Bulletin of Mathematical Biology

, Volume 81, Issue 3, pp 919–935 | Cite as

The “Memory” Effect in a Chain of Biochemical Reactions with a Positive Feedback is Enhanced by Substrate Saturation Described by Michaelis–Menten Kinetics

  • Pranas Katauskis
  • Feliksas Ivanauskas
  • Aidas AlaburdaEmail author


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.


Memory Positive feedback Modeling Long-term potentiation Reaction–diffusion equations Michaelis–Menten kinetics 


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsVilnius UniversityVilniusLithuania
  2. 2.Institute of Biosciences, Life Sciences CenterVilnius UniversityVilniusLithuania

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