Synaptic plasticity, the change in efficacy of connections between neurons, is thought to underlie learning and memory. Synaptic plasticity is sensitive to the rate and the timing of presynaptic and postsynaptic action potentials. Multiple stimulation protocols have been found to be effective in changing synaptic efficacy by inducing long-term potentiation (LTP) or depression (LTD). In many of those protocols, increases in postsynaptic calcium concentration have been shown to play a crucial role. Here, we propose a calcium-based model of a synapse in which potentiation and depression are activated above calcium thresholds.

In the calcium-based plasticity model, pre- and postsynaptic spikes induce calcium transients. Synaptic depression or potentiation is induced whenever the compound calcium trace crosses the depression or the potentiation threshold, respectively.

The here published python and c++ code implements the calculations to obtain the change in synaptic strength for pre-post spike-pairs, pre-spike and post-pair, irregular spike-pair stimulation and when calcium transients are further subjected to short-term plasticity.

The provided scripts are related and grouped according to the publications below. Please refer to those publications for more details regarding the scientific background, the details of the model, and the results obtained.

Graupner M and Brunel N (2012). Calcium-based plasticity model explains sensitivity of synaptic changes to spike pattern, rate, and dendritic location. PNAS 109 (10): 3991-3996.

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Graupner M, Wallisch P and Ostojic S (2016). Natural Firing Patterns Imply Low Sensitivity of Synaptic Plasticity to Spike Timing Compared with Firing Rate. J Neurosci 36(44):11238-11258

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Deperrois N and Graupner M (2020). Short-term depression and long-term plasticity together tune sensitive range of synaptic plasticity. accepted in PLoS Comput Biol; bioRxiv 565291; doi: 10.1101/565291.

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Yulia Dembitskaya, Silvana Valtcheva, Yihui Cui, Zhiwei Zheng, Srdjan Ostojic, Michael Graupner, and Laurent Venance (2026). Irregular and bursty neuronal firing extend spike-timing dependent plasticity window to behavioral timescales. submitted for publication.

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• The timeAboveThreshold class calculates the time the compound calcium trace spends above a given threshold for pre-post spike-pair, pre-spike and post-burst, as well as irregular spike pairs stimulation protocols. It furthermore calculates the time above threshold for the non-linear calcium model with regular and irregular spike pair stimulation (see Graupner et al. 2016, Fig. 9).
• The timeAboveThreshold class implements further an event-based integration in which calcium and the synaptic efficacy are updated in an analytically exact way upon the occurrence of pre- and postsynaptic spikes. See Higgins et al. (2014) for details of the event-based implementation.
• For bistable model implementations : The up and down transition probabilities are furthermore calculated and converted into a change in synaptic strength considering the initial distribution of synapses and the ratio of synaptic strength between the UP and the DOWN state.
• The basic results are plotted.

The essence of the model is captured by the below animation. Pre- and postsynatpic spikes induce calcium transients. Whenever the compound calcium trace crosses depression and/or potentiation threshold, the synaptic weight is decreased or increased.

All scripts are running with Python 3. Standard python packages such as numpy, scipy, pylab, time, os, sys and matplotlib are required.

This project is licensed under the GNU General Public License v3.0. Note that the software is provided "as is", without warranty of any kind, express or implied. If you use the code or data, please cite us!.