The need for a concept of shape homeostasis

摘要

A major step forward for developmental biology will be accomplished when someone figures out how to extend the concept of homeostasis to apply to shapes, in the sense of geometric properties of cells, tissues and organs. I propose that the biggest obstacle to this forward step is that biological researchers are not yet familiar with the properties of tensor variables, as compared with scalars. This key difference is that tensor properties can and usually do have different amounts in different directions, whereas scalar properties cannot vary with direction. Examples of tensor variables include stress, strain, curvature, permeability, and stiffness. Examples of scalar properties include chemical concentrations, osmotic pressure, hydrostatic pressure, adhesiveness and electrical voltage. Even D'Arcy Thompson treated mechanical tension (which is the classic example of a tensor variable) as if it were a scalar constant. This greatly reduced the number of geometric shapes that he could explain as being directly produced by forces. For example, in order to generate cylinders, surface contractions need to be twice as strong in one direction as compared with the perpendicular direction. Unless surface contractions vary with direction, only spheres can be generated.