The strength of many synapses is modified by various use and time-depe
ndent processes, including facilitation and depression. A general desc
ription of synaptic transfer characteristics must account for the hist
ory-dependence of synaptic efficacy and should be able to predict the
postsynaptic response to any temporal pattern of presynaptic activity.
To generate such a description, we use an approach similar to the dec
oding method used to reconstruct a sensory input from a neuronal firin
g pattern. Specifically, a mathematical fit of the postsynaptic respon
se to an isolated action potential is multiplied by an amplitude facto
r that depends on a time-dependent function summed over all previous p
resynaptic spikes. The amplitude factor is, in general, a nonlinear fu
nction of this sum. Approximate forms of the time-dependent function a
nd the nonlinearity are extracted from the data, and then both functio
ns are constructed more precisely by a learning algorithm. This approa
ch, which should be applicable to a wide variety of synapses, is appli
ed here to several crustacean neuromuscular junctions, After training
on data from random spike sequences, the method predicts the postsynap
tic response to an arbitrary train of presynaptic action potentials. U
sing a model synapse, we relate the functions used in the fit to under
lying biophysical processes. Fitting different neuromuscular junctions
allows us to compare their responses to sequences of action potential
s and to contrast the time course and degree of facilitation or depres
sion that they exhibit.