A number of research groups have proposed generative, Ca2+ based plasticity models in recent years. Such rules are based on the premise that moderate, above-basal levels of post-synaptic Ca2+ lead to long term depression (LTD) and that high levels lead to long term potentiation (LTP). We present such a rule and discuss its assumptions and implications.
Our rule has similarities with two models in  in that Ca2+ may enter the post-synaptic density (PSD) through voltage gated channels Ca2+(V) and NMDA receptor (NMDAR) mediated channels Ca2+(V, NMDA). Unlike Model 1 in their study and the model of the Shouval group , our model achieves spike time dependent LTD without the requirement that back-propagating action potentials (BAP's) have a long tail. Thus, we do not assume this tail is sufficient to expel Mg2+ from glutamate-bound NMDAR's. In our model, LTP and LTD processes are compounded while Ca2+ exceeds LTP and LTD thresholds respectively. We do not use a specific function of peak Ca2+ or the time-integral of pre- and post-synaptic interactions.
The simple formulation of our model makes fewer assumptions about the underlying biology of NMDAR-dependent plasticity than the models in  and , but our simulations of spike-time dependent plasticity (STDP) experiments show similar output to theirs. For post-before-pre spike pairings, depression is graded because the respective time courses of Ca2+ and NMDAR-activation are sufficiently long to interact with one another. Ca2+(V) is spatially non-specific because it is driven by the BAP, but NMDAR's provide an indicator of pre-synaptic plasticity that interacts with this Ca2+ source. We use NMDAR's in this role for convenience, as other molecules could serve this purpose. This mechanism is similar to Model 2 in  where the two Ca2+ sources are separate. Here, the Ca2+ sources are combined to exceed the LTP threshold, resulting in the much-debated LTD window at long-latency pre-before-post pairings.
Our model points to several mechanisms for experimental study. For instance, spatially non-specific Ca2+(V) must integrate with Ca2+(V, NMDA) in the PSD very quickly to produce LTP. Alternatives to rapid integration at the PSD include the possibility that plasticity-inducing processes determine the relative levels of Ca2+ inside and outside the PSD, that Ca2+(V, NMDA) exceeds Ca2+(V) by some margin, or that Ca2+-dependent release from internal stores plays a role in this regard.