Information in the brain is stored in a form of an altered synaptic strength between neurons. The long-term potentiation (LTP), a phenomenon when a short-term increase in neural activity is transformed into a long-lasting increase in strengths of synaptic connectivity, provides an experimental substrate of memory. Using reaction-diffusion equations, we established an LTP model, describing the dynamics of glutamate (Glu), calcium (Ca2+) and nitric oxide (NO) in response to the stimulus-a presynaptic action potential. NO can diffuse to the presynaptic terminal and facilitate the Glu release forming a positive feedback loop. Therefore, the LTP can be considered as a chain of biochemical reactions with a positive feedback loop. In this study, we investigated numerically the role of interactions in a chain of biochemical reactions with a positive feedback on the bistable behavior or memory. We conclude that the positive feedback system with the linear interaction between substances does not exhibit a bistable behavior. However, introduction of substrate saturation described by Michaelis-Menten kinetics for NO decay can lead to an increase in synaptic strength lasting for dozens or even hundreds of seconds. Our finding extends a possible role of NO in LTP: a short high intensity stimulus is "memorized" as a long-lasting elevation of NO concentration.
Keywords: Long-term potentiation; Memory; Michaelis–Menten kinetics; Modeling; Positive feedback; Reaction–diffusion equations.