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Analog Pattern Matching in a Model of Dendritic Spines

Pattern matching, the ability to recognize and maximally respond to an input pattern that is similar to a previously learned pattern, is an essential step in any learning process. To investigate the properties of pattern matching in biological neurons, and in particular the role of a calcium-dependent potassium conductance, a circuit model of a small area of dendritic membrane with a number of dendritic spines is developed. Circuit model simulations show that dendritic membrane depolarization is greater in response to a previously learned pattern of synaptic inputs than in response to a novel pattern of synaptic inputs. These simulations, in combination with an analysis of the circuit model equations, reveal that when a synaptic input pattern is similar to the learned pattern of synaptic inputs, the total dendritic depolarization is a linear combination of dendritic depolarization contributed by individual spines. When at least one synaptic input differs markedly from the learned value, dendritic depolarization is a nonlinear combination of individual spine depolarizations. These principles of spine interactions are captured in a computationally simple set of 'similarity measure' equations which are shown to reproduce the response surface of the circuit model output. Thus, these similarity measure equations not only describe a biologically plausible model of pattern matching, they also satisfy computational requirements for use in artificial neural networks.