Although neurons are known to transmit messages through action potentials, the specific coding mechanism of these action potentials is a tad murky. Since the degree voltage of action potential is not thought to matter (and since it is generally the same), the obligation of encoding a message is falls upon the frequency and timing of the action potentials received in the postsynaptic cell. This theory of encoding through some sort of time code is known as spike timing.
If time is the code through which messages are sent, then neurons must be able to be to consistently respond with high temporal precision. In this paper, the researchers’ model attempts to explain how to maximize the reliability of the neurons assuming that the input and background noise remain at constant amplitude. While it is known that faster currents will result in more easily conserved spike times with repetition, they were interested in determining whether faster is always better, or whether there is an ideal scale where inputs will produce the most reliable firing.
Their model looks at the data both through the lens of pure math and by analyzing some actual neuron cells. Mathematically, they reduce reliability to a measure of two identical neurons receiving two identical fluctuating inputs (in the form of action potentials) in the presence of variable background noise. The higher the correlation between these voltage traces, the more likely it is that the neuron will “correctly” fire or not fire based on the inputs instead of the background noise. By manipulating the data, they determined how this reliability measure would depend on the r, the firing rate. The shorter the r the faster the firing rate. You can see the result of their measurements in their Figure 1 (right). In both of the mathematical models (simple neuron and Hodgkin-Huxley), the reliability coefficient reaches a local maximum near 2 ms and begins to drop near 5 ms.
In addition to their theoretical models, the authors also looked at the reliability of mitral cells and neocortical pyramidal cells in mice and by passing various currents through them, which they measured in a voltage clamp. Just as in their simulated models, the spike-time reliability was shown to have a local maximum near 5 ms.
The researchers go onto discuss the applicability of their model to different types of neurons and suggest that while it particularly highly toned for integrators such as pyramidal cells, it may not make accurate predictions for neurons whose time scales are coupled, meaning slow bursts and fast spikes. Nevertheless, their model makes the point that most neurons have adapted to respond most efficiently to fast synaptic currents, increasing the overall processing speed of the brain.
Galan RB, Ermentrout GB, Urban NN 2008 Optimal Time Scale for Spike-Time Reliability: Theory, Simulations, and Experiments. Journal of Neurophysiology 99: 277-283. doi:10.1152/jn.00563.2007.