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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.


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Correspondence to Dominic Standage.

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Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Standage, D., Trappenberg, T. An efficient Ca2+ based plasticity rule with combined Ca2+sources. BMC Neurosci 8, P93 (2007).

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  • NMDA Receptor
  • Long Term Potentiation
  • Long Term Depression
  • Gated Channel
  • Spike Time