Maintenance of memory by negative-feedback of synaptic protein elimination: Modeling KIBRA-PKM$\zeta$ dynamics in LTP.

Activity-dependent modifications of synaptic efficacies are a cellular substrate of learning and memory. Current theories propose that the long-term maintenance of synaptic efficacies and memory is accomplished via a positive-feedback loop at the level of production of a protein species or a protein state. Here we propose a qualitatively different theoretical framework based on negative feedback at the level of protein elimination. This theory is motivated by recent experimental findings regarding the binding of PKM{zeta} and KI-BRA, two synaptic proteins involved in maintenance of memory, and on how this binding downregulates the proteins degradation. We demonstrate this theoretical framework with two different models. First, a simple abstract model to explore generic features of the negative-feedback process. Second, a biophysical model based on PKM{zeta}-KIBRA dimers that cooperatively form larger complexes at active synapses. These larger complexes have slower degradation and diffusion, allowing for bistability of potentiated and unpotentiated synaptic states. The results of these models are qualitatively consistent with existing experiments showing reversal of long-term potentiation and erasure of long-term memory by inhibition of KIBRA-PKM{zeta} interactions. The theory generates novel predictions that could be experimentally tested to further validate or reject the negative-feedback theory.