View source for Bursting

[[Image:bursting-recording.png|thumb|380px|right|alt=Trace of oxytocin-sensitive neuron showing a few bursts as extremely dense collection of spikes in voltage|Trace of modeled [[oxytocin]]-sensitive [[neuron]] showing bursts {{dubious|date=February 2014}}]]

'''Bursting''', or '''burst firing''', is an extremely diverse<ref name='wagenaar06'>{{cite journal|title=An extremely rich repertoire of bursting patterns during the development of cortical cultures|journal=BMC Neuroscience|date=2006-02-07|first=Daniel|last=Wagenaar |author2=Jerome Pine |author3=Steve M. Potter|volume=7|pages=11|doi= 10.1186/1471-2202-7-11|pmid=16464257|pmc=1420316 |doi-access=free }}</ref> general phenomenon of the activation patterns of [[neurons]] in the [[central nervous system]]<ref name='cooper2002'>{{cite journal|title=The significance of action potential bursting in the brain reward circuit |journal=Neurochemistry International |doi=  10.1016/S0197-0186(02)00068-2|pmid=12176075|year=2002|last1=Cooper|first1=D|volume=41|issue=5|pages=333–340|s2cid=22492183 }}</ref><ref name='jeffreys1982'>{{cite journal|title=Synchronized bursting of CA1 hippocampal pyramidal cells in the absence of synaptic transmission|journal=Letters to Nature|date=1982-12-02|first=JGR|last=Jeffreys|author2=HL Hass|volume=300|issue=5891|pages=448–450|doi= 10.1038/300448a0|pmid=6292731|bibcode = 1982Natur.300..448J |s2cid=2767619}}</ref> and [[spinal cord]]<ref name='pre-bot1991'>{{cite journal|title=Pre-Botzinger complex: a brainstem region that may generate respiratory rhythm in mammals|journal=Science|date=November 1991|first=JC|last=Smith|author2=HH Ellenberger |author3=K Ballanyi |author4=DW Richter |author5=JL Feldman |pmid=1683005|volume=254|issue=5032|pages=726–729|doi= 10.1126/science.1683005|bibcode = 1991Sci...254..726S |pmc=3209964}}</ref> where periods of rapid [[action potential]] spiking are followed by quiescent periods much longer than typical inter-spike intervals. Bursting is thought to be important in the operation of robust [[central pattern generator]]s,<ref name='marder2000'>{{cite journal|title=Motor pattern generation|journal=Current Opinion in Neurobiology|year=2000|first=E|last=Marder|volume=10|issue=6|pages=691–698|doi=10.1016/S0959-4388(00)00157-4|pmid=11240277|s2cid=19743807}}</ref><ref name="prebot1" /><ref name="prebot2" /> the transmission of [[neural code]]s,<ref name='kepecs2002'>{{cite journal|title=Bursting Neurons Signal Input Slope|journal=Journal of Neuroscience|year=2002|first=A|last=Kepecs|author2=X Wang |author3=J Lisman |pmid=12388612|pmc=6757694|volume=22|issue=20|pages=9053–62|doi=10.1523/JNEUROSCI.22-20-09053.2002}}</ref><ref name='kepecs2003'>{{cite journal|doi=10.1080/net.14.1.103.118|title=Information encoding and computation with spikes and bursts|journal=Network: Computation in Neural Systems|date=2003-01-01|first=A|last=Kepecs|author2=J Lisman|volume=14|issue=1|pages=103–118|pmid=12613553|s2cid=1553645}}</ref> and some [[Neuropathology|neuropathologies]] such as [[epilepsy]].<ref name='prince1978'>{{cite journal|doi=10.1146/annurev.ne.01.030178.002143|title=Neurophysiology of Epilepsy|journal=Annual Review of Neuroscience|date=March 1978|first=David A|last=Prince|pmid=386906|volume=1|pages=395–415}}</ref> The study of bursting both directly and in how it takes part in other neural phenomena has been very popular since the beginnings of [[cellular neuroscience]] and is closely tied to the fields of [[neural synchronization]], [[neural coding]], [[Neuroplasticity|plasticity]], and [[attention]].

