The anomaly cancellation condition of the Standard Model may be unnatural in theories with extra dimensions as an anomaly of a low-energy 4-dimensional theory can be canceled by an inflow from a bulk. This inflow may give rise to an observable effect at low energies. We analyze several physical models in which this effect exists and estimate constraints on its value, imposed by the modern experimental data. We show that the effect can be large enough to be observed even when these constraints are satisfied. Positive result of such an experiment would be a low-energy signature of the existence of extra dimensions. © 2005 Elsevier B.V. All rights reserved.