Does spin-orbit coupling play a role in metal-nonmetal transition in two-dimensional systems?

We propose an experiment, which would allow to pinpoint the role of spin-orbit coupling in the metal-nonmetal transition observed in a number of two-dimensional systems at low densities. Namely, we demonstrate that in a parallel magnetic field the interplay between the spin-orbit coupling and the Zeeman splitting leads to a characteristic anisotropy of resistivity with respect to the direction of the in-plane magnetic field. Though our analytic calculation is done in the deeply insulating regime, the anisotropy is expected to persist far beyond that regime.