  The use of tank-treading as a means of propulsion for microswimmers in
viscous shear flows is taken into exam. We discuss the possibility that a
vesicle be able to control the drift in an external shear flow, by varying
locally the bending rigidity of its own membrane. By analytical calculation in
the quasi-spherical limit, the stationary shape and the orientation of the
tank-treading vesicle in the external flow, are determined, working to lowest
order in the membrane inhomogeneity. The membrane inhomogeneity acts in the
shape evolution equation as an additional force term, that can be used to
balance the effect of the hydrodynamic stresses, thus allowing the vesicle to
assume shapes and orientations that would otherwise be forbidden. The vesicle
shapes and orientations required for migration transverse to the flow, together
with the bending rigidity profiles that would lead to such shapes and
orientations, are determined. A simple model is presented, in which a vesicle
is able to migrate up or down the gradient of a concentration field, by
stiffening or softening of its membrane, in response to the variations in the
concentration level experienced during tank-treading.
