Bursting
Encyclopedia
Bursting is an extremely diverse general phenomenon of the activation patterns of neurons in the central nervous system
and spinal cord
where periods of rapid spiking
are followed by quiescent, silent, periods. Bursting is thought to be important in the operation of robust central pattern generators, the transmission of neural codes, and some neuropathologies such as epilepsy
. 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
, 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.
, spikes, in relative isolation as discrete input postsynaptic potential
combine and drive membrane voltage above the firing 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 subsystems, the fast and slow subsystems, linked together. The fast subsystem (see action potential
) is responsible for each spike the neuron produces and the slow subsystem is responsible for modulating 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
. Intrinsic bursting is a more specialized phenomenon and is believed to play a much more diverse role in neural computation.
When not bursting, the timing of separate neuron spikes are assumed independent and therefore are modeled by a Cox process
. The Interspike Interval (ISI) histograms should then show a Poisson distribution
. Spikes within a burst pattern are no longer independent and often closer together causing a bursting cell's ISI histogram to be bimodal with a mass at an ISI improbably short for a Cox process. Once a characteristic ISI for a neuron is found it is possible to determine an optimal cutoff threshold for spikes to be considered as a single burst and compute the chances of misclassification
.
form
Central nervous system
The central nervous system is the part of the nervous system that integrates the information that it receives from, and coordinates the activity of, all parts of the bodies of bilaterian animals—that is, all multicellular animals except sponges and radially symmetric animals such as jellyfish...
and spinal cord
Spinal cord
The spinal cord is a long, thin, tubular bundle of nervous tissue and support cells that extends from the brain . The brain and spinal cord together make up the central nervous system...
where periods of rapid spiking
Action potential
In physiology, an action potential is a short-lasting event in which the electrical membrane potential of a cell rapidly rises and falls, following a consistent trajectory. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and...
are followed by quiescent, silent, periods. Bursting is thought to be important in the operation of robust central pattern generators, the transmission of neural codes, and some neuropathologies such as epilepsy
Epilepsy
Epilepsy is a common chronic neurological disorder characterized by seizures. These seizures are transient signs and/or symptoms of abnormal, excessive or hypersynchronous neuronal activity in the brain.About 50 million people worldwide have epilepsy, and nearly two out of every three new cases...
. 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
Neural coding
Neural coding is a neuroscience-related field concerned with how sensory and other information is represented in the brain by networks of neurons. The main goal of studying neural coding is to characterize the relationship between the stimulus and the individual or ensemble neuronal responses and...
, plasticity
Neuroplasticity
Neuroplasticity is a non-specific neuroscience term referring to the ability of the brain and nervous system in all species to change structurally and functionally as a result of input from the environment. Plasticity occurs on a variety of levels, ranging from cellular changes involved in...
, and attention
Attention
Attention is the cognitive process of paying attention to one aspect of the environment while ignoring others. Attention is one of the most intensely studied topics within psychology and cognitive neuroscience....
.
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
Phenotype
A phenotype is an organism's observable characteristics or traits: such as its morphology, development, biochemical or physiological properties, behavior, and products of behavior...
of the cell.
Overview
Neurons typically operate by firing single action potentialsAction potential
In physiology, an action potential is a short-lasting event in which the electrical membrane potential of a cell rapidly rises and falls, following a consistent trajectory. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and...
, spikes, in relative isolation as discrete input postsynaptic potential
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 initiate or inhibit action potentials...
combine and drive membrane voltage above the firing threshold
Threshold potential
The threshold potential is the membrane potential to which a membrane must be depolarized to initiate an action potential.It often can be between −40 and -55 mV, but it can vary based upon several factors...
. 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 subsystems, the fast and slow subsystems, linked together. The fast subsystem (see action potential
Action potential
In physiology, an action potential is a short-lasting event in which the electrical membrane potential of a cell rapidly rises and falls, following a consistent trajectory. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and...
) is responsible for each spike the neuron produces and the slow subsystem is responsible for modulating the shape and intensity of these spikes before eventually triggering quiescence.
Input-driven bursting often encodes
Neural coding
Neural coding is a neuroscience-related field concerned with how sensory and other information is represented in the brain by networks of neurons. The main goal of studying neural coding is to characterize the relationship between the stimulus and the individual or ensemble neuronal responses and...
the intensity of input into the bursting frequency where a neuron then acts as an integrator
Integrator
An integrator is a device to perform the mathematical operation known as integration, a fundamental operation in calculus.The integration function is often part of engineering, physics, mechanical, chemical and scientific calculations....
