Analytical Solution of Spike-timing Dependent Plasticity Based on Synaptic Biophysics

Spike timing plasticity (STDP) is a special form of synaptic plasticity where the relative timing of post- and presynaptic activity determines the change of the synaptic weight. On the postsynaptic side, active back-propagating spikes in dendrites seem to play a crucial role in the induction of spike timing dependent plasticity. We argue that postsynaptically the temporal change of the membrane potential determines the weight change. Coming from the presynaptic side induction of STDP is closely related to the activation of NMDA channels. Therefore, we will calculate analytically the change of the synaptic weight by correlating the derivative of the membrane potential with the activity of the NMDA channel. Thus, for this calculation we utilise biophysical variables of the physiological cell. The final result shows a weight change curve which conforms with measurements from biology. The positive part of the weight change curve is determined by the NMDA activation. The negative part of the weight change curve is determined by the membrane potential change. Therefore, the weight change curve should change its shape depending on the distance from the soma of the postsynaptic cell. We find temporally asymmetric weight change close to the soma and temporally symmetric weight change in the distal dendrite.