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1 Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA; Center for the Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, PA, USA; Center for Neuroscience, University of PIttsburgh, Pittsburgh, PA, USA
2 Center for the Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, PA, USA; Center for Neuroscience, University of PIttsburgh, Pittsburgh, PA, USA
3 Center for the Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, PA, USA; Center for Neuroscience, University of PIttsburgh, Pittsburgh, PA, USA; Department of Neurobiology, University of Pittsburgh, Pittsburgh, PA, USA
4 Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA; Center for Neuroscience, University of PIttsburgh, Pittsburgh, PA, USA; Laboratory for Biological Modeling, NIDDK, NIH, Bethesda, MD, USA
* To whom correspondence should be addressed. E-mail: rubin{at}math.pitt.edu.
Calcium has been proposed as a post-synaptic signal underlying synaptic spike-timing dependent plasticity (STDP). We examine this hypothesis with computational modeling based on experimental results from hippocampal cultures, some of which are presented here, in which pairs and triplets of pre- and post-synaptic spikes induce potentiation and depression in a temporally asymmetric way. Specifically, we present a set of model biochemical detectors, based on plausible molecular pathways, which make direct use of the time course of the calcium signal to reproduce these experimental STDP results. Our model features a modular structure, in which long-term potentiation (LTP) and depression (LTD) components compete to determine final plasticity outcomes; one aspect of this competition is a veto through which appropriate calcium time courses suppress LTD. Simulations of our model are also shown to be consistent with classical LTP and LTD induced by repeated pre-synaptic stimulation. Overall, our results provide computational evidence that, while the post-synaptic calcium time course contains sufficient information to distinguish various experimental long-term plasticity paradigms, small changes in the properties of back-propagation of action potentials or in synaptic dynamics can alter the calcium time course in ways that will significantly affect STDP induction by any detector based exclusively on post-synaptic calcium. This may account for the variability of STDP outcomes seen within hippocampal cultures, under repeated application of a single experimental protocol, as well as for that seen in multiple spike experiments across different systems.
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