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The Rho GTPase proteins Rac1, RhoA and Cdc42 have a central role in regulating the actin cytoskeleton in dendritic spines, thereby exerting control over the structural and functional plasticity of spines and, ultimately, learning and memory. Although previous work has shown that precise spatiotemporal coordination of these GTPases is crucial for some forms of cell morphogenesis, the nature of such coordination during structural spine plasticity is unclear. Here we describe a three-molecule model of structural long-term potentiation (sLTP) of murine dendritic spines, implicating the localized, coincident activation of Rac1, RhoA and Cdc42 as a causal signal of sLTP. This model posits that complete tripartite signal overlap in spines confers sLTP, but that partial overlap primes spines for structural plasticity. By monitoring the spatiotemporal activation patterns of these GTPases during sLTP, we find that such spatiotemporal signal complementation simultaneously explains three integral features of plasticity: the facilitation of plasticity by brain-derived neurotrophic factor (BDNF), the postsynaptic source of which activates Cdc42 and Rac1, but not RhoA; heterosynaptic facilitation of sLTP, which is conveyed by diffusive Rac1 and RhoA activity; and input specificity, which is afforded by spine-restricted Cdc42 activity. Thus, we present a form of biochemical computation in dendrites involving the controlled complementation of three molecules that simultaneously ensures signal specificity and primes the system for plasticity.