  Epithelial tissue elongation by convergent extension is a key motif of animal
morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet
in contrast to a fluid, epithelial cells adhere to each other and maintain the
tissue layer under actively generated internal tension. To resolve this
apparent paradox, we formulate a model in which tissue flow in the
tension-dominated regime occurs through adiabatic remodeling of force balance
in the network of adherens junctions. We propose that the slow dynamics within
the manifold of force-balanced configurations is driven by positive feedback on
myosin-generated cytoskeletal tension. Shifting force balance within a tension
network causes active cell rearrangements (T1 transitions) resulting in net
tissue deformation oriented by initial tension anisotropy. Strikingly, we find
that the total extent of tissue deformation depends on the initial cellular
packing order. T1s degrade this order so that tissue flow is self-limiting. We
explain these findings by showing that coordination of T1s depends on coherence
in local tension configurations, quantified by a geometric order parameter in
tension space. Our model reproduces the salient tissue- and cell-scale features
of germ band elongation during Drosophila gastrulation, in particular the
slowdown of tissue flow after approximately twofold elongation concomitant with
a loss of order in tension configurations. This suggests local cell geometry
contains morphogenetic information and yields experimentally testable
predictions. Furthermore, defining biologically controlled active tension
dynamics on the manifold of force-balanced states may provide a general
approach to the description of morphogenetic flow.
