Glass sponges (Hexactinellida) are so far the only sponges known to be able to conduct electrical signals. They can do this because their tissues are syncytial (there are no membrane boundaries between cells), and are able to propagate an action potential. In cellular sponges (Demosponges, Calcarea and Homoscleromorphs) we are not aware of any junctions (e.g. gap junctions) that would allow an electrical current to pass, and there is so far no evidence of any behaviour rapid enough to suggest that electrical signalling occurs. However with more work, such a system may be found.
It is very difficult to record from the tissues because they’re so thin (~1-2um), so we have been using a molecular approach. Gabrielle Tompkins-MacDonald was able to isolate potassium channels from a sponge, and express them in frog oocytes to record their ability to control current passage into and out of the cell. The first channels analyzed are inward rectifier K channels. Our analysis suggests sponge Kir channels pre-date the diversification of K channel families. Recordings show they are strong inward rectifiers which suggest a potential ability to recover membrane potential after depolarization. To read more see: Tompkins-MacDonald et al. JExpBiol 2009