SC6 Modeling Neural Plasticity in Spiking Networks


One of the most fascinating properties of the brain is its capacity constantly to respond and adapt to its environment. It is widely assumed that learning and memory responsible for this process are implemented through changes in the strength of synaptic connections between neurons. Neural activity can induce potentiation or depression of synaptic strength through synaptic plasticity rules. Activity patterns of both presynaptic and postsynaptic neurons play a role in this process of synaptic modification. In early models of synaptic plasticity, the firing rates of pre- and postsynaptic neurons have been the basis for activity-dependent synaptic change. More recently, however, other quantities such as the membrane potential, or the precise spike timing of neurons have been used as the basis for synaptic change.

In this course we will provide an overview of different models of synaptic plasticity. Most of them follow from Hebb's conjecture that synchronous pre- and postsynaptic activity results in synaptic potentiation. In particular, if neuron A is successful at driving the firing of neuron B, then the synapse from A to B should be strengthened. Over the years, many experimental studies have reported the effect of the timing of individual spikes on long-term synaptic modification, in which synapses cooperate or compete to wire pre- and postsynaptic neurons. Repeated pairings of pre- and postsynaptic stimulation in different systems have shown that both the magnitude and the sign of synaptic change depend on the timing between pre- and postsynaptic spikes. A synapse becomes potentiated if the presynaptic neuron is repetitively activated within ~20 ms before the firing of the postsynaptic neuron, and if the temporal firing order is reversed then the synapse is depressed. This rule has been termed spike time-dependent plasticity, or STDP.

We will discuss various models of STDP that modify synaptic strength based on the timing of pairs of spikes, triplets of spikes, bursts of spikes, and even subthreshold fluctuations of the membrane potential in pre- and postsynaptic neurons. We will derive mathematical equations for the implications of these rules on the dynamics of synaptic connection strengths in networks of spiking neurons, and simulate these networks numerically. We will start with feedforward networks, but we will extend the principles to plasticity in recurrent networks.


- Formulate different models of spike timing dependent plasticity (pair-based, triplet-based, voltage-based).
- Derive the equation for the evolution of synaptic connection strength in feedforward spiking networks.
- Analyze the dynamics in recurrent networks of spiking neurons with plastic synapses.

The goal will be to understand how different activity-dependent plasticity mechanisms shape the dynamics and computation in networks of spiking neurons.


R. Kempter, W. Gerstner, and J. L. van Hemmen (1999). Hebbian learning and spiking neurons. Phys Rev E, 59:4498-4514.

J. Gjorgjieva, T. Toyoizumi and S. J. Eglen (2009). Burst-time-dependent plasticity robustly guides ON/OFF segregation in the lateral geniculate nucleus. PLoS Comp Biol 5(12): e1000618. 

Clopath C, Büsing L, Vasilaki E, Gerstner W (2010). Connectivity reflects coding: a model of voltage-based STDP with homeostasis. Nat Neurosci 13:344 –352.

J. Gjorgjieva, C. Clopath, J. Audet and J.-P. Pfister (2011). A triplet spike-timing-dependent plasticity model generalizes the Bienenstock-Cooper-Munro rule to higher-order spatiotemporal correlations. Proc Natl Acad Sci USA 108:19383-19388. 

N. Ravid Tannenbaum and Y. Burak (2016). Shaping neural circuits by high order synaptic interactions. PLoS Comp Biol 12(8):e1005056.

Course location


Course requirements


Instructor information.

Instructor's name

Julijana Gjorgjieva


cf. website


Julijana Gjorgjieva is a Reseach Group Leader at the Max Planck Institute for Brain Research in Frankfurt and an Assistant Professor in Computational Neuroscience at the Technical University of Munich. She studied Mathematics at Harvey Mudd College in Claremont, California and obtained her PhD in 2011 at the University of Cambridge in the UK. After doing postdocs with Haim Sompolinsky and Markus Meister at Harvard University and Eve Marder at Brandeis University in the US, she started her group in Frankfurt in the summer of 2016. Julijana’s work is aimed at understanding the main principles governing the organization and computation in neural circuits, from sensory to motor. She addresses these questions using two types of methods: normative approaches, such as optimization of information transfer, to determine the emergence of cell type diversity, and bottom-up approaches to understand how neural computation arises from the interaction of different mechanisms acting at various levels, from single neurons to synaptic connections and circuits.