From recent studies; synaptic communication formed by the action of structural changes to the spine, is considered to represent the basis for learning mechanisms. Dendritic spine in biological studies, structural changes in shape and size existing spine occurring subsequent growth and new alert has been shown to form protrusions spine. In this study, two and three neurons in the network motifs of growth spine long-term and short-term memory functions were investigated. Motif cells in the single-compartment models modeled with Hodgkin-Huxley neurons and synaptic contact with dendritic spine growth was modeled with time constant. Results of the change in the time constant of the motif by modeling the growth of spine long or short term memory showed that exhibits the behavior.