Synapses on dendritic spines of pyramidal neurons show a remarkable ability to induce phosphorylation of transcription factors at the nuclear level with a short latency, incompatible with a diffusion process from the dendritic spines to the nucleus. To account for these findings, we formulated a novel extension of the classical cable theory by considering the fact that the endoplasmic reticulum (ER) is an effective charge separator, forming an intrinsic compartment that extends from the spine to the nuclear membrane. We use realistic parameters to show that an electrotonic signal may be transmitted along the ER from the dendritic spines to the nucleus. We found that this type of signal transduction can additionally account for the remarkable ability of the cell nucleus to differentiate between depolarizing synaptic signals that originate from the dendritic spines and back-propagating action potentials. This study considers a novel computational role for dendritic spines, and sheds new light on how spines and ER may jointly create an additional level of processing within the single neuron.