Observed bursts are named by the number of discrete action potentials they are composed of: a ''doublet'' is a two-spike burst, a ''triplet'' three and a ''quadruplet'' four. Neurons that are intrinsically prone to bursting behavior are referred to as ''bursters'' and this tendency to burst may be a product of the environment or the [[phenotype]] of the cell.

==Physiological context==

===Overview===
Neurons typically operate by firing single [[action potential]] spikes in relative isolation as discrete input [[postsynaptic potential]]s combine and drive the [[membrane potential]] across the [[threshold potential|threshold]]. Bursting can instead occur for many reasons, but neurons can be generally grouped as exhibiting ''input-driven'' or ''intrinsic'' bursting. Most cells will exhibit bursting if they are driven by a constant, subthreshold input<ref name='nesb'>{{cite journal|doi=10.1142/S0218127400000840|title=Neural excitability, spiking and bursting|journal=International Journal of Bifurcation and Chaos|date=2000-01-01|first=Eugene|last=Izhikevich|volume=10|issue=6|pages=1171–1266|url=ftp://ftp-sop.inria.fr/odyssee/Team/Olivier.Faugeras/ArticlesCoursENS-MVA/izhikevich-nesb.pdf|access-date=2009-11-30 |bibcode = 2000IJBC...10.1171I |citeseerx=10.1.1.421.2424}}</ref> and particular cells which are genotypically prone to bursting (called ''bursters'') have complex feedback systems which will produce bursting patterns with less dependence on input and sometimes even in isolation.<ref name="jeffreys1982" /><ref name="nesb" />

In each case, the physiological system is often {{citation needed|date=February 2014}} thought as being the action of two linked subsystems. The ''fast subsystem'' is responsible for each spike the neuron produces.  The ''slow subsystem'' modulates the shape and intensity of these spikes before eventually triggering quiescence.

Input-driven bursting often {{citation needed|date=February 2014}} [[Neural coding|encodes]] the intensity of input into the bursting frequency<ref name="nesb" /> where a neuron then acts as an [[integrator]]. Intrinsic bursting is a more specialized phenomenon and is believed {{by whom|date=February 2014}} to play a much more diverse role in [[neural computation]]. {{clarify|date=February 2014}}

===Fast subsystem===
{{expand section|date=February 2014}}

===Slow subsystem===
Bursts differ from [[tonic (physiology)|tonic]] firing, typically associated with [[Poisson distribution|Poisson distributed]] spike times for a given average firing rate, in that bursting involves a physiological "slow subsystem" that eventually depletes as the bursting continues and then must be replenished before the cell can burst again (compare ''[[refractory period (physiology)|refractory period]]'').<ref name="nesb" /> During the bursting event, this slow subsystem modulates the timing and intensity of the emitted spikes and is thought {{by whom|date=February 2014}} to be important in the computational aspects {{clarify|date=February 2014}} of the resulting burst pattern. There are many discovered mechanisms of slow subsystems including voltage-<ref name='prebot1'>{{cite journal|title=Models of Respiratory Rhythm Generation in the Pre-Botzinger Complex. I. Bursting Pacemaker Neurons|journal=Journal of Neurophysiology|year=1999|first=Robert|last=Butera|author2=John Rinzel |author3=Jeffrey Smith |volume=82|issue=1|pages=382–97|pmid=10400966|doi=10.1152/jn.1999.82.1.382|s2cid=396589 }}</ref><ref name='wang1999'>{{cite journal|title=Fast burst firing and short-term synaptic plasticity: a model of neocortical chattering neurons|journal=Neuroscience|year=1999|first=X|last=Wang|volume=89|issue=2|pages=347–362|doi=10.1016/S0306-4522(98)00315-7|pmid=10077318|s2cid=24600653}}</ref><ref name='huguenard1992'>{{cite journal|title=Simulation of the currents involved in rhythmic oscillations in thalamic relay neurons|journal=Journal of Neurophysiology|year=1992|first=John|last=Huguenard|author2=D McCormick|pmid=1279135|volume=68|issue=4|pages=1373–83|doi=10.1152/jn.1992.68.4.1373|citeseerx=10.1.1.320.1988}}</ref> and {{chem2|Ca(2+)}}-gated<ref name='kloppenburg2000'>{{cite journal|title=Highly Localized Ca2+ Accumulation Revealed by Multiphoton Microscopy in an Identified Motoneuron and Its Modulation by Dopamine|journal=Journal of Neuroscience|date=2000-04-01|first=Peter|last=Kloppenburg|author2=Warren Zipfel |author3=Watt Webb |author4=Ronald Harris-Warrick |pmid=10729332|pmc=6772235|volume=20|issue=7|pages=2523–33|doi=10.1523/JNEUROSCI.20-07-02523.2000}}</ref> currents and spiking interplay between [[dendrite]]s and the [[perikaryon|cell body]].<ref name='doiron2003'>{{cite journal|title=Inhibitory feedback required for network oscillatory responses to communication but not prey stimuli|journal=Nature|date=2003-01-30|first=Brent|last=Doiron|author2=Maurice J Chacron |author3=Leonard Maler |author4=André Longtin |author5=Joseph Bastian |volume=421|issue=6922|pages=539–543|doi=10.1038/nature01360|bibcode = 2003Natur.421..539D |pmid=12556894|s2cid=4407550}}</ref>

