Neural coding: Difference between revisions

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== Hypothesized coding schemes ==

=== Rate coding ===

The rate coding model ofhypothesizes [[neuron]]althat firinginformation communicationabout statesa thatsignal asis contained in the intensityspike offiring arate. stimulusIt increases,is thesometimes called [[frequency]] orcoding though strictly speaking rate of [[actiondiscrete potential]]s,events oris "spikenot firing",a frequency but a increasestempo. RateThus, codingcalling isthis sometimesmodel calleda frequencytempo codingcode would be physically correct.

It appeared after experiments by [[Edgar Adrian|ED Adrian]] and [[Yngve Zotterman|Y Zotterman]] in 1926.<ref>{{cite journal|vauthors=Adrian ED, Zotterman Y|year=1926|title=The impulses produced by sensory nerve endings: Part II: The response of a single end organ.|journal=J Physiol|volume=61|issue=2|pages=151–171|doi=10.1113/jphysiol.1926.sp002281|pmc=1514782|pmid=16993780}}</ref> In this simple experiment, different weights were hung from a [[muscle]]. As the weight of the stimulus increased, the number of spikes recorded from sensory nerves innervating the muscle also increased. The authors concluded that action potentials were discrete events and that their tempo, rather than individual parameters, was the basis of neural communication. In the following decades, the measurement of firing rates became a standard tool for describing the properties of all types of neurons, partly due to the relative ease of measuring rates experimentally. However, this approach neglects all the information possibly contained in the exact timing of the spikes and interspike intervals and the internal parameters of each action potential. In recent years, more and more experimental evidence has suggested that a straightforward firing rate concept based on temporal averaging may be too simplisticto describe brain activity.<ref name="Stein" /> Even at the peripheral level (sensors and effectors), the firing rate increases non-linearly with increasing stimulus intensity.<ref name="Kandel">{{cite book|last1=Kandel|first1=E.|url=https://books.google.com/books?id=48hpAAAAMAAJ|title=Principles of Neural Science|last2=Schwartz|first2=J.|last3=Jessel|first3=T.M.|publisher=Elsevier|year=1991|isbn=978-0444015624|edition=3rd}}</ref> There is no direct connection between the spike rate and the signal. In addition, the sequence of action potentials generated by a given stimulus varies from trial to trial, so neuronal responses are typically treated statistically or probabilistically. Even the term "firing rate" has various definitions, which refer to different averaging procedures, such as an average over time or an average over several repetitions of an experiment.

Rate coding is a traditional coding scheme, assuming that most, if not all, information about the stimulus is contained in the firing rate of the neuron. Because the sequence of action potentials generated by a given stimulus varies from trial to trial, neuronal responses are typically treated statistically or probabilistically. They may be characterized by firing rates, rather than as specific spike sequences. In most sensory systems, the firing rate increases, generally non-linearly, with increasing stimulus intensity.<ref name="Kandel">{{cite book |last1=Kandel |first1=E. |last2=Schwartz |first2=J. |last3=Jessel |first3=T.M. |title=Principles of Neural Science |publisher=Elsevier |year=1991 |isbn=978-0444015624 |edition=3rd |url=https://books.google.com/books?id=48hpAAAAMAAJ}}</ref> Under a rate coding assumption, any information possibly encoded in the temporal structure of the spike train is ignored. Consequently, rate coding is inefficient but highly robust with respect to the ISI '[[noise]]'.<ref name="Stein"/>

During rate coding, precisely calculating firing rate is very important. In fact, the term "firing rate" has a few different definitions, which refer to different averaging procedures, such as an '''average over time''' (rate as a single-neuron spike count) or an '''average over several repetitions''' (rate of PSTH) of experiment.

In rate coding, learning is based on activity-dependent synaptic weight modifications.

Rate coding was originally shown by [[Edgar Adrian|ED Adrian]] and [[Yngve Zotterman|Y Zotterman]] in 1926.<ref>{{cite journal|vauthors=Adrian ED, Zotterman Y|year=1926|title=The impulses produced by sensory nerve endings: Part II: The response of a single end organ.|journal=J Physiol|volume=61|issue=2|pages=151–171|doi=10.1113/jphysiol.1926.sp002281|pmid=16993780|pmc=1514782}}</ref> In this simple experiment different weights were hung from a [[muscle]]. As the weight of the stimulus increased, the number of spikes recorded from sensory nerves innervating the muscle also increased. From these original experiments, Adrian and Zotterman concluded that action potentials were unitary events, and that the frequency of events, and not individual event magnitude, was the basis for most inter-neuronal communication.

In the following decades, measurement of firing rates became a standard tool for describing the properties of all types of sensory or [[Cerebral cortex|cortical]] neurons, partly due to the relative ease of measuring rates experimentally. However, this approach neglects all the information possibly contained in the exact timing of the spikes. During recent years, more and more experimental evidence has suggested that a straightforward firing rate concept based on temporal averaging may be too simplistic to describe brain activity.<ref name="Stein"/>

==== Spike-count rate (average over time) ====

The spike-count rate, also referred to as temporal average, is obtained by counting the number of spikes that appear during a trial and dividing by the duration of trial.<ref name=":0" /> The length T of the time window is set by the experimenter and depends on the type of neuron recorded from and to the stimulus. In practice, to get sensible averages, several spikes should occur within the time window. Typical values are T = 100 ms or T = 500 ms, but the duration may also be longer or shorter.([https://lcnwww.epfl.ch/gerstner/SPNM/node7.html Chapter 1.5] in the textbook 'Spiking Neuron Models' <ref name=":0" />)

This procedure stems from the assumption that neurons average their rates. If we accept this hypothesis, we must understand that neurons compute this average relative to the time window that has a meaning for them, not for an experimenter. If we analyse an activity that repeats with strict periodicity, it is not difficult to determine its period and calculate the average value. But neurons do not exhibit monotonous spiking. So, we do not know whether the neural code is actually average rate, and we cannot confirm or refute it because we do not know the system clock of the brain. As a result, we can average infinitely using our arbitrary time windows, but it will give nothing for deciphering the code.

The spike-count rate can be determined from a single trial, but at the expense of losing all temporal resolution about variations in neural response during the course of the trial. Temporal averaging can work well in cases where the stimulus is constant or slowly varying and does not require a fast reaction of the [[organism]] — and this is the situation usually encountered in experimental protocols. Real-world input, however, is hardly stationary, but often changing on a fast time scale. For example, even when viewing a static image, humans perform [[saccades]], rapid changes of the direction of gaze. The image projected onto the retinal [[photoreceptor cell|photoreceptors]] changes therefore every few hundred milliseconds ([https://lcnwww.epfl.ch/gerstner/SPNM/node7.html Chapter 1.5] in <ref name=":0" />)

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For sufficiently small Δt, r(t)Δt is the average number of spikes occurring between times t and t+Δt over multiple trials. If Δt is small, there will never be more than one spike within the interval between t and t+Δt on any given trial. This means that r(t)Δt is also the [[fraction (mathematics)|fraction]] of trials on which a spike occurred between those times. Equivalently, r(t)Δt is the [[probability]] that a spike occurs during this time interval.

As an experimental procedure, the time-dependent firing rate measure is a useful method to evaluate neuronal activity, in particular in the case of time-dependent stimuli. The obvious problem with this approach is that it can not be the coding scheme used by neurons in the brain. Neurons can not wait for the stimuli to repeatedly present in an exactly same manner before generating a response.<ref name=":0" /> Moreover, the dynamics of many environmental signals are measured in milliseconds, and during these milliseconds, neurons can only fire once or twice. With such a number of spikes, it is impossible to encode the signal by their average rate. But there are also faster signals. For example, a bat is capable of echolocation with a resolution of microseconds.<ref>{{Cite journal|last=McKenna|first=T.M.|last2=McMullen|first2=T.A.|last3=Shlesinger|first3=M.F.|date=1994-06|title=The brain as a dynamic physical system|url=https://linkinghub.elsevier.com/retrieve/pii/0306452294904898|journal=Neuroscience|language=en|volume=60|issue=3|pages=587–605|doi=10.1016/0306-4522(94)90489-8}}</ref> Thus, the signal measurement time window is within one spike. This is completely contrary to the average rate paradigm.

Can a code consisting of identical spikes provide the nervous system's observable information density, speed, and efficiency? Unfortunately for the adherents of the rate code paradigm, the answer to this question is negative. Such code is ineffective in all respects. Tempo variation does not carry enough information to represent a complex multi-parameter signal. It requires the creation of many spikes to encode simple parameters. Thus, it is too slow and energetically expensive. That is why it does not correspond to the reality of the brain. However, this model is still widely used not only in experiments but also in [[neural networks]] models. As a result, over the past decades, a vast amount of data has accumulated, but it has not brought us any closer to deciphering the meaning of the code.

Nevertheless, the experimental time-dependent firing rate measure can make sense, if there are large populations of independent neurons that receive the same stimulus. Instead of recording from a population of N neurons in a single run, it is experimentally easier to record from a single neuron and average over N repeated runs. Thus, the time-dependent firing rate coding relies on the implicit assumption that there are always populations of neurons.

=== Temporal coding ===