Establishment, maintenance, and remodeling of curvature in biology.

A new hypothesis is presented, which explains how exponential tissue concentration gradients of biphasic morphogens that inhibit and stimulate basic growth rates of cells at high and low concentration respectively, determine curvatures of folds and invaginations, tubular, dome-shaped, lenticular, and spherical biological structures. For example, TGF-beta induces endothelial cells and smooth muscle cells to form tubular, vessel-like structures in vitro and blood vessels in vivo. The morphogen modulates cell growth rates via inhibitory and stimulatory receptor pathways respectively, forming a concave curvature as seen from the source concentration end of a radial, vessel-wall diffusion/perfusion driven exponential morphogen concentration gradient. From the source, inhibition declines along the radial gradient, switching to increasing stimulation beyond a neutral point, at which growth inhibition equals growth stimulation. The source concentration, shape of the gradient, and nature of the inhibitory and stimulatory pathways determine mural curvature, independent of mural-cell basic growth rate.