Bursting
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Bursting, or burst firing, is an extremely diverse general phenomenon of the activation patterns of
neurons A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. N ...
in the
central nervous system The central nervous system (CNS) is the part of the nervous system consisting primarily of the brain and spinal cord. The CNS is so named because the brain integrates the received information and coordinates and influences the activity of all par ...
and
spinal cord The spinal cord is a long, thin, tubular structure made up of nervous tissue, which extends from the medulla oblongata in the brainstem to the lumbar region of the vertebral column (backbone). The backbone encloses the central canal of the spi ...
where periods of rapid
action potential An action potential occurs when the membrane potential of a specific cell location rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, ...
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 Central pattern generators (CPGs) are self-organizing biological neural circuits that produce rhythmic outputs in the absence of rhythmic input. They are the source of the tightly-coupled patterns of neural activity that drive rhythmic and stereot ...
s, the transmission of
neural code Neural coding (or Neural representation) is a neuroscience field concerned with characterising the hypothetical relationship between the stimulus and the individual or ensemble neuronal responses and the relationship among the electrical activit ...
s, and some neuropathologies such as
epilepsy Epilepsy is a group of non-communicable neurological disorders characterized by recurrent epileptic seizures. Epileptic seizures can vary from brief and nearly undetectable periods to long periods of vigorous shaking due to abnormal electrical ...
. 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 Cellular neuroscience is a branch of neuroscience concerned with the study of neurons at a cellular level. This includes Morphology (biology), morphology and physiology, physiological properties of single neurons. Several techniques such as intrace ...
and is closely tied to the fields of
neural synchronization Neural oscillations, or brainwaves, are rhythmic or repetitive patterns of neural activity in the central nervous system. Neural tissue can generate oscillation, oscillatory activity in many ways, driven either by mechanisms within individual ne ...
,
neural coding Neural coding (or Neural representation) is a neuroscience field concerned with characterising the hypothetical relationship between the stimulus and the individual or ensemble neuronal responses and the relationship among the electrical activity o ...
,
plasticity Plasticity may refer to: Science * Plasticity (physics), in engineering and physics, the propensity of a solid material to undergo permanent deformation under load * Neuroplasticity, in neuroscience, how entire brain structures, and the brain it ...
, and
attention Attention is the behavioral and cognitive process of selectively concentrating on a discrete aspect of information, whether considered subjective or objective, while ignoring other perceivable information. William James (1890) wrote that "Atte ...
. 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 In genetics, the phenotype () is the set of observable characteristics or traits of an organism. The term covers the organism's morphology or physical form and structure, its developmental processes, its biochemical and physiological proper ...
of the cell.


Physiological context


Overview

Neurons typically operate by firing single
action potential An action potential occurs when the membrane potential of a specific cell location rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, ...
spikes in relative isolation as discrete input
postsynaptic potential Postsynaptic potentials are changes in the membrane potential of the postsynaptic terminal of a chemical synapse. Postsynaptic potentials are graded potentials, and should not be confused with action potentials although their function is to ini ...
s combine and drive the
membrane potential Membrane potential (also transmembrane potential or membrane voltage) is the difference in electric potential between the interior and the exterior of a biological cell. That is, there is a difference in the energy required for electric charges ...
across the 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 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. In each case, the physiological system is often 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 encodes the intensity of input into the bursting frequency where a neuron then acts as an
integrator An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output. Integration is an importan ...
. Intrinsic bursting is a more specialized phenomenon and is believed to play a much more diverse role in
neural computation Neural computation is the information processing performed by networks of neurons. Neural computation is affiliated with the philosophical tradition known as Computational theory of mind, also referred to as computationalism, which advances the th ...
.


Fast subsystem


Slow subsystem

Bursts differ from tonic firing, typically associated with
Poisson distributed In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known co ...
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''). During the bursting event, this slow subsystem modulates the timing and intensity of the emitted spikes and is thought to be important in the computational aspects of the resulting burst pattern. There are many discovered mechanisms of slow subsystems including voltage- and -gated currents and spiking interplay between
dendrite Dendrites (from Greek δένδρον ''déndron'', "tree"), also dendrons, are branched protoplasmic extensions of a nerve cell that propagate the electrochemical stimulation received from other neural cells to the cell body, or soma, of the n ...
s and the
cell body The soma (pl. ''somata'' or ''somas''), perikaryon (pl. ''perikarya''), neurocyton, or cell body is the bulbous, non-process portion of a neuron or other brain cell type, containing the cell nucleus. The word 'soma' comes from the Greek '' σῶμ ...
. The slow subsystem also is connected to
endogenous Endogenous substances and processes are those that originate from within a living system such as an organism, tissue, or cell. In contrast, exogenous substances and processes are those that originate from outside of an organism. For example, es ...
bursting patterns in neurons, where the pattern can be maintained completely by internal mechanism without any synaptic input. This process also relies on
calcium channel A calcium channel is an ion channel which shows selective permeability to calcium ions. It is sometimes synonymous with voltage-gated calcium channel, although there are also ligand-gated calcium channels. Comparison tables The following tables e ...
s, which depolarize the neuron by allowing an influx of calcium
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...
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 cascade Second messengers are intracellular signaling molecules released by the cell in response to exposure to extracellular signaling molecules—the first messengers. (Intercellular signals, a non-local form or cell signaling, encompassing both first me ...
within the cell which lower calcium influx and promote calcium efflux and 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.


