Non-linear summation of excitatory synaptic inputs to small neurones: a case study in spinal motoneurones of the young Xenopus tadpole.

1. We examined the steady-state summation of postsynaptic potentials (PSPs) in small, electrotonically compact neurones with short dendrites, using a one-compartment electrical equivalent model of the passive membrane with conductances to represent chemical synapses and electrotonic junctional connections to neighbouring neurones. 2. Our model shows that PSP summation is non-linear and for small depolarizations is mainly determined by the increase in total neurone conductance due to the opening of synaptic channels. At bigger depolarizations the change in synaptic driving force becomes an equally important cause of non-linearity. 3. Non-linear summation of AMPA-mediated PSPs was measured experimentally when two monosynaptic pathways to motoneurones were stimulated. The conductances underlying these PSPs were calculated relative to the resting neurone conductance using our model. These conductance ratios were hardly affected by the size of electrotonic coupling conductances. The non-linearity in PSP summation could be predicted by the model provided that the depolarizations remained negative to potentials at which voltage-dependent channels open. 4. The model was used to estimate the relative contributions of glutamatergic, cholinergic and electrotonic excitation to EPSPs measured in Xenopus tadpole spinal motoneurones during swimming. Estimates of synaptic conductances and electrotonic coupling to other motoneurones suggest that ligand-gated conductance mediated by glutamate may be twice that due to acetylcholine. 5. We conclude that in small electrotonically compact motoneurones of the Xenopus tadpole, our simple model can predict the non-linearity in PSP summation and may allow the conductances of different synaptic inputs to be compared. Furthermore, excitatory synaptic conductances can increase the resting neurone conductance significantly and limit depolarization. Our general model may also be applicable to other small neurones.