The brain stores memories by adjusting the strengths of connections between neurons. Such synaptic plasticity comes in different forms that strengthen or weaken synapses and range from very short-lived to long-lasting. One of the most well-studied forms of plasticity is long-term potentiation, LTP, a phenomenon whereby synaptic strength is persistently increased in response to stimulation. Different forms of LTP are known to play important roles in both short-term and long-term memory. Many different proteins have been identified in the sub-cellular molecular processes that are involved in LTP. An important question is how these proteins, with lifetimes measured in hours or days, can maintain memories for months or years. We present a computational model that shows how this problem can be solved by two interconnected feedback loops of molecular reactions, one involving the atypical protein kinase PKM{\zeta} and its messenger RNA, the other involving PKM{\zeta} and GluR2-containing AMPA receptors. The model demonstrates that robust bistability - stable equilibria  in the synapse's potentiated and unpotentiated states - can arise from  simple molecular reactions. Our simulations are able to account for a wide range of empirical results, including induction and maintenance of late-phase LTP, cellular memory reconsolidation and the effect of different pharmaceutical interventions.
In long-term potentiation (LTP), one of the most studied types of neural plasticity, synaptic strength is persistently increased in response to stimulation. Although a number of different proteins have been implicated in the sub-cellular molecular processes underlying induction and maintenance of LTP, the precise mechanisms remain unknown. A particular challenge is to demonstrate that a proposed molecular mechanism can provide the level of stability needed to maintain memories for months or longer, in spite of the fact that many of the participating molecules have much shorter life spans. Here we present a computational model that combines simulations of several biochemical reactions that have been suggested in the LTP literature and show that the resulting system does exhibit the required stability. At the core of the model are two interlinked feedback loops of molecular reactions, one involving the atypical protein kinase PKM{\zeta} and its messenger RNA, the other involving PKM{\zeta} and GluA2-containing AMPA receptors. We demonstrate that robust bistability - stable equilibria both in the synapse's potentiated and unpotentiated states - can arise from a set of simple molecular reactions. The model is able to account for a wide range of empirical results, including induction and maintenance of late-phase LTP, cellular memory reconsolidation and the effects of different pharmaceutical interventions.
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that are involved in LTP. An important question is how these proteins, with lifetimes measured in hours or days, can
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