Morphoelastic models discriminate between different mechanisms of left-right asymmetric stomach morphogenesis.

The mechanisms by which the vertebrate stomach undergoes its evolutionarily conserved leftward bending remain incompletely understood. Although the left and right sides of the organ are known to possess different gene expression patterns and undergo distinct morphogenetic events, the physical mechanisms by which these differences generate morphological asymmetry remain unclear. Here, we develop a continuum model of asymmetric stomach morphogenesis. Using a morphoelastic framework, we investigate the morphogenetic implications of a variety of hypothetical, tissue-level growth differences between the left and right sides of a simplified tubular organ. Simulations reveal that, of the various differential growth mechanisms tested, only one category is consistent with the leftward stomach curvature observed in wild-type embryos: equal left and right volumetric growth rates, coupled with transversely isotropic tissue thinning on the left side. Simulating this mechanism in a defined region of the model over a longer period of growth leads to mature stomach-like curvatures.

Flexural rigidity of pressurized model notochords in regular packing patterns.

The biomechanics of embryonic notochords are studied using an elastic membrane model. An initial study varying internal pressure and stiffness ratio determines tension and geometric ratios as a function of internal pressure, membrane stiffness ratio, and cell packing pattern. A subsequent three-point bending study determines flexural rigidity as a function of internal pressure, configuration, and orientation. Flexural rigidity is found to be independent of membrane stiffness ratio. Controlling for number and volume of cells and their internal pressure, the eccentric staircase pattern of cell packing has more than double the flexural rigidity of the radially symmetric bamboo pattern. Moreover, the eccentric staircase pattern is found to be more than twice as stiff in lateral bending than in dorsoventral bending. This suggests a mechanical advantage to the eccentric WT staircase pattern of the embryonic notochord, over patterns with round cross-section.

Physical models of notochord cell packing reveal how tension ratios determine morphometry.

The physical and geometric aspects of notochords are investigated using a model of finite-length notochords, with interior vacuolated cells arranged in two common packing configurations, and sheath modeled as homogeneous and thin. The key ratios governing packing patterns and eccentricity are number of cells per unit length λ and cell tension ratio Γ. By analyzing simulations that vary Γ and total number of cells N, we find that eccentricity, λ, and internal pressure approach consistent asymptotic values away from the tapering ends, as N increases. The length of the tapering ends is quantified as a function of Γ and pattern. Formulas are derived for geometric ratios, pressure, and energy as functions of Γ and pattern. These observations on the relationship between mechanics, geometry, and pattern provide a framework for further work which may provide insight into the roles of mechanosensing and pressure-volume regulation in the notochord.