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 In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as ...
(CV) of the interspike intervals (ISI) that is larger than one, or a
Fano factor In statistics, the Fano factor, like the coefficient of variation, is a measure of the dispersion of a probability distribution of a Fano noise. It is named after Ugo Fano, an Italian American physicist. The Fano factor is defined as :F=\frac, ...
of the spike count that is larger than one, because bursting leads to spike patterns that are more irregular than a
Poisson process In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one ...
(which has a CV and Fano factor equal to unity). Alternatively, the 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 In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a p ...
, 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 perturbed form : ''fast subsystem'': \dot = f(x, u) : ''slow subsystem'': \dot = \mu g(x, u) where f and g are both Hodgkin–Huxley style relations, \dot is a vector representing the cell parameters relevant to the fast subsystem, \dot is a vector representing the parameters of the slow modulation subsystem, and \mu \ll 1 is the ratio of the time scales between the fast and slow subsystems. Models of neuron dynamics generally exhibit a number of stable and unstable
attractor In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain ...
s in
phase space In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually ...
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 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. Of the most common 16, a few are well studied.


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.


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. 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.


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 A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range. Description In electronics and signal processing, a filter is usually a two-por ...
ing effect in order to encode for specific destination neurons and
multiplex Multiplex may refer to: * Multiplex (automobile), a former American car make * Multiplex (comics), a DC comic book supervillain * Multiplex (company), a global contracting and development company * Multiplex (assay), a biological assay which measu ...
signals along a single
axon An axon (from Greek ἄξων ''áxōn'', axis), or nerve fiber (or nerve fibre: see spelling differences), is a long, slender projection of a nerve cell, or neuron, in vertebrates, that typically conducts electrical impulses known as action po ...
. More generally, due to short-term synaptic depression and facilitation specific synapses can be resonant for certain frequencies and thus become viable specific targets for bursting cells. When combined with burst-dependent long-term plasticity, such multiplexing can allow neurons to coordinate synaptic plasticity across hierarchical networks.


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. 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. Since synchronization is related to
plasticity Plasticity may refer to: Science * Plasticity (physics), in engineering and physics, the propensity of a solid material to undergo permanent deformation under load * Neuroplasticity, in neuroscience, how entire brain structures, and the brain it ...
and
memory Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembered, ...
via
Hebbian plasticity Hebbian theory is a neuroscientific theory claiming that an increase in synaptic efficacy arises from a presynaptic cell's repeated and persistent stimulation of a postsynaptic cell. It is an attempt to explain synaptic plasticity, the adaptation ...
and
long-term potentiation In neuroscience, long-term potentiation (LTP) is a persistent strengthening of synapses based on recent patterns of activity. These are patterns of synaptic activity that produce a long-lasting increase in signal transmission between two neurons ...
the interplay with plasticity and intrinsic bursting is very important.


Information content and channel robustness

Due to the all-or-nothing nature of action potentials, single spikes can only encode
information Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...
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. 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 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 A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. No ...
s and provides a popular connection between
neural coding Neural coding (or Neural representation) is a neuroscience field concerned with characterising the hypothetical relationship between the stimulus and the individual or ensemble neuronal responses and the relationship among the electrical activity o ...
and
information theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...
.


Example bursting neuron circuits


Hippocampus

The
subiculum The subiculum (Latin for "support") is the most inferior component of the hippocampal formation. It lies between the entorhinal cortex and the CA1 subfield of the hippocampus proper. The subicular complex comprises a set of related structures in ...
, a component of the
hippocampal formation The hippocampal formation is a compound structure in the Temporal lobe#Medial temporal lobe, medial temporal lobe of the brain. It forms a c-shaped bulge on the floor of the temporal horn of the Lateral ventricles, lateral ventricle. There is no ...
, is thought to perform relaying of signals originating in the hippocampus to many other parts of the brain. 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. Once these circuits have been activated, the subicular signal reverts to a single spiking mode.


pre-Bötzinger complex

The
pre-Bötzinger complex The preBötzinger complex, sometimes written pre-Bötzinger complex (preBötC), is a functionally and anatomically specialized site in the ventral-lateral region of the lower medulla oblongata (i.e., lower brainstem). The preBötC is part of the ven ...
(preBötC) is located in ventrolateral
medulla Medulla or Medullary may refer to: Science * Medulla oblongata, a part of the brain stem * Renal medulla, a part of the kidney * Adrenal medulla, a part of the adrenal gland * Medulla of ovary, a stroma in the center of the ovary * Medulla of th ...
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 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.


Cerebellar cortex

Cerebellar The cerebellum (Latin for "little brain") is a major feature of the hindbrain of all vertebrates. Although usually smaller than the cerebrum, in some animals such as the mormyrid fishes it may be as large as or even larger. In humans, the cerebel ...
Purkinje neurons have been proposed to have two distinct bursting modes: dendritically driven, by dendritic spikes, and somatically driven, wherein the persistent current is the burst initiator and the SK current is the burst terminator. Purkinje neurons may utilise these bursting forms in information coding to the
deep cerebellar nuclei The cerebellum has four deep cerebellar nuclei embedded in the white matter in its center. 4 pairs of nuclei are embedded deep in the medullary centre, in the medial to lateral direction. They are fastigial nuclei, globose nuclei, emboliform nucl ...
.


See also

*
Action potential An action potential occurs when the membrane potential of a specific cell location rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, ...
*
Central pattern generator Central pattern generators (CPGs) are self-organizing biological neural circuits that produce rhythmic outputs in the absence of rhythmic input. They are the source of the tightly-coupled patterns of neural activity that drive rhythmic and stereot ...
*
Dynamical systems In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a p ...
*
Information theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...


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
Bursting
''Scholarpedia'', 1(3):1300 Neuroscience Electrophysiology