500
8 Morphogenesis
8.10 Mesenchymal Morphogenesis
Mesenchyme plays a major role in the development of blood vessels, bones,
muscles, connective tissues (e.g., cartilage, tendons, ligaments), and most organs.
Numerous studies of mesenchymal morphogenesis have focused on the problem
of pattern formation, which is the spatial organization of differentiated cells in
the body. For example, the skeleton, vasculature, and animal coat markings form
characteristic patterns.
Turing (1952) pioneered mathematical models for pattern formation based on
the positional information hypothesis of Wolpert (1969), who proposed that cell
differentiation in the embryo is dictated by local concentrations of morphogens.
Turing showed that reaction-diffusion equations involving two chemical species can
generate spatial patterns of chemical concentration that resemble patterns found
on animal coats, e.g., stripes and spots. The fundamental idea is that a small
disturbance in an initially homogeneous domain locally increases the concentration
of an activator, which diffuses outward. A faster diffusing inhibitor, however, limits
the extent of this diffusion, leading to higher concentrations only within a limited
distance from the original disturbance. Depending on parameter values and domain
geometry, the interactions of multiple disturbances can create a wide variety of
patterns (Murray 2003).
Realizing that chemical prepatterns cannot readily correct abnormal morphogenesis, Murray and colleagues proposed a mechanical theory for mesenchymal
morphogenesis and used models based on this theory to simulate pattern formation
(Oster et al. 1983) (see also Chapter 6 in Murray 2003). The postulated mechanism stems from evidence showing that cells exert tractions that deform their
surroundings (Harris et al. 1980; Harris 1984). The equations governing this socalled Murray-Oster theory are presented next.
8.10.1 Murray-Oster Theory for Mesenchymal Morphogenesis
Murray-Oster theory treats mesenchyme as a mixture of cells and extracellular
matrix. Mesenchymal cells migrate and exert traction forces that deform the matrix.
Matrix deformation, in turn, moves cells directly by convection and causes local
changes in matrix density and anisotropy that influence the direction of cell
migration.
As in the original paper (Oster et al. 1983), only small-strain versions of the
equations are considered here. In addition, the equations do not include chemical
factors, which play important roles in cell migration and vascular pattern formation
(Czirok and Little 2012). Several related models have since included these and other
effects (Murray 2003; Ambrosi et al. 2005; Scianna et al. 2013).
Balance of Mass In general, mass is not conserved in developing mesenchymal
tissues. Cell mass can be added by proliferation, subtracted by atrophy, and either
8 Morphogenesis
8.10 Mesenchymal Morphogenesis
Mesenchyme plays a major role in the development of blood vessels, bones,
muscles, connective tissues (e.g., cartilage, tendons, ligaments), and most organs.
Numerous studies of mesenchymal morphogenesis have focused on the problem
of pattern formation, which is the spatial organization of differentiated cells in
the body. For example, the skeleton, vasculature, and animal coat markings form
characteristic patterns.
Turing (1952) pioneered mathematical models for pattern formation based on
the positional information hypothesis of Wolpert (1969), who proposed that cell
differentiation in the embryo is dictated by local concentrations of morphogens.
Turing showed that reaction-diffusion equations involving two chemical species can
generate spatial patterns of chemical concentration that resemble patterns found
on animal coats, e.g., stripes and spots. The fundamental idea is that a small
disturbance in an initially homogeneous domain locally increases the concentration
of an activator, which diffuses outward. A faster diffusing inhibitor, however, limits
the extent of this diffusion, leading to higher concentrations only within a limited
distance from the original disturbance. Depending on parameter values and domain
geometry, the interactions of multiple disturbances can create a wide variety of
patterns (Murray 2003).
Realizing that chemical prepatterns cannot readily correct abnormal morphogenesis, Murray and colleagues proposed a mechanical theory for mesenchymal
morphogenesis and used models based on this theory to simulate pattern formation
(Oster et al. 1983) (see also Chapter 6 in Murray 2003). The postulated mechanism stems from evidence showing that cells exert tractions that deform their
surroundings (Harris et al. 1980; Harris 1984). The equations governing this socalled Murray-Oster theory are presented next.
8.10.1 Murray-Oster Theory for Mesenchymal Morphogenesis
Murray-Oster theory treats mesenchyme as a mixture of cells and extracellular
matrix. Mesenchymal cells migrate and exert traction forces that deform the matrix.
Matrix deformation, in turn, moves cells directly by convection and causes local
changes in matrix density and anisotropy that influence the direction of cell
migration.
As in the original paper (Oster et al. 1983), only small-strain versions of the
equations are considered here. In addition, the equations do not include chemical
factors, which play important roles in cell migration and vascular pattern formation
(Czirok and Little 2012). Several related models have since included these and other
effects (Murray 2003; Ambrosi et al. 2005; Scianna et al. 2013).
Balance of Mass In general, mass is not conserved in developing mesenchymal
tissues. Cell mass can be added by proliferation, subtracted by atrophy, and either