Efficient Coding Predicts Synaptic Conductance

Synapses are information efficient in the sense that their natural conductance values convey as many bits per Joule as possible, but efficiency falls rapidly if the conductance is forced to deviate from its natural value (Harris et al, 2015. However, the exact manner in which efficiency falls as conductance deviates from its natural value remains unexplained. Recently, Malkin et al (2026) showed that synaptic noise is minimised given the available energy, consistent with a minimal energy boundary. This minimal energy boundary is a necessary, but not sufficient, condition for maximising information efficiency. By expressing the minimal energy boundary in terms of Shannon's information theory (Shannon, 1949), we show that synapses operate at signal-to-noise ratios which maximise information efficiency, and that this accurately predicts the decrease in efficiency values observed in Harris et al (2015) across a wide range of synaptic conductances. Crucially, the proposed model contains no free parameters because it is derived from the biophysics of the synapse. The results reported here are consistent with the general principle that neuronal systems in the brain have evolved to be as efficient as possible in terms of the number of bits per Joule.