Optimal stimulus waveforms for eliciting a spike: How close is the spike-triggered average?

Computing the average input stimulus preceding a spike, the spike-triggered average (STA), has been a powerful tool for discovering a neuron's `preferred' stimulus feature that enables efficient encoding of sensory information. Recent work in the squid giant axon has shown that STA waveforms can be remarkably similar to the energetically optimal stimulus waveforms for eliciting a spike. In the present study, we show using the Hodgkin-Huxley model that the STA can deviate from the global optimal solution if there is averaging of multiple solutions across different time scales and of multiple modes of spike induction. These findings inform attempts to develop model-free stochastic algorithms for finding energy-optimal stimuli, which is relevant to the efficient delivery of exogenous therapeutic stimuli in neurological diseases.