The slow subsystem also is connected to [[endogenous]] bursting patterns in neurons, where the pattern can be maintained completely by internal mechanism without any [[synapse|synaptic]] input. This process also relies on [[calcium channel]]s, which [[Depolarization|depolarize]] the neuron by allowing an influx of calcium [[ion]]s. So long as internal calcium ion concentrations remain at an elevated level, the neuron will continue to undergo periods of rapid spiking. However, elevated calcium ion levels also trigger a [[Second messenger system|second messenger cascade]] within the cell which lower calcium influx and promote calcium efflux and [[buffer solution|buffering]]. As calcium concentrations decline, the period of rapid bursting ceases, and the phase of quiescence begins. When calcium levels are low, the original calcium channels will reopen, restarting the process and creating a bursting pattern.<ref>{{cite web|last=Bryne|first=John|title=Feedback/recurrent inhibition in nanocircuits|url=http://neuroscience.uth.tmc.edu/s1/introduction.html|work=Neuroscience Online|publisher=University of Texas Health Center|access-date=2013-07-27|archive-url=https://web.archive.org/web/20150426062849/http://neuroscience.uth.tmc.edu/s1/introduction.html|archive-date=2015-04-26|url-status=dead}}</ref>

==Statistical detection==
In isolation or in mathematical models bursting can be recognized since the environment and state of the neuron can be carefully observed and modulated. When observing neurons in the wild, however, bursting may be difficult to distinguish from normal firing patterns. In order to recognize bursting patterns in these contexts statistical methods are used to determine threshold parameters.

Bursting is characterized by a [[coefficient of variation]] (CV) of the interspike intervals (ISI) that is larger than one, or a [[Fano factor]] of the spike count that is larger than one, because bursting leads to spike patterns that are more irregular than a [[Poisson process]] (which has a CV and Fano factor equal to unity). Alternatively, the [[Serial correlation|serial correlation coefficient]] of the ISI sequence is positive for bursting patterns, because in this case short ISIs tend to be followed by more short ISIs (at least if the bursts consist of more than two spikes).

==Mathematical models==
Neuron behavior is often modeled as single-compartment, non-linear [[dynamical systems]], where the neuron states represent physiological quantities such as membrane voltage, current flow, and the concentrations of various ions intra- and extracellularly. These models most generally take the singularly [[perturbation theory|perturbed]] form

: ''fast subsystem'': <math>\dot{x} = f(x, u)</math>
: ''slow subsystem'': <math>\dot{u} = \mu g(x, u)</math>

where <math>f</math> and <math>g</math> are both [[Hodgkin–Huxley model|Hodgkin–Huxley]] style relations, <math>\dot{x}</math> is a vector representing the cell parameters relevant to the fast subsystem, <math>\dot{u}</math> is a vector representing the parameters of the slow modulation subsystem, and <math>\mu \ll 1</math> is the ratio of the time scales between the fast and slow subsystems.<ref name="nesb" />

Models of neuron dynamics generally exhibit a number of stable and unstable [[attractor]]s in [[phase space]] which represent resting states. When the system is sufficiently perturbed by input stimuli it may follow a complex return path back to the [[stable attractor]] representing an action potential. In bursting neurons, these dynamic spaces [[bifurcation theory|bifurcate]] between quiescent and bursting modes according to the dynamics of the slow system. These two bifurcations may take many forms and the choice of bifurcation both from quiescent to bursting and bursting to quiescent can affect the behavioral aspects of the burster.