. Intrinsic bursting is a more specialized phenomenon and is believed to play a much more diverse role in neural computation.
Slow subsystem
Bursts differ from tonic firing, rapid spiking at similar rates to bursting but continuing for long periods of time, in that bursting involves a physiological "slow subsystem" eventually depletes as the bursting continues and then must be replenished before the cell can burst again. 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 Ca2+ gated currents and spiking interplay between dendrites and the cell body.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.When not bursting, the timing of separate neuron spikes are assumed independent and therefore are modeled by a Cox process
Cox process
A Cox process , also known as a doubly stochastic Poisson process or mixed Poisson process, is a stochastic process which is a generalization of a Poisson process...
. The Interspike Interval (ISI) histograms should then show a Poisson distribution
Poisson distribution
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 and/or space if these events occur with a known average rate and independently of the time since...
. Spikes within a burst pattern are no longer independent and often closer together causing a bursting cell's ISI histogram to be bimodal with a mass at an ISI improbably short for a Cox process. Once a characteristic ISI for a neuron is found it is possible to determine an optimal cutoff threshold for spikes to be considered as a single burst and compute the chances of misclassification
Type I and type II errors
In statistical test theory the notion of statistical error is an integral part of hypothesis testing. The test requires an unambiguous statement of a null hypothesis, which usually corresponds to a default "state of nature", for example "this person is healthy", "this accused is not guilty" or...
.
Mathematical models
Neuron behavior is often modeled as a single-compartment, non-linear dynamical systems where the neuron states representative of physiological quantities such as membrane voltage, current flow, and the concentrations of various ions intra- and extracellularly. These models most generally take the singularly perturbedPerturbation theory
Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem...
form
-
where
and 
are both Hodgkin–Huxley style relations, 
is a vector representing the cell parameters relevant to the fast subsystem, 
is a vector representing the parameters of the slow modulation subsystem, and 
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 attractors in phase spacePhase spaceIn mathematics and physics, a phase space, introduced by Willard Gibbs in 1901, is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the 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 attractorStable attractorA stable attractor in chaos theory or biology is an equilibrium state into which a system settles until disrupted by a change in the environment...
representing an action potential. In bursting neurons, these dynamic spaces bifurcateBifurcation theoryBifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations...
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.
Common combinations of bifurcations saddle node Saddle-node bifurcationIn the mathematical area of bifurcation theory a saddle-node bifurcation, tangential bifurcation or fold bifurcation is a local bifurcation in which two fixed points of a dynamical system collide and annihilate each other. The term 'saddle-node bifurcation' is most often used in reference to...
on an invariant circlesaddle homoclinic orbit Homoclinic orbitIn mathematics, a homoclinic orbit is a trajectory of a flow of a dynamical system which joins a saddle equilibrium point to itself. More precisely, a homoclinic orbit lies in the intersection of the stable manifold and the unstable manifold of an equilibrium.Homoclinic orbits and homoclinic points...
supercritical Andronov-Hopf Hopf bifurcationIn the mathematical theory of bifurcations, a Hopf or Poincaré–Andronov–Hopf bifurcation, named after Henri Poincaré, Eberhard Hopf, and Aleksandr Andronov, is a local bifurcation in which a fixed point of a dynamical system loses stability as a pair of complex conjugate eigenvalues of...
fold limit cycle saddle node Saddle-node bifurcationIn the mathematical area of bifurcation theory a saddle-node bifurcation, tangential bifurcation or fold bifurcation is a local bifurcation in which two fixed points of a dynamical system collide and annihilate each other. The term 'saddle-node bifurcation' is most often used in reference to...
(fold)fold/ circle fold/ homoclinic fold/ Hopf fold/ fold cycle saddle node Saddle-node bifurcationIn the mathematical area of bifurcation theory a saddle-node bifurcation, tangential bifurcation or fold bifurcation is a local bifurcation in which two fixed points of a dynamical system collide and annihilate each other. The term 'saddle-node bifurcation' is most often used in reference to...
on an invariant circlecircle/ circle circle/ homoclinic circle/ Hopf circle/ fold cycle supercritical Andronov-Hopf Hopf bifurcationIn the mathematical theory of bifurcations, a Hopf or Poincaré–Andronov–Hopf bifurcation, named after Henri Poincaré, Eberhard Hopf, and Aleksandr Andronov, is a local bifurcation in which a fixed point of a dynamical system loses stability as a pair of complex conjugate eigenvalues of...Hopf/ circle Hopf/ homoclinic Hopf/ Hopf Hopf/ fold cycle subcritical Andronov-Hopf Hopf bifurcationIn the mathematical theory of bifurcations, a Hopf or Poincaré–Andronov–Hopf bifurcation, named after Henri Poincaré, Eberhard Hopf, and Aleksandr Andronov, is a local bifurcation in which a fixed point of a dynamical system loses stability as a pair of complex conjugate eigenvalues of...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.
