Reply to Gratiy et al.

homogeneous locally neutral medium,we have two independent current conservation laws: one law applies to the freecharge current i and another one applies to the displacement current i. Note that in a homogeneous medium i is not necessarily negligible, but the application of the current conservation law on i can be done independently of the existence of i because the two laws are independent. In the Gratiy et al. (2013) commentary, the authors assume that the displacement current is negligible, which is equivalent to consider the system as a homogeneous conductor with no capacitive effect. In this case, the free-charge conservation law applies, and there cannot be electric monopolar effects. Thus the reasoning of Gratiy et al. is only true in a very particular case of Maxwell equations, when i is neglected. However, if the medium is not electrically homogeneous, which is necessarily the case in neurons at subcellular scales (organelles, fluids, membranes, cytoskeleton, etc.), then the conclusion is opposite. In this case, we have · j →f f