Mechanics of mesenchymal contribution to clefting force in branching morphogenesis

Branching morphogenesis is ubiquitous and may involve several different mechanisms. Glandular morphogenesis is affected by growth, cell rearrangements, changes in the basal lamina, changes in the stromal ECM, changes in cell–cell and cell–ECM adhesions, mesenchymal contractility, and possibly other mechanisms. We have developed a 3D model of the mechanics of clefting, focusing in this paper solely on the potential role of mesenchyme-generated traction forces. The tissue mechanics are assumed to be those of fluids, and the hypothesized traction forces are modeled as advected by the deformations which they generate. We find that mesenchymal traction forces are sufficient to generate a cleft of the correct size and morphology, in the correct time frame. We find that viscosity of the tissues affects the time course of morphogenesis, and also affects the resulting form of the organ. Morphology is also strongly dependent on the initial distribution of contractility. We suggest an in vitro method of examining the role of mesenchyme in branching morphogenesis.

[1]  N. K. Wessells,et al.  An analysis of salivary gland morphogenesis: role of cytoplasmic microfilaments and microtubules. , 1972, Developmental biology.

[2]  G. Forgacs,et al.  Viscoelastic properties of living embryonic tissues: a quantitative study. , 1998, Biophysical journal.

[3]  J. Davies,et al.  A role for microfilament-based contraction in branching morphogenesis of the ureteric bud. , 2005, Kidney international.

[4]  M. Flint.  The development of the lungs , 1906 .

[5]  E. Borghese.  Explantation experiments on the influence of the connective tissue capsule on the development of the epithelial part of the submandibular gland of Mus musculus. , 1950, Journal of anatomy.

[6]  Robert T. Tranquillo,et al.  Fibroblast‐populated collagen microsphere assay of cell traction force: Part 1. Continuum model , 1993 .

[7]  R T Tranquillo,et al.  The fibroblast-populated collagen microsphere assay of cell traction force--Part 2: Measurement of the cell traction parameter. , 1995, Journal of biomechanical engineering.

[8]  Zhilin Li,et al.  The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics) , 2006 .

[9]  J. Murray,et al.  A mechanism for early branching in lung morphogenesis , 1995, Journal of mathematical biology.

[10]  H. Akaike.  A new look at the statistical model identification , 1974 .

[11]  B. Spooner,et al.  Collagen involvement in branching morphogenesis of embryonic lung and salivary gland. , 1980, Developmental biology.

[12]  Peter Delves,et al.  Encyclopedia of life sciences , 2009 .

[13]  D. Drew,et al.  Theory of Multicomponent Fluids , 1998 .

[14]  Y. Wang,et al.  Cell locomotion and focal adhesions are regulated by substrate flexibility. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Frank Costantini,et al.  Renal branching morphogenesis: concepts, questions, and recent advances. , 2006, Differentiation; research in biological diversity.

[16]  Y. Nakanishi,et al.  Mechanical aspects of the mesenchymal influence on epithelial branching morphogenesis of mouse salivary gland , 1987 .

[17]  T. Sakakura,et al.  Mesenchyme-dependent morphogenesis and epithelium-specific cytodifferentiation in mouse mammary gland. , 1976, Science.

[18]  Y Nakanishi,et al.  Epithelial shape change in mouse embryonic submandibular gland: Modulation by extracellular matrix components , 1989, BioEssays : news and reviews in molecular, cellular and developmental biology.

[19]  J. M. Flint.  The angiology, angiogenesis, and organogenesis of the submaxillary gland , 1903 .

[20]  Xiaohai Wan,et al.  Pressure jump conditions for stokes equations with discontinuous viscosity in 2D and 3D , 2006 .

[21]  E. Borghese.  The development in vitro of the submandibular and sublingual glands of Mus musculus. , 1950, Journal of anatomy.

[22]  R T Tranquillo,et al.  An anisotropic biphasic theory of tissue-equivalent mechanics: the interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance. , 1997, Journal of biomechanical engineering.

[23]  Jonathon Howard,et al.  Slow local movements of collagen fibers by fibroblasts drive the rapid global self-organization of collagen gels , 2002, The Journal of cell biology.

[24]  M. Dembo,et al.  On the mechanics of the first cleavage division of the sea urchin egg. , 1997, Experimental cell research.

[25]  Y. Nakanishi,et al.  Effects of mesenchyme on epithelial tissue architecture revealed by tissue recombination experiments between the submandibular gland and lung of embryonic mice , 1998, Development, growth & differentiation.

[26]  H Nogawa,et al.  Substitution for mesenchyme by basement-membrane-like substratum and epidermal growth factor in inducing branching morphogenesis of mouse salivary epithelium. , 1991, Development.

[27]  S. Lubkin.  Branched organs: mechanics of morphogenesis by multiple mechanisms. , 2008, Current topics in developmental biology.

[28]  Y Nakanishi,et al.  Cell proliferation is not required for the initiation of early cleft formation in mouse embryonic submandibular epithelium in vitro. , 1987, Development.

[29]  A. Harris,et al.  Silicone rubber substrata: a new wrinkle in the study of cell locomotion. , 1980, Science.

[30]  H. Moral.  Zur Kenntnis von der Speicheldrüsen-Entwickelung der Maus , 1916, Anatomische Hefte.

[31]  Y. Nakanishi,et al.  Epithelial morphogenesis in mouse embryonic submandibular gland: Its relationships to the tissue organization of epithelium and mesenchyme , 1997, Development, growth & differentiation.

