Spike-timing-dependent plasticity

Synaptic weights can be modified by spiking activity. Weight modifications at a given synapse depend on the relative timing between presynaptic and postsynaptic spikes. Down to the biophysical level, there is a number of synaptic variables which are continuously evolving according to some differential equations, and those variables can be modified by presynaptic and postsynaptic spikes. In spike-timing-dependent plasticity (STDP) rules, the synaptic weight changes at the times of presynaptic and postsynaptic spikes only, as a function of the other synaptic variables. In Brian, an STDP rule can be specified by defining an STDP object, as in the following example:

dA_pre/dt=-A_pre/tau_pre : 1
dA_post/dt=-A_post/tau_post : 1

The STDP object acts on the Connection object myconnection. Equations of the synaptic variables are given in a string (argument eqs) as for defining neuron models. When a presynaptic (postsynaptic) spike is received, the code pre (post) is executed, where the special identifier w stands for the synaptic weight (from the specified connection matrix). Optionally, an upper limit can be specified for the synaptic weights (wmax).

The example above defines an exponential STDP rule with hard bounds and all-to-all pair interactions.

Current limitations

  • The differential equations must be linear.
  • Presynaptic and postsynaptic variables must not interact, that is, a variable cannot be modified by both presynaptic and postsynaptic spikes. However, synaptic weight modifications can depend on all variables.
  • STDP currently works only with homogeneous delays, not heterogeneous ones.

Exponential STDP

In many applications, the STDP function is piecewise exponential. In that case, one can use the ExponentialSTDP class:


Here the synaptic weight modification function is:

f(s) = Ap*exp(-s/taup) if s >0
       Am*exp(s/taum) if s <0

where s is the time of the postsynaptic spike minus the time of the presynaptic spike. The modification is generally relative to the maximum weight wmax (see below). The interactions keyword determines how pairs of pre/post synaptic spikes interact: all if contributions from all pairs are added, nearest for only nearest neighbour interactions, nearest_pre if only the nearest presynaptic spike and all postsynaptic spikes are taken into account and nearest_post for the symmetrical situation. The weight update can be additive, i.e., w=w+wmax*f(s), or multiplicative: w=w+w*f(s) for depression (usually s<0) and w=w+(wmax-w)*f(s) for potentiation (usually s>0). It can also be mixed: multiplicative for depression, additive for potentiation.


By default, transmission delays are assumed to be axonal, i.e., synapses are located on the soma: if the delay of the connection C is d, then presynaptic spikes act after a delay d while postsynaptic spikes act immediately. This behaviour can be overriden with the keywords delay_pre and delay_post, in both classes STDP and Exponential STDP.

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