Condensation of Cells - Mechanisms of Morphogenesis - page 163

FIGURE 14.2 Minimization of free energy by grouping more adhesive cells. In the diagram, low-expressing
cells have six molecules of cadherin each (one per face of the hexagonal cells) and high-expressers have eighteen
molecules each (three per face). Cadherins connected homophilically to partners on other cells are shown in blue
and ones still unconnected are shown in red. Grouping high-expressers together in the middle reduces the overall
fraction of unconnected cadherins and thus reduces the overall free energy. In reality, cells will not be hexagons and
cadherins will be free to move within the membrane to maximize their chances of finding partners on any
neighbouring cell.

problems as soon as direct measurements of cadherin binding strength were made; it turns
out that there is little difference in binding strength between cadherin 2 with itself or with
cadherin 3 (see Chapter 21).
The purely thermodynamic model presented above ought not to depend on 'biological'
features of the cells. The observation that inhibiting the formation of an actin cytoskeleton
using cytochalasin D inhibits cell sorting 9 is therefore worrying. It may reflect the incapa-
bility of cadherins to adhere properly without an underlying cytoskeleton, or it may reflect
adirectroleforthecytoskeleton.Avariationon the Steinberg hypothesis, first proposed by
A.K. Harris 13 andsubsequentlyrefinedbyothers, 14,15 makes great use of contractile forces
under the cell membrane. Formation of cadherin-mediated adhesions recruits contractile
microfilaments to the membrane (Chapter 5). These pull on the junctions and the forces
they create have components normal to the membrane, directed into the cell, and also
tangential to the membrane, directed away from non-adhering regions of membrane to
adhering ones ( Figure 14.3 ). Both of these forces are resisted by the cadherin adhesion
systems. The source of resistance to inwards forces is obvious (cadherins keep hold of their
partners in the other cell). The source of resistance to tangential forces is the energy that is
released when further adhesions are made in virgin membrane, 14 which appears as an
outwards-directed tangential force ( Figure 14.3 ).
The total tangential force in the area of contact is called the interfacial force g . For two
identical cells of a type we shall call A for the purposes of writing an equation, the interfa-
cial force g

AA , is given by:

F adh A
where the 'A' superscripts are just used to keep track of the cell type involved (the '2'
arises because each cell contributes its own cytoskeletal force). If the interface is between

g AA ¼ 2 F csk A