The complete classification of quiescent-to-bursting and bursting-to-quiescent bifurcations leads to 16 common forms and 120 possible forms if the dimensionality of the fast subsystem is not constrained.<ref name="nesb" /> Of the most common 16, a few are well studied.

{| class="wikitable" style="text-align:center; width:300px; height:200px" border="1"
|+Common combinations of bifurcations
|-
!  !! [[Saddle-node bifurcation|saddle node]] on an invariant circle !! saddle [[homoclinic orbit]] !! supercritical [[Hopf bifurcation|Andronov-Hopf]] !! fold limit cycle
|-
! [[Saddle-node bifurcation|saddle node]] (fold)
| fold/ circle || fold/ homoclinic || fold/ Hopf || fold/ fold cycle
|-
! [[Saddle-node bifurcation|saddle node]] on an invariant circle
| circle/ circle || circle/ homoclinic || circle/ Hopf || circle/ fold cycle
|-
! supercritical [[Hopf bifurcation|Andronov-Hopf]]
| Hopf/ circle || Hopf/ homoclinic || Hopf/ Hopf || Hopf/ fold cycle
|-
! subcritical [[Hopf bifurcation|Andronov-Hopf]]
| subHopf/ circle || subHopf/ homoclinic || subHopf/ Hopf || subHopf/ fold cycle
|-
|}

===Square-wave burster===
The '''fold/homoclinic''', also called square-wave, burster is so named because the shape of the voltage trace during a burst looks similar to a square wave due to fast transitions between the resting state attractor and the spiking limit cycle.<ref name="nesb" />

==Purposes==
Bursting is a very general phenomenon and is observed in many contexts in many neural systems. For this reason it is difficult to find a specific meaning or purpose for bursting and instead it plays many roles. In any given circuit observed bursts may play a part in any or all of the following mechanisms and may have a still more sophisticated impact on the network.

===Synaptic plasticity===
Synaptic strengths between neurons follow changes that depend on spike timing and bursting. For excitatory synapses of the cortex, pairing an action potential in the pre-synaptic neuron with a burst in the post-synaptic neuron leads to long-term potentiation of the synaptic strength, while pairing an action potential in the pre-synaptic neuron with a single spike in the post-synaptic neuron leads to long-term depression of the synaptic strength.<ref name='payeur2021'>{{cite journal |doi=10.1038/s41593-021-00857-x |issn=1097-6256 |title=Burst-dependent synaptic plasticity can coordinate learning in hierarchical circuits |journal=Nature Neuroscience |year=2021 |first=Alexandre |last=Payeur |author2=J Guergiuev |author3=F Zenke |author4=B A Richards |author5=R Naud |volume=24 |issue=6 |pages=1010–1019 |pmid=33986551|s2cid=214793776 }}</ref> Such dependence of synaptic plasticity on the spike timing patterns is referred to as burst-dependent plasticity. Burst-dependent plasticity is observed with variations in multiple areas of the brain. <ref name='friedenberger2023'>{{cite journal |doi=10.1113/JP281510 |title=Silences, spikes and bursts: Three-part knot of the neural code |journal=Journal of Physiology |year=2023 |first=Zachary |last=Friedenberger |author2=E Harkin |author3=K Toth |author4=R Naud |volume=601 |issue=23 |pages=5165–5193  |doi-access=free |arxiv=2302.07206 }}</ref>