[32]  Y. Fukuda,et al.  The role of interstitial collagens in cleft formation of mouse embryonic submandibular gland during initial branching. , 1988, Development.

[33]  L. Cutler.  The Role of Extracellular Matrix in the Morphogenesis and Differentiation of Salivary Glands , 1990, Advances in dental research.

[34]  H. Nogawa.  Determination of the curvature of epithelial cell mass by mesenchyme in branching morphogenesis of mouse salivary gland. , 1983, Journal of embryology and experimental morphology.

[35]  J. Kishi,et al.  Scanning electron microscopic observation of mouse embryonic submandibular glands during initial branching: preferential localization of fibrillar structures at the mesenchymal ridges participating in cleft formation. , 1986, Journal of embryology and experimental morphology.

[36]  G. Forgacs,et al.  Before programs: the physical origination of multicellular forms. , 2006, The International journal of developmental biology.

[37]  J. Murray,et al.  A mechanical model for the formation of vascular networks in vitro , 1996, Acta biotheoretica.

[38]  W. Cardoso,et al.  Bud formation precedes the appearance of differential cell proliferation during branching morphogenesis of mouse lung epithelium in vitro , 1998, Developmental dynamics : an official publication of the American Association of Anatomists.

[39]  G F Oster,et al.  A mechanical model for mesenchymal morphogenesis , 1983, Journal of mathematical biology.

[40]  V. Mow,et al.  Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. , 1980, Journal of biomechanical engineering.

[41]  J. M. Flint.  The development of the reticulated basement membranes in the submaxillary gland , 1902 .

[42]  H. Parmar,et al.  Epithelial-stromal interactions in the mouse and human mammary gland in vivo. , 2004, Endocrine-related cancer.

[43]  Keiichi Yoshida,et al.  Branching Morphogenesis of Mouse Embryonic Submandibular Epithelia Cultured under Three Different Conditions , 1994, Development, growth & differentiation.

[44]  F. Doljanski.  The Sculpturing Role of Fibroblast-Like Cells in Morphogenesis , 2004, Perspectives in biology and medicine.

[45]  Yu-Li Wang,et al.  Substrate rigidity regulates the formation and maintenance of tissues. , 2006, Biophysical journal.

[46]  Z Li,et al.  Force and deformation on branching rudiments: cleaving between hypotheses , 2002, Biomechanics and modeling in mechanobiology.

[47]  Y Nakanishi,et al.  Mouse embryonic submandibular gland epithelium loses its tissue integrity during early branching morphogenesis , 1996, Developmental dynamics : an official publication of the American Association of Anatomists.

[48]  T. Jackson,et al.  Multiphase mechanics of capsule formation in tumors. , 2002, Journal of biomechanical engineering.

[49]  B. Spooner,et al.  Embryonic salivary gland epithelial branching activity is experimentally independent of epithelial expansion activity. , 1989, Developmental biology.

[50]  R. Brekken,et al.  Enhanced growth of tumors in SPARC null mice is associated with changes in the ECM. , 2003, The Journal of clinical investigation.

[51]  Steinberg,et al.  Liquid properties of embryonic tissues: Measurement of interfacial tensions. , 1994, Physical review letters.

[52]  H. Moral.  Über die ersten Entwickelungsstadien der Glandula submaxillaris , 1913, Anatomische Hefte.

[53]  Y. Takahashi,et al.  Branching morphogenesis of mouse salivary epithelium in basement membrane-like substratum separated from mesenchyme by the membrane filter. , 1991, Development.

[54]  M S Kolodney,et al.  Isometric contraction by fibroblasts and endothelial cells in tissue culture: a quantitative study , 1992, The Journal of cell biology.

[55]  C. Grobstein,et al.  Collagenase: effect on the morphogenesis of embryonic salivary epithelium in vitro. , 1965, Science.

[56]  P. Janmey,et al.  Tissue Cells Feel and Respond to the Stiffness of Their Substrate , 2005, Science.

[57]  N. K. Wessells,et al.  Effects of collagenase on developing epithelia in vitro: lung, ureteric bud, and pancreas. , 1968, Developmental biology.

[58]  K. Kratochwil.  Organ specificity in mesenchymal induction demonstrated in the embryonic development of the mammary gland of the mouse. , 1969, Developmental biology.

[59]  S. Sen,et al.  Matrix Elasticity Directs Stem Cell Lineage Specification , 2006, Cell.

[60]  Donald E Ingber,et al.  Control of basement membrane remodeling and epithelial branching morphogenesis in embryonic lung by Rho and cytoskeletal tension , 2005, Developmental dynamics : an official publication of the American Association of Anatomists.

[61]  M. Bissell,et al.  Of extracellular matrix, scaffolds, and signaling: tissue architecture regulates development, homeostasis, and cancer. , 2006, Annual review of cell and developmental biology.

[62]  Melinda Larsen,et al.  Cell and fibronectin dynamics during branching morphogenesis , 2006, Journal of Cell Science.

[63]  J. Kishi,et al.  Collagenase inhibitor stimulates cleft formation during early morphogenesis of mouse salivary gland. , 1986, Developmental biology.

[64]  K. Ito,et al.  An augmented approach for Stokes equations with a discontinuous viscosity and singular forces , 2007 .

[65]  G. S. Davis,et al.  Germ-layer surface tensions and "tissue affinities" in Rana pipiens gastrulae: quantitative measurements. , 1997, Developmental biology.

[66]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .