An efficient Ca²⁺ based plasticity rule with combined Ca²⁺sources

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 [1] 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 [2], 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 [1] and [2], 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 [1] 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.