  The fast blood stream of animals is associated with large shear stresses.
Consequently, blood cells have evolved a special morphology and a specific
internal architecture allowing them to maintain their integrity over several
weeks. For instance, non-mammalian red blood cells, mammalian erythroblasts and
platelets have a peripheral ring of microtubules, called the marginal band,
that flattens the overall cell morphology by pushing on the cell cortex. In
this article, we model how the shape of these cells stems from the balance
between marginal band elasticity and cortical tension. We predict that the
diameter of the cell scales with the total microtubule polymer, and verify the
predicted law across a wide range of species. Our analysis also shows that the
combination of the marginal band rigidity and cortical tension increases the
ability of the cell to withstand forces without deformation. Finally, we model
the marginal band coiling that occurs during the disc-to-sphere transition
observed for instance at the onset of blood platelet activation. We show that
when cortical tension increases faster than crosslinkers can unbind, the
marginal band will coil, whereas if the tension increases slower, the marginal
band may shorten as microtubules slide relative to each other.
