  Experimental studies have demonstrated that spermatozoa synchronize their
flagella when swimming in close proximity. In a Newtonian fluid, it was shown
theoretically that such synchronization arises passively due to hydrodynamic
forces between the two swimmers if their waveforms exhibit a front-back
geometrical asymmetry. Motivated by the fact that most biological fluids
possess a polymeric microstructure, we address here synchronization in a
viscoelastic fluid analytically. Using a two-dimensional infinite sheet model
we show that the presence of polymeric stresses removes the geometrical
asymmetry constraint, and therefore even symmetric swimmers synchronize. Such
synchronization occurs on asymptotically faster time scales than in a Newtonian
fluid, and the swimmers are seen to be driven into a stable in-phase
conformation minimizing the energy dissipated in the surrounding fluid.
