “Stable Inversion of Nonlinear Non-Minimum Phase Systems,” Int'l J. Control, vol. 64, no. 1, pp. 81-97, 1996.
[41] S. Devasia and B. Paden, “Stable Inversion for Nonlinear Nonminimum-Phase Time-Varying Systems,” IEEE Trans. Automatic Control, vol. 43, no. 2, pp. 283-288, Feb. 1998.
[42] R. Raffard, K. Amondlirdviman, J. Axelrod, and C. Tomlin, “An Adjoint-Based Parameter Identification Algorithm Applied to Planar Cell Polarity Signaling,” IEEE Trans. Automatic Control, vol. 53, no. SI, pp. 109-121, Jan. 2008.
[43] A. Silletti, A. Cenedese, and A. Abate, “The Emergent Structure of the Drosophila Wing - A Dynamic Model Generator,” Proc. Int'l Conf. Computer Vision, Theory and Applications (VISAPP 09), pp. 406-410, Feb. 2009.
[44] R. Phillips, J. Kondev, and J. Theriot, Physical Biology of the Cell, first ed. Garland Science, 2009.
[45] L. Tsai, Robot Analysis: The Mechanics of Serial and Parallel Manipulators. Wiley & Sons, 1999.
[46] J. Dormand and P. Prince, “A Family of Embedded Runge-Kutta Formulae,” J. Computational Applied Math., vol. 6, pp. 19-26, 1980.
[47] J. Ahrens, B. Geveci, and C. Law, “ParaView: An End-User Tool for Large Data Visualization,” The Visualization Handbook, C. Hansen, and C. Johnson, eds., Elsevier, 2005.
[48] A. Kiger, B. Baum, S. Jones, M. Jones, A. Coulson, C. Echeverri, and N. Perrimon, “A Functional Genomic Analysis of Cell Morphology Using RNA Interference,” J. Biology, vol. 2, no. 4,article 72, pp. 1-15, 2003.
[49] M. Peifer, “The Product of the Drosophila Segment Polarity gene Armadillo is Part of a Multi-Protein Complex Resembling the Vertebrate Adherens Junction,” J. Cell Science, vol. 105, no. 4, pp. 993-1000, 1993.
72 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool