Neural coding: Difference between revisions

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{{short description|Method by which information is represented in the brain}}

'''Neural coding''' (or '''neural representation''') isrefers a [[neuroscience]] field concerned with characterisingto the hypothetical relationship between thea [[Stimulus (physiology)|stimulus]] and theits respective neuronal responses, and the relationship among the [[Electrophysiology|electricalsignalling activitiesrelationships]] among networks of the neurons in thean [[Neuronal ensemble|ensemble]].<ref name="Brown">{{cite journal |vauthors=Brown EN, Kass RE, Mitra PP |title=Multiple neural spike train data analysis: state-of-the-art and future challenges |journal=Nat. Neurosci. |volume=7 |issue=5 |pages=456–61 |date=May 2004 |pmid=15114358 |doi=10.1038/nn1228 |s2cid=562815 }}</ref><ref>{{Cite journal|last=Johnson|first=K. O.|date=June 2000|title=Neural coding|journal=Neuron|volume=26|issue=3|pages=563–566|issn=0896-6273|pmid=10896153|doi=10.1016/S0896-6273(00)81193-9|doi-access=free}}</ref> Based on[[Action potentials]], which act as the theoryprimary carrier of information in [[biological neural networks]], are [[Goldman equation|generally]] [[Resting potential|uniform]] regardless of the type of stimulus or the [[Neuron#Classification|specific type of neuron]]. The [[Channel capacity|simplicity]] of action potentials as a methodology of encoding information factored with the indiscriminate process of [[Summation (neurophysiology)|summation]] is seen as discontiguous with the specification capacity that neurons [[Neurotransmission#Cotransmission|demonstrate at the presynaptic terminal]], as well as the broad ability for complex neuronal processing and regional specialisation for which the [[Large-scale brain network|brain-wide integration]] of such is seen as fundamental to complex derivations; such as [[intelligence]], [[consciousness]], [[Social dynamics|complex social interaction]], [[reasoning]] and [[motivation]].

sensoryAs andsuch, othertheoretical informationframeworks isthat representeddescribe inencoding the [[brain]] by [[Biological neural network|networksmechanisms of neurons]],action itpotential issequences believedin thatrelationship [[neuron]]sto canobserved encodepatterns bothare [[Digitalseen data|digital]]as andfundamental [[analogto signal|analog]]neuroscientific informationunderstanding.<ref name="thorpe">{{cite book |first=S.J. |last=Thorpe |chapter=Spike arrival times: A highly efficient coding scheme for neural networks |chapter-url=https://www.researchgate.net/publication/247621744 |format=PDF |pages=91–94 |editor1-first=R. |editor1-last=Eckmiller |editor2-first=G. |editor2-last=Hartmann |editor3-first=G. |editor3-last=Hauske | editor3-link = Gert Hauske |title=Parallel processing in neural systems and computers |url=https://books.google.com/books?id=b9gmAAAAMAAJ |year=1990 |publisher=North-Holland |isbn=978-0-444-88390-2}}</ref>

== Overview ==

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A sequence, or 'train', of spikes may contain information based on different coding schemes. In some neurons the strength with which a postsynaptic partner responds may depend solely on the 'firing rate', the average number of spikes per unit time (a 'rate code'). At the other end, a complex '[[temporal code]]' is based on the precise timing of single spikes. They may be locked to an external stimulus such as in the visual<ref>Burcas G.T & Albright T.D. Gauging sensory representations in the brain. http://www.vcl.salk.edu/Publications/PDF/Buracas_Albright_1999_TINS.pdf</ref> and [[auditory system]] or be generated intrinsically by the neural circuitry.<ref name="Gerstner97">{{cite journal |vauthors=Gerstner W, Kreiter AK, Markram H, Herz AV |title=Neural codes: firing rates and beyond |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=94 |issue=24 |pages=12740–1 |date=November 1997 |pmid=9398065 |pmc=34168 |bibcode=1997PNAS...9412740G |doi=10.1073/pnas.94.24.12740|doi-access=free }}</ref>

Whether neurons use rate coding or temporal coding is a topic of intense debate within the neuroscience community, even though there is no clear definition of what these terms mean.<ref name=":0">{{Cite book|last=Gerstner, Wulfram.|url=https://www.worldcat.org/oclc/57417395|title=Spiking neuron models : single neurons, populations, plasticity|date=2002|publisher=Cambridge University Press|others=Kistler, Werner M., 1969-|isbn=0-511-07817-X|___location=Cambridge, U.K.|oclc=57417395}}</ref>

=== Rate code ===

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Despite its shortcomings, the concept of a spike-count rate code is widely used not only in experiments, but also in models of [[neural networks]]. It has led to the idea that a neuron transforms information about a single input variable (the stimulus strength) into a single continuous output variable (the firing rate).

There is a growing body of evidence that in [[Purkinje neurons]], at least, information is not simply encoded in firing but also in the timing and duration of non-firing, quiescent periods.<ref>{{cite journal |author=Forrest MD |title=Intracellular Calcium Dynamics Permit a Purkinje Neuron Model to Perform Toggle and Gain Computations Upon its Inputs. |journal=Frontiers in Computational Neuroscience |volume=8 |pages=86 |year=2014 | doi=10.3389/fncom.2014.00086 |pmid=25191262 |pmc=4138505|doi-access=free }}</ref><ref>{{cite journal |author=Forrest MD |title=The sodium-potassium pump is an information processing element in brain computation |journal= Frontiers in Physiology |volume=5 |issue=472 |pages=472 | date=December 2014 |doi=10.3389/fphys.2014.00472 |pmid=25566080 |pmc=4274886 |doi-access=free }}</ref> There is also evidence from retinal cells, that information is encoded not only in the firing rate but also in spike timing.<ref name=":1">{{Cite journal|last1=Gollisch|first1=T.|last2=Meister|first2=M.|date=2008-02-22|title=Rapid Neural Coding in the Retina with Relative Spike Latencies|url=https://www.sciencemag.org/lookup/doi/10.1126/science.1149639|journal=Science|language=en|volume=319|issue=5866|pages=1108–1111|doi=10.1126/science.1149639|pmid=18292344|bibcode=2008Sci...319.1108G|s2cid=1032537|issn=0036-8075|url-access=subscription}}</ref> More generally, whenever a rapid response of an organism is required a firing rate defined as a spike-count over a few hundred milliseconds is simply too slow.<ref name=":0" />

==== Time-dependent firing rate (averaging over several trials) ====

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Until recently, scientists had put the most emphasis on rate encoding as an explanation for [[post-synaptic potential]] patterns. However, functions of the brain are more temporally precise than the use of only rate encoding seems to allow.<ref name=":1" /> In other words, essential information could be lost due to the inability of the rate code to capture all the available information of the spike train. In addition, responses are different enough between similar (but not identical) stimuli to suggest that the distinct patterns of spikes contain a higher volume of information than is possible to include in a rate code.<ref name="Zador, Stevens">{{cite web|last=Zador, Stevens|first=Charles, Anthony|title=The enigma of the brain|url=https://docs.google.com/a/stolaf.edu/viewer?a=v&pid=gmail&attid=0.1&thid=1369b5e1cdf273f9&mt=application/pdf&url=https://mail.google.com/mail/u/0/?ui%3D2%26ik%3D0a436eb2a7%26view%3Datt%26th%3D1369b5e1cdf273f9%26attid%3D0.1%26disp%3Dsafe%26realattid%3Df_h0ty13ea0%26zw&sig=AHIEtbQB4vngr9nDZaMTLUOcrk5DzePKqA|work=© Current Biology 1995, Vol 5 No 12|access-date=August 4, 2012}}</ref>

Temporal codes (also called [https://lcnwww.epfl.ch/gerstner/SPNM/node8.html spike codes] <ref name=":0" />), employ those features of the spiking activity that cannot be described by the firing rate. For example, '''time-to-first-spike''' after the stimulus onset, '''phase-of-firing''' with respect to background oscillations, characteristics based on the second and higher statistical [[Moment (mathematics)|moments]] of the ISI [[probability distribution]], spike randomness, or precisely timed groups of spikes ('''temporal patterns''') are candidates for temporal codes.<ref name="Kostal">{{cite journal |vauthors=Kostal L, Lansky P, Rospars JP |title=Neuronal coding and spiking randomness |journal=Eur. J. Neurosci. |volume=26 |issue=10 |pages=2693–701 |date=November 2007 |pmid=18001270 |doi=10.1111/j.1460-9568.2007.05880.x |s2cid=15367988 }}</ref> As there is no absolute time reference in the nervous system, the information is carried either in terms of the relative timing of spikes in a population of neurons (temporal patterns) or with respect to an [[neural oscillations|ongoing brain oscillation]] (phase of firing).<ref name="thorpe" /><ref name="Stein" /> One way in which temporal codes are decoded, in presence of [[neural oscillations]], is that spikes occurring at specific phases of an oscillatory cycle are more effective in depolarizing the [[Chemical synapse|post-synaptic neuron]].<ref name = "Gupta2016">{{Cite journal|last1=Gupta|first1=Nitin|last2=Singh|first2=Swikriti Saran|last3=Stopfer|first3=Mark|date=2016-12-15|title=Oscillatory integration windows in neurons|journal=Nature Communications|volume=7|doi=10.1038/ncomms13808|issn=2041-1723|pmc=5171764|pmid=27976720|pagearticle-number=13808|bibcode=2016NatCo...713808G}}</ref>

The temporal structure of a spike train or firing rate evoked by a stimulus is determined both by the dynamics of the stimulus and by the nature of the neural encoding process. Stimuli that change rapidly tend to generate precisely timed spikes<ref>{{Cite journal|last1=Jolivet|first1=Renaud|last2=Rauch|first2=Alexander|last3=Lüscher|first3=Hans-Rudolf|last4=Gerstner|first4=Wulfram|date=2006-08-01|title=Predicting spike timing of neocortical pyramidal neurons by simple threshold models|url=https://doi.org/10.1007/s10827-006-7074-5|journal=Journal of Computational Neuroscience|language=en|volume=21|issue=1|pages=35–49|doi=10.1007/s10827-006-7074-5|pmid=16633938|s2cid=8911457|issn=1573-6873}}</ref> (and rapidly changing firing rates in PSTHs) no matter what neural coding strategy is being used. Temporal coding in the narrow sense refers to temporal precision in the response that does not arise solely from the dynamics of the stimulus, but that nevertheless relates to properties of the stimulus. The interplay between stimulus and encoding dynamics makes the identification of a temporal code difficult.

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[[File:NoisyNeuralResponse.png|thumb|Neural responses are noisy and unreliable.]]

This type of code is used to encode continuous variables such as joint position, eye position, color, or sound frequency. Any individual neuron is too noisy to faithfully encode the variable using rate coding, but an entire population ensures greater fidelity and precision. For a population of unimodal tuning curves, i.e. with a single peak, the precision typically scales linearly with the number of neurons. Hence, for half the precision, half as many neurons are required. In contrast, when the tuning curves have multiple peaks, as in [[grid cell]]s that represent space, the precision of the population can scale exponentially with the number of neurons. This greatly reduces the number of neurons required for the same precision.<ref name="Mat">{{cite journal |vauthors=Mathis A, Herz AV, Stemmler MB |title=Resolution of nested neuronal representations can be exponential in the number of neurons |journal=Phys. Rev. Lett. |volume=109 |issue=1 |pagesarticle-number=018103 |date=July 2012 |pmid=23031134 |bibcode=2012PhRvL.109a8103M |doi=10.1103/PhysRevLett.109.018103|doi-access=free }}</ref>

