Modeling the early stages of vascular network assembly

In vertebrates, networks of capillary vessels supply tissues with nutrients. Capillary patterns are closely mimicked by endothelial cells cultured on basement membrane proteins that allow single randomly dispersed cells to self‐organize into vascular networks. Here we provide a model including chemoattraction as the fundamental mechanism for cell‐to‐cell communication in order to identify key parameters in the complexity of the formation of vascular patterns. By flanking biological experiments, theoretical insights and numerical simulations, we provide strong evidence that endothelial cell number and the range of activity of a chemoattractant factor regulate vascular network formation and size. We propose a mechanism linking the scale of formed endothelial structures to the range of cell‐to‐cell interaction mediated by the release of chemoattractants.

[1]  Judah Folkman,et al.  Angiogenesis in vitro , 1980, Nature.

[2]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[3]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[4]  Zhang,et al.  Dynamic scaling of growing interfaces. , 1986, Physical review letters.

[5]  H. Kleinman,et al.  Role of laminin and basement membrane in the morphological differentiation of human endothelial cells into capillary-like structures , 1988, The Journal of cell biology.

[6]  H. Kleinman,et al.  Two different laminin domains mediate the differentiation of human endothelial cells into capillary-like structures in vitro , 1989, Cell.

[7]  D. Noden.  Embryonic origins and assembly of blood vessels. , 1989, The American review of respiratory disease.

[8]  D. Sokoloff,et al.  The almighty chance , 1990 .

[9]  J. Gollub,et al.  The almighty chance , 1990 .

[10]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

[11]  J. Douglas,et al.  Endothelial cell origin and migration in embryonic heart and cranial blood vessel development , 1991, The Anatomical record.

[12]  A. I. Saichev,et al.  Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves, Rays, Particles , 1991 .

[13]  C. Bugg,et al.  Three-dimensional structure of recombinant human granulocyte-macrophage colony-stimulating factor. , 1992, Journal of molecular biology.

[14]  L. Naldini,et al.  Hepatocyte growth factor is a potent angiogenic factor which stimulates endothelial cell motility and growth , 1992, The Journal of cell biology.

[15]  M. Iruela-Arispe,et al.  Reorganization of basement membrane matrices by cellular traction promotes the formation of cellular networks in vitro. , 1992, Laboratory investigation; a journal of technical methods and pathology.

[16]  M. Basta,et al.  An introduction to percolation , 1994 .

[17]  Atsushi Namiki,et al.  Hypoxia Induces Vascular Endothelial Growth Factor in Cultured Human Endothelial Cells (*) , 1995, The Journal of Biological Chemistry.

[18]  Berk,et al.  Scale-invariant behavior and vascular network formation in normal and tumor tissue. , 1995, Physical review letters.

[19]  C. Cross,et al.  Bloom and Fawcett: A Textbook of Histology , 1995 .

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

[21]  CeciliaGarlanda,et al.  Heterogeneity of Endothelial Cells , 1997 .

[22]  A. Taylor,et al.  Muscle capillarization O2 diffusion distance, and VO2 kinetics in old and young individuals. , 1997, Journal of applied physiology.

[23]  A. Mantovani,et al.  Molecular mechanisms of blood vessel formation. , 1997, Trends in biochemical sciences.

[24]  B. Keyt,et al.  The crystal structure of vascular endothelial growth factor (VEGF) refined to 1.93 A resolution: multiple copy flexibility and receptor binding. , 1997, Structure.

[25]  C. Garlanda,et al.  Heterogeneity of endothelial cells. Specific markers. , 1997, Arteriosclerosis, thrombosis, and vascular biology.

[26]  P. Krieg,et al.  VEGF mediates angioblast migration during development of the dorsal aorta in Xenopus. , 1998, Development.

[27]  Daniel B. Rifkin,et al.  Fibroblast Growth Factor-2 (FGF-2) Induces Vascular Endothelial Growth Factor (VEGF) Expression in the Endothelial Cells of Forming Capillaries: An Autocrine Mechanism Contributing to Angiogenesis , 1998, The Journal of cell biology.

[28]  E Ben-Jacob,et al.  Cooperative organization of bacterial colonies: from genotype to morphotype. , 1998, Annual review of microbiology.

[29]  Robinson,et al.  Self-organized criticality in termite architecture: a role for crowding in ensuring ordered nest expansion , 1999, Journal of theoretical biology.

[30]  J. Peng,et al.  Increased hemangioblast commitment, not vascular disorganization, is the primary defect in flt-1 knock-out mice. , 1999, Development.

[31]  R K Jain,et al.  Diffusion of macromolecules in agarose gels: comparison of linear and globular configurations. , 1999, Biophysical journal.

[32]  J. Isner,et al.  VEGF contributes to postnatal neovascularization by mobilizing bone marrow‐derived endothelial progenitor cells , 1999, The EMBO journal.

[33]  P. Krieg,et al.  Molecular Mechanisms of Vascular Development , 1999 .

[34]  G. Neufeld,et al.  Vascular endothelial growth factor (VEGF) and its receptors , 1999, FASEB journal : official publication of the Federation of American Societies for Experimental Biology.

[35]  C J Weijer,et al.  The control of chemotactic cell movement during Dictyostelium morphogenesis. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[36]  P. Carmeliet.  Mechanisms of angiogenesis and arteriogenesis , 2000, Nature Medicine.

[37]  B. L. Roman,et al.  Building the vertebrate vasculature: research is going swimmingly , 2000, Bioessays.

[38]  Paul Ekman,et al.  Lie detection and language comprehension , 2000, Nature.

[39]  K. Alitalo,et al.  Vascular Abnormalities and Deregulation of VEGF in Lkb1-Deficient Mice , 2001, Science.

[40]  L. Holmgren,et al.  Angiomotin: an angiostatin binding protein that regulates endothelial cell migration and tube formation. , 2001, The Journal of cell biology.

[41]  Paul Schliekelman,et al.  Statistical Methods in Bioinformatics: An Introduction , 2001 .

[42]  D. Sumpter,et al.  Phase transition between disordered and ordered foraging in Pharaoh's ants , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[43]  A. Popel,et al.  A computational study of the effect of vasomotion on oxygen transport from capillary networks. , 2001, Journal of theoretical biology.

[44]  M. Colombo,et al.  IL-12 Inhibition of Endothelial Cell Functions and Angiogenesis Depends on Lymphocyte-Endothelial Cell Cross-Talk1 , 2001, The Journal of Immunology.

[45]  T. J. Poole,et al.  The role of FGF and VEGF in angioblast induction and migration during vascular development , 2001, Developmental dynamics : an official publication of the American Association of Anatomists.

[46]  Holger Gerhardt,et al.  Spatially restricted patterning cues provided by heparin-binding VEGF-A control blood vessel branching morphogenesis. , 2002, Genes & development.

[47]  Jotun Hein,et al.  Statistical Methods in Bioinformatics: An Introduction , 2002 .

[48]  L Preziosi,et al.  Percolation, morphogenesis, and burgers dynamics in blood vessels formation. , 2003, Physical review letters.

[49]  J. Michael.  Textbook of Medical Physiology , 2005 .