Synaptic plasticity is believed to represent the neural correlate of mammalian learning and memory function. It has been demonstrated that changes in synaptic conductance can be induced by approximately synchronous pairings of pre- and post- synaptic action potentials delivered at low frequencies. It has also been established that NMDAr-dependent calcium influx into dendritic spines represents a critical signal for plasticity induction, and can account for this spike-timing dependent plasticity (STDP) as well as experimental data obtained using other stimulation protocols. However, subsequent empirical studies have delineated a more complex relationship between spike-timing, firing rate, stimulus duration and post-synaptic bursting in dictating changes in the conductance of hippocampal excitatory synapses. Here, we present a detailed biophysical model of single dendritic spines on a CA1 pyramidal neuron, describe the NMDAr-dependent calcium influx generated by different stimulation protocols, and construct a parsimonious model of calcium driven kinase and phosphatase dynamics that dictate the probability of stochastic transitions between binary synaptic weight states in a Markov model. We subsequently demonstrate that this approach can account for a range of empirical observations regarding the dynamics of synaptic plasticity induced by different stimulation protocols, under regimes of pharmacological blockade and metaplasticity. Finally, we highlight the strengths and weaknesses of this parsimonious, unified computational synaptic plasticity model, discuss differences between the properties of cortical and hippocampal plasticity highlighted by the experimental literature, and the manner in which further empirical and theoretical research might elucidate the cellular basis of mammalian learning and memory function.
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The authors would like to thank Samuel Wang, Gayle Wittenberg and Guoqiang Bi for providing experimental data.
Action Editor: Carson C. Chow
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Summary of synaptic plasticity data generated with τbAP,s = 55 ms and τNMDA,s = 152 ms. (a) Overall synaptic weight change generated by 100 spike pairings delivered at 5 Hz with βP = 0.45, βD = 0.24, kP = 0.04 and kD = 4 × 10-4, where kinase and phosphatase dynamics are controlled by peaks in intracellular calcium concentration. Horizontal dashed line represents zero change in total synaptic weight. (b) Synaptic weight change generated by 100 triplet pairings delivered at 5 Hz with all other parameter values the same as (a). (c) Synaptic weight change generated by tetanic pre-synaptic stimulation delivered at various firing rates in the presence of stochastic post-synaptic activity that follows the statistics described in (Wittenberg and Wang 2006), and all other parameter values the same as in (a). (d) Synaptic weight change generated by 100 pre-synaptic inputs delivered at 2 Hz while the post-synaptic membrane voltage is held fixed at various levels of depolarisation, and all other parameter values the same as in (a). (e) Synaptic weight change generated by 10 causal pre- and / or post- synaptic burst pairings delivered at 5 Hz in the experimental data from (Pike et al. 1999) (grey) and in the model (red), where all other parameters are the same as in (a). (f) Synaptic weight change generated by 60 triplet pairings with various temporal offsets delivered at 1 Hz in the experimental data from (Wang et al. 2005) (grey) and in the model (red), where all other parameters are the same as in (a). (PDF 32 kb)
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Bush, D., Jin, Y. Calcium control of triphasic hippocampal STDP. J Comput Neurosci 33, 495–514 (2012). https://doi.org/10.1007/s10827-012-0397-5
- Synaptic plasticity