Synaptic Plasticity with Discrete state synapses
  Experimental observations on synaptic plasticity at individual glutamatergic synapses from the CA3 Shaffer collateral pathway onto CA1 pyramidal cells in the hippocampus suggest that the transitions in synaptic strength occur among discrete levels at individual synapses (~\cite{Peter} and S. S.-H. Wang, unpublished data used with the authors' permission). This happens for both long term potentiation (LTP) and long term depression (LTD) induction protocols. O'Connor, Wittenberg, and Wang have argued that three states would account for their observations on individual synapses in the CA3-CA1 pathway. We develop a quantitative model of this three state system with transitions among the states determined by a competition between kinases and phosphatases shown by O'Connor et al. to be determinant of LTP and LTD, respectively. Specific predictions for various plasticity protocols are given by coupling this description of discrete synaptic AMPA conductance changes to a model of postsynaptic membrane potential and associated intracellular calcium fluxes to yield the transition rates among the states. We then present various LTP and LTD induction protocols to the model system and report the resulting whole cell changes in AMPA conductance. We also examine the effect of our discrete state synaptic plasticity model on the synchronization of realistic oscillating neurons. We show that one-to-one synchronization is enhanced by the plasticity we discuss here and the presynaptic and postsynaptic oscillations are in phase. Synaptic strength saturates naturally in this model and does not require artificial upper or lower cutoffs, in contrast to earlier models of plasticity. 
H. D. Abarbanel, S. S. Talathi, L. Gibb, M. Rabinovich