===Multiplexing and routing===
Some neurons, sometimes called ''resonators'', exhibit sensitivity for specific input frequencies and fire either more quickly or exclusively when stimulated at that frequency. Intrinsically bursting neurons can use this [[band-pass filter]]ing effect in order to encode for specific destination neurons and [[multiplexing|multiplex]] signals along a single [[axon]].<ref name="nesb" /> More generally, due to short-term synaptic depression and [[Neural facilitation|facilitation]] specific synapses can be resonant for certain frequencies and thus become viable specific targets for bursting cells.<ref name='izhikevich2003'>{{cite journal|doi=10.1016/S0166-2236(03)00034-1|title=Bursts as a unit of neural information: selective communication via resonance|journal=Trends in Neurosciences|year=2003|first=Eugene|last=Izhikevich|author2=N Desai |author3=E Walcott |pmid=12591219|volume=26|issue=3|pages=161–7|s2cid=698477}}</ref> When combined with burst-dependent long-term plasticity, such multiplexing can allow neurons to coordinate synaptic plasticity across hierarchical networks.<ref name='payeur2021' /><ref name='naud2018'>{{cite journal|doi=10.1073/pnas.1720995115 |title=Sparse bursts optimize information transmission in a multiplexed neural code|journal=PNAS|year=2018|first=Richard|last=Naud|author2=H Sprekeler |volume=115|issue=27|pages=E6329–E6338|pmid=29934400|pmc=6142200|bibcode=2018PNAS..115E6329N |doi-access=free}}</ref>

===Synchronization===
Burst synchronization refers to the alignment of bursting and quiescent periods in interconnected neurons. In general, if a network of bursting neurons is linked it will eventually synchronize for most types of bursting.<ref name="nesb" /><ref name='rulkov2001'>{{cite journal|title=Regularization of synchronized chaotic bursts|journal=Physical Review Letters|date=March 2001|first=NF|last=Rulkov|volume=86|issue=1|pages=183–6|doi=10.1103/PhysRevLett.86.183|pmid=11136124|bibcode=2001PhRvL..86..183R|arxiv = nlin/0011028 |s2cid=7016788}}</ref><ref name='belykh2005'>{{cite journal|title=Synchronization of bursting neurons: what matters in the network topology|journal=Physical Review Letters|year=2005|first=I|last=Belykh|author2=E de Lange |author3=M Hasler |volume=94|issue=18|pages=2181|doi=10.1103/PhysRevLett.94.188101|bibcode=2005PhRvL..94r8101B|pmid=15904412}}</ref> Synchronization can also appear in circuits containing no intrinsically bursting neurons, however its appearance and stability can often be improved by including intrinsically bursting cells in the network.<ref name="prebot2" /> Since synchronization is related to [[Plasticity (physics)|plasticity]] and [[memory]] via [[Hebbian theory|Hebbian plasticity]] and [[long-term potentiation]] the interplay with plasticity and intrinsic bursting is very important{{Citation needed|date=July 2010}}.

===Information content and channel robustness===
Due to the all-or-nothing nature of action potentials, single spikes can only encode [[Information theory|information]] in their interspike intervals (ISI). This is an inherently low fidelity method of transferring information as it depends on very accurate timing and is sensitive to noisy loss of signal: if just a single spike is mistimed or not properly received at the synapse it leads to a possibly unrecoverable loss in coding{{Citation needed|date=July 2010}}. Since intrinsic bursts are thought to be derived by a computational mechanism in the slow subsystem, each can represent a much larger amount of information in the specific shape of a single burst leading to far more robust transmission. Physiological models show that for a given input the interspike and interburst timings are much more variable than the timing of the burst shape itself<ref name="kepecs2003" /> which also implies that timing between events is a less robust way to encode information.

The expanded alphabet for communication enabled by considering burst patterns as discrete signals allows for a greater [[channel capacity]] in [[neuronal communication]]s and provides a popular connection between [[neural coding]] and [[information theory]].

