Biological neurons have a trade-off between high information transfer (high firing rate) and energy conservation (low firing rate). One would suspect that the maximization of this function has a single solution, and that the mean firing rate and variability should be similar across all neurons. Yet this is far from the case. Is there a principled computational explanation for this variability?
3$\begingroup$ Just a quick question. Why do you expect one solution? Couldn't the optimum vary from brain region to brain region and in general depend in a complicated way on the topology? $\endgroup$– Artem KaznatcheevApr 13, 2012 at 3:11
2$\begingroup$ Artem: One solution is the simplest answer... but experimentally this does not seem to be the situation. Mean firing rates vary even with one region. There may be topological answer, I do not know. $\endgroup$– Kyler BApr 13, 2012 at 3:41
$\begingroup$ Each neuron is performing a different computational role in the network, so you would expect some to have different firing rates from others. $\endgroup$– honiMay 15, 2015 at 7:11
I am not sure whether the three assumptions on which your question is based are really valid.
(1) Why should a high transformation transfer be linked to a high firing rate? Depending on the role of a single neuron within a group, not firing might carry as much as information as firing.
(2) Energy conservation might not be linked to the behavior of a single neuron, but rather to the organism as a whole. For instance, if the constant firing of a neuron stops your legs from constant (dis-functional) shaking, the energy "wasted" on the firing neuron can lower the energy consumption of the system as a whole.
(3) Although not explicitly stated, your question might suggest that the mean firing rate of a given neuron is relatively constant over time. This is not necessarily the case, as the firing characteristics of neurons are "tuned" over time, depending on its activity. This process is called homeostatic synaptic plasticity and has received much attention recently.
For a review see: Turrigiano GG. (2008) The self-tuning neuron: synaptic scaling of excitatory synapses. Cell. 422-35.
$\begingroup$ I think you are missing the point of the question with (1) and (2). Regardless if it is the presence of a signal or the absence that triggers something, if you speed up everything by a factor of 10, your whole information processing will speed up by a factor of 10 (as a crude analogy, think refresh rate on processors). However, your energy consumption will also increase (crude analogy: heat loss in processors). $\endgroup$ Apr 13, 2012 at 14:08
$\begingroup$ @Artem Kaznatcheev: Many thanks for your comment. Actually I fear that the processor analogy might not be very useful in this context. I agree with you: if the processing rate of a processor is increased by a factor of 10, the information transfer is ten times larger, regardless of whether "firing" or "no-firing" is signaled in a given processing step. $\endgroup$– H.MusterApr 13, 2012 at 16:55
$\begingroup$ comment continued: For the neuron, however, this is not necessarily true. Although increasing the firing rate by a factor of 10 results in 10 times more transmitted signals, this does not make sense for a "silent" neuron. For a neuron that does not fire, speeding up by a factor of 10 is simply not defined (probably because of the lack of discrete processing steps). $\endgroup$– H.MusterApr 13, 2012 at 17:00