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The fast blood stream of animals is associated with large shear stresses.Consequently, blood cells have evolved a special morphology and a specificinternal architecture allowing them to maintain their integrity over severalweeks. For instance, non-mammalian red blood cells, mammalian erythroblasts andplatelets have a peripheral ring of microtubules, called the marginal band,that flattens the overall cell morphology by pushing on the cell cortex. Inthis article, we model how the shape of these cells stems from the balancebetween marginal band elasticity and cortical tension. We predict that thediameter of the cell scales with the total microtubule polymer, and verify thepredicted law across a wide range of species. Our analysis also shows that thecombination of the marginal band rigidity and cortical tension increases theability of the cell to withstand forces without deformation. Finally, we modelthe marginal band coiling that occurs during the disc-to-sphere transitionobserved for instance at the onset of blood platelet activation. We show thatwhen cortical tension increases faster than crosslinkers can unbind, themarginal band will coil, whereas if the tension increases slower, the marginalband may shorten as microtubules slide relative to each other.

Balance of microtubule stiffness and cortical tension determines the size of blood cells with marginal band across species