==Example bursting neuron circuits==

===Hippocampus===
The [[subiculum]], a component of the [[hippocampal formation]], is thought to perform relaying of signals originating in the hippocampus to many other parts of the brain.<ref name='swanson1977'>{{cite journal|title=An autoradiographic study of the organization of the efferent connections of the hippocampal formation in the rat|journal=Journal of Computational Neurology|date=1977-03-01|first=LW|last=Swanson|author2=WM Cowan|volume=172|issue=1|pages=49–84|pmid=65364 |doi=10.1002/cne.901720104 |s2cid=40742028}}<!--|accessdate=2009-11-30--></ref> In order to perform this function, it uses intrinsically bursting neurons to convert promising single stimuli into longer lasting burst patterns as a way to better focus attention on new stimuli and activate important processing circuits.<ref name='cooper2002'/><ref name='swadlow2002'>{{cite journal|title=Activation of a cortical column by a thalamocortical impulse|journal=Journal of Neuroscience|date=2002-01-01|first=H|last=Swadlow|author2=A Gusev |author3=T Bezdudnaya |pmid=12196600|pmc=6757983|volume=22|issue=17|pages=7766–7773|doi=10.1523/JNEUROSCI.22-17-07766.2002}}</ref> Once these circuits have been activated, the subicular signal reverts to a single spiking mode.<ref name='cooper2005'>{{cite journal|title=Output-mode transitions are controlled by prolonged inactivation of sodium channels in pyramidal neurons of subiculum|journal=PLOS Biology|date=June 2005|first=DC|last=Cooper|author2=S Chung |author3=N Spruston |volume=3|issue=6|pages=1123|pmid=15857153|doi=10.1371/journal.pbio.0030175|pmc=1088280 |doi-access=free }}</ref>

===pre-Bötzinger complex===
The [[Pre-Botzinger complex|pre-Bötzinger complex]] (preBötC) is located in  ventrolateral [[Medulla oblongata|medulla]] and is proposed to generate the rhythm underlying inspiratory efforts in mammals. Since the frequency that the lungs need to operate at can vary according to metabolic demand, preBötC activity is modulated over a wide range of frequencies and is able to entrain the respiratory system to meet metabolic demand. While pacemaker neurons do not necessarily require intrinsically bursting neurons<ref name="rulkov2001" /> the preBötC contains a heterogeneous population of both regular spiking and intrinsically bursting neurons. Intrinsically bursting neurons are thought to make the preBötC oscillations more robust to changing frequencies and the regularity of inspiratory efforts.<ref name='prebot2'>{{cite journal|title=Models of respiratory rhythm generation in the pre-Botzinger complex. II. Populations of Coupled Pacemaker Neurons|journal=Journal of Neurophysiology|date=January 1999|first=Robert|last=Butera|author2=John Rinzel |author3=Jeffrey Smith |s2cid=17905991|volume=82|issue=1|pages=1349–56|pmid=10400967|doi=10.1152/jn.1999.82.1.398}}</ref>

===Cerebellar cortex===
[[Cerebellum|Cerebellar]] [[Purkinje cell|Purkinje neurons]] have been proposed to have two distinct bursting modes: [[Dendrite|dendritically]] driven, by dendritic [[Calcium channel|{{chem|Ca|2+}} spikes]],<ref>{{cite journal |vauthors=Forrest MD, Wall MJ, Press DA, Feng J |title=The Sodium-Potassium Pump Controls the Intrinsic Firing of the Cerebellar Purkinje Neuron |journal=PLOS ONE |volume=7 |issue=12 |pages=e51169 |date=December 2012 |pmid=23284664 |pmc=3527461 |doi=10.1371/journal.pone.0051169|bibcode = 2012PLoSO...751169F |doi-access=free }}</ref> and [[Perikaryon|somatically]] driven, wherein the persistent [[Sodium channel|{{chem|Na|+}} current]] is the burst initiator and the [[Calcium-activated potassium channel|SK {{chem|K|+}} current]] is the burst terminator.<ref>{{cite journal |author=Forrest MD |title=Mathematical Model of Bursting in Dissociated Purkinje Neurons |journal=PLOS ONE |volume=8 |issue=8 |pages=e68765 |date=August 2013 |doi=10.1371/journal.pone.0068765|bibcode = 2013PLoSO...868765F |pmid=23967054 |pmc=3742666|doi-access=free }}</ref> Purkinje neurons may utilise these bursting forms in information coding to the [[deep cerebellar nuclei]].

==See also==
*[[Action potential]]
*[[Central pattern generator]]
*[[Dynamical systems]]
*[[Information theory]]

==References==
{{reflist|30em}}
Rinzel J. (1986) A formal Classification of Bursting Mechanisms in Excitable Systems. Proceedings of the International Congress of Mathematicians. Berkeley, California, USA

==External links==
Izhikevich E. M. (2006) [http://www.scholarpedia.org/article/Bursting Bursting]. ''Scholarpedia'', 1(3):1300

[[Category:Neuroscience]]
[[Category:Electrophysiology]]