My rudimentary understanding of the neuronal firing rate is that it varies person to person, and neuron to neuron. So any specific number for a firing rate would be specific to the test subject and type of neuron etc. However aside from this I'm interested to find out if any medication or specific dietary constituents have been shown to increase neuronal firing rate in average test subjects. To be clear I understand that some medication has been shown to help suffers of diseases such as Alzheimer's, but I'm interested in the typical human brain.
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You've received a few great comments from our neuroscience-savvy users that indicate ways in which this question can be construed as particularly challenging or maybe even unanswerable. However, I think there's a much more basic and limited understanding of your question that takes into account your self-professed unfamiliarity with neuropharmacology and permits a perfectly good intro-level answer. I don't specialize in this – I'm a psychologist, but more of a dabbler in neuroscience – but I'll take a crack at it anyway.
Agonists activate cellular receptors. Excitatory receptors produce excitatory postsynaptic potentials (EPSPs); i.e., they encourage neurons (of which they are components) to "fire". Hence the simple answer: any agonist of a neuron's excitatory receptors increases its firing rate by definition.
Glutamate is an excitatory neurotransmitter. It binds to glutamate receptors, which increase the likelihood or frequency of action potentials (i.e., firing events) in their neurons when activated. NMDA receptors (a type of glutamate receptor) play a role in long-term potentiation (effectively increasing the probability of firing and other criteria of synaptic strength), so the effects of glutamate sometimes outlast its direct activity.
Wikipedia lists several NMDA agonists, some of which are prescribed as ingested drugs. D-Cycloserine has applications in anxiety and addiction treatments. However, there is a balance to maintain, and the objective of medication is generally to restore a normative balance given some abnormality or damage.
Evidently treating Alzheimer's isn't as simple as increasing EPSPs – that might even be a move in the wrong direction. Nicotine may help with Alzheimer's, but the mechanism is more complex:
It would seem nicotine's direct action is agonistic, but its mediated effect is antagonistic, and that's the effect that matters for Alzheimer's outcomes. Another wrinkle to nicotine's pharmacology is its agonistic role with acetylcholine, a neurotransmitter that plays excitatory and inhibitory roles for different purposes. This demonstrates the practical complexity of action potentials' causes and consequences.