Purposes of bursting
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.
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 filterBand-pass filterA band-pass filter is a device that passes frequencies within a certain range and rejects frequencies outside that range.Optical band-pass filters are of common usage....
ing effect in order to encode for specific destination neurons and multiplexMultiplexingThe multiplexed signal is transmitted over a communication channel, which may be a physical transmission medium. The multiplexing divides the capacity of the low-level communication channel into several higher-level logical channels, one for each message signal or data stream to be transferred...
signals along a single axonAxonAn axon is a long, slender projection of a nerve cell, or neuron, that conducts electrical impulses away from the neuron's cell body or soma....
. More generally, due to short-term synaptic depression and facilitationNeural facilitationNeural facilitation, also known as paired pulse facilitation, is a concept in neuroscience where an increase in the postsynaptic potential is evoked by a second impulse....
specific synapses can be resonant for certain frequencies and thus become viable specific targets for bursting cells.
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 plasticityPlasticity (physics)In physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the...
and memoryMemoryIn psychology, memory is an organism's ability to store, retain, and recall information and experiences. Traditional studies of memory began in the fields of philosophy, including techniques of artificially enhancing memory....
via Hebbian plasticityHebbian theoryHebbian theory describes a basic mechanism for synaptic plasticity wherein an increase in synaptic efficacy arises from the presynaptic cell's repeated and persistent stimulation of the postsynaptic cell...
and Long-term potentiationLong-term potentiationIn neuroscience, long-term potentiation is a long-lasting enhancement in signal transmission between two neurons that results from stimulating them synchronously. It is one of several phenomena underlying synaptic plasticity, the ability of chemical synapses to change their strength...
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 informationInformation theoryInformation theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
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 capacityChannel capacityIn electrical engineering, computer science and information theory, channel capacity is the tightest upper bound on the amount of information that can be reliably transmitted over a communications channel...
in neuronal communications and provides a popular connection between neural codingNeural codingNeural coding is a neuroscience-related field concerned with how sensory and other information is represented in the brain by networks of neurons. The main goal of studying neural coding is to characterize the relationship between the stimulus and the individual or ensemble neuronal responses and...
and information theoryInformation theoryInformation theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
.
Hippocampus
The subiculumSubiculumThe subiculum is the most inferior component of the hippocampal formation. It lies between the entorhinal cortex and the CA1 subfield of the hippocampus proper.-Paths:...
, a component of the hippocampal formationHippocampal formationThe hippocampal formation is a compound structure in the medial temporal lobe of the brain. There is currently no consensus concerning which brain regions are encompassed by the term, with some authors defining it as the dentate gyrus, the hippocampus proper and the subiculum; and others including...
, 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 ComplexPre-Botzinger complexThe Pre-Bötzinger Complex is a cluster of interneurons in the ventrolateral medulla of the brainstem, which is essential to the generation of respiratory rhythm in mammals...
(preBötC) is located in the ventrolateral medullaMedullaMedulla refers to the middle of something and derives from the Latin word for marrow. Its anatomical uses include:* Medulla oblongata, a part of the brain stem* Renal medulla, a part of the kidney* Adrenal medulla, a part of the adrenal gland...
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 level of metabollic demand, the preBötC activity is modulated over a wide range of frequencies and able to entrain the respiratory system to meet metabollic demand. While pacemaker neurons do not necessary 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.
See also
- Action PotentialAction potentialIn physiology, an action potential is a short-lasting event in which the electrical membrane potential of a cell rapidly rises and falls, following a consistent trajectory. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and...
- Tonic Firing
- Information TheoryInformation theoryInformation theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
- Synchrony
- Central pattern generatorCentral pattern generatorCentral pattern generators are neural networks that produce rhythmic patterned outputs without sensory feedback. CPGs have been shown to produce rhythmic outputs resembling normal "rhythmic motor pattern production" even in isolation from motor and sensory feedback from limbs and other muscle...
- Dynamical Systems
External links
Izhikevich E. M. (2006) Bursting. Scholarpedia, 1(3):1300- Action Potential