  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unpublished data used with the authors' permission).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.