==== Topology of population dynamics ====

[[Dimensionality reduction]] and [[topological data analysis]], have revealed that the population code is constrained to low-dimensional manifolds,<ref>{{cite journal| title=Neural population dynamics during reaching|first1=MM|last1=Churchland|first2=JP|last2=Cunningham |first3=MT|last3=Kaufmann|first4=JD|last4=Foster|first5=P|last5=Nuyujukian|first6=SI|last6=Ryu|first7=KV|last7=Shenoy|journal=Nature|issue=7405|pages=51–56|date=2012|volume=487 |doi=10.1038/nature11129|pmid=22722855 |pmc=3393826 |bibcode=2012Natur.487...51C }}</ref> sometimes also referred to as [[attractors]]. The position along the neural manifold correlates to certain behavioral conditions like head direction neurons in the anterodorsal thalamic nucleus forming a ring structure,<ref>{{cite journal |last1=Chaudhuri |first1=R |last2=Gercek |first2=B |last3=Pandey |first3=B |last4=Peyrache |first4=A |last5=Fiete |first5=I |title=The intrinsic attractor manifold and population dynamics of a canonical cognitive circuit across waking and sleep |journal=Nature Neuroscience |date=2019 |volume=22 |issue=9 |pages=1512–150 |doi=10.1038/s41593-019-0460-x}}</ref> [[grid cells]] encoding spatial position in [[entorhinal cortex]] along the surface of a [[torus]],<ref>{{cite journal |last1=Gardner |first1=RJ |last2=Hermansen |first2=E |last3=Pachitariu |first3=M |last4=Burak |first4=Y |last5=Baas |first5=NA |last6=Dunn |first6=BA |last7=Moser |first7=MB |last8=Moser |first8=EI |title=Toroidal topology of population activity in grid cells |journal=Nature |date=2022 |volume=602 |issue=7895 |pages=123–128 |doi=10.1038/s41586-021-04268-7|pmid=35022611 |hdl=11250/3023140 |hdl-access=free |pmc=8810387 |bibcode=2022Natur.602..123G }}</ref> or [[motor cortex]] neurons encoding hand movements<ref>{{cite journal |last1=Gallego |first1=JA |last2=Perich |first2=MG |last3=Miller |first3=LE |last4=Solla |first4=SA |title=Neural Manifolds for the Control of Movement |journal=Neuron |date=2017 |volume=94 |issue=5 |pages=978–984 |doi=10.1016/j.neuron.2017.05.025|pmid=28595054 |hdl=10261/151381 |hdl-access=free |pmc=6122849 }}</ref> and preparatory activity.<ref>{{cite journal |last1=Churchland |first1=MM |last2=KV |first2=Shenoy |title=Preparatory activity and the expansive null-space |journal=Nature Reviews Neuroscience |date=2024 |volume=25 |issue=4 |pages=213–236 |doi=10.1038/s41583-024-00796-z}}</ref> The low-dimensional manifolds are known to change in a state dependent manner, such as eye closure in the [[visual cortex]],<ref>{{cite journal |last1=Morales-Gregorio |first1=A |last2=Kurth |first2=AC |last3=Ito |first3=J |last4=Kleinjohann |first4=A |last5=Barthelemy |first5=FV |last6=Brochier |first6=T |last7=Gruen |first7=S |last8=van Albada |first8=S |title=Neural manifolds in V1 change with top-down signals from V4 targeting the foveal region |journal=Cell Reports |date=2024 |volume=43 |issue=7 |page=114371 |doi=10.1016/j.celrep.2024.114371|doi-access=free |pmid=38923458 }}</ref> or breathing behavior in the [[ventral respiratory column]].<ref>{{cite journal |last1=Bush |first1=NE |last2=Ramirez |first2=JM |title=ventral respiratory column |journal=Nature Neuroscience |date=2024 |volume=27 |issue=2 |pages=259–271 |doi=10.1038/s41593-023-01520-3|pmid=38182835 |pmc=10849970 }}</ref>

=== Sparse coding ===