In mammalian cortex, most excitatory inputs occur on dendritic spines, avoiding dendritic shafts. Although spines biochemically isolate inputs, nonspiny neurons can also implement biochemical compartmentalization; so, it is possible that spines have an additional function. We have recently shown that the spine neck can filter membrane potentials going into and out of the spine. To investigate the potential function of this electrical filtering, we used two-photon uncaging of glutamate and compared the integration of electrical signals in spines vs. dendritic shafts from basal dendrites of mouse layer 5 pyramidal neurons. Uncaging potentials onto spines summed linearly, whereas potentials on dendritic shafts reduced each other's effect. Linear integration of spines was maintained regardless of the amplitude of the response, distance between spines (as close as <2 m), distance of the spines to the soma, dendritic diameter, or spine neck length. Our findings indicate that spines serve as electrical isolators to prevent input interaction, and thus generate a linear arithmetic of excitatory inputs. Linear integration could be an essential feature of cortical and other spine-laden circuits.second harmonic ͉ pyramidal cell ͉ glutamate uncaging ͉ two-photon I n neocortex and many other brain areas, most excitatory inputs terminate on dendritic spines (1); so, spines must therefore likely be of major importance for the functioning of neural circuits (2). Spines can compartmentalize calcium (3), partly because their peculiar morphologies, with a small head separated from the dendrite by a slender neck, enable the biochemical isolation between inputs (4-6). This compartmentalization is thought to underlie input-specific forms of synaptic plasticity, such as long-term potentiation (7-9).Theoretical work spanning several decades has suggested that spines are ideally poised to play a major role in altering the electrical properties of synaptic inputs (2, 10 -14). Indeed, recent work has called into question the view that the sole function of spines is one of biochemical compartmentalization. First, nonspiny neurons can compartmentalize calcium with as good a degree of biochemical isolation between inputs as spiny cells (15,16). Also, by using glutamate uncaging and second harmonic measurements of membrane potential on spines of layer 5 pyramidal neurons, we have demonstrated that the spine neck filters membrane potentials (17). The filtering was bidirectional, i.e., both spine potentials transmitted to the dendrite and dendritic potentials transmitted to the spine were strongly attenuated. This implies that spines could isolate inputs electrically, an idea previously suggested based on theoretical calculations (11,12,18). More generally, passive cable models predict that inputs onto dendrites will shunt each other if they are close (19,20). Therefore, dendritic spines could provide an electrically isolated postsynaptic region to prevent interaction between different excitatory inputs, resulting in a linear integration (21).Co...