  Cell spreading and motility on an adhesive substrate are driven by the active
physical forces generated by the actin cytoskeleton. We have recently shown
that coupling curved membrane complexes to protrusive forces, exerted by the
actin polymerization that they recruit, provides a mechanism that can give rise
to spontaneous membrane shapes and patterns. In the presence of an adhesive
substrate, this model was shown to give rise to an emergent motile phenotype,
resembling a motile cell. Here, we utilize this ``minimal-cell" model to
explore the impact of external shear flow on the cell shape and migration on a
uniform adhesive flat substrate. We find that in the presence of shear the
motile cell reorients such that its leading edge, where the curved active
proteins aggregate, faces the shear flow. The flow-facing configuration is
found to minimize the adhesion energy by allowing the cell to spread more
efficiently over the substrate. For the non-motile vesicle shapes, we find that
they mostly slide and roll with the shear flow. We compare these theoretical
results with experimental observations, and suggest that the tendency of many
cell types to move against the flow may arise from the very general, and
non-cell-type-specific mechanism predicted by our model.
