Bursting

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Trace of modeled oxytocin-sensitive neuron showing bursts Bursting-recording.png
Trace of modeled oxytocin-sensitive neuron showing bursts

Bursting, or burst firing, is an extremely diverse [1] general phenomenon of the activation patterns of neurons in the central nervous system [2] [3] and spinal cord [4] 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 generators, [5] [6] [7] the transmission of neural codes, [8] [9] and some neuropathologies such as epilepsy. [10] 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.

Contents

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 potentials combine and drive the membrane potential 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 [11] 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. [3] [11]

In each case, the physiological system is often [ citation needed ] 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 ] encodes the intensity of input into the bursting frequency [11] where a neuron then acts as an integrator. Intrinsic bursting is a more specialized phenomenon and is believed [ by whom? ] to play a much more diverse role in neural computation. [ clarification needed ]

Fast subsystem

Slow subsystem

Bursts differ from tonic firing, typically associated with 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 ). [11] During the bursting event, this slow subsystem modulates the timing and intensity of the emitted spikes and is thought [ by whom? ] to be important in the computational aspects [ clarification needed ] of the resulting burst pattern. There are many discovered mechanisms of slow subsystems including voltage- [6] [12] [13] and Ca2+-gated [14] currents and spiking interplay between dendrites and the cell body. [15]

The slow subsystem also is connected to endogenous bursting patterns in neurons, where the pattern can be maintained completely by internal mechanism without any synaptic input. This process also relies on calcium channels, which depolarize the neuron by allowing an influx of calcium ions. 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 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. [16]

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 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 perturbed form

fast subsystem:
slow subsystem:

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. [11]

Models of neuron dynamics generally exhibit a number of stable and unstable attractors 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 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. [11] Of the most common 16, a few are well studied.

Common combinations of bifurcations
saddle node on an invariant circlesaddle homoclinic orbit supercritical Andronov-Hopf fold limit cycle
saddle node (fold)fold/ circlefold/ homoclinicfold/ Hopffold/ fold cycle
saddle node on an invariant circlecircle/ circlecircle/ homocliniccircle/ Hopfcircle/ fold cycle
supercritical Andronov-Hopf Hopf/ circleHopf/ homoclinicHopf/ HopfHopf/ fold cycle
subcritical Andronov-Hopf subHopf/ circlesubHopf/ homoclinicsubHopf/ HopfsubHopf/ 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. [11]

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. [17] 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. [18]

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 filtering effect in order to encode for specific destination neurons and multiplex signals along a single axon. [11] 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. [19] When combined with burst-dependent long-term plasticity, such multiplexing can allow neurons to coordinate synaptic plasticity across hierarchical networks. [17] [20]

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. [11] [21] [22] 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. [7] Since synchronization is related to plasticity and memory via Hebbian plasticity and long-term potentiation the interplay with plasticity and intrinsic bursting is very important[ citation needed ].

Information content and channel robustness

Due to the all-or-nothing nature of action potentials, single spikes can only encode 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 ]. 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 [9] 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 communications 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. [23] 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. [2] [24] Once these circuits have been activated, the subicular signal reverts to a single spiking mode. [25]

pre-Bötzinger complex

The pre-Bötzinger complex (preBötC) is located in ventrolateral 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 [21] 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. [7]

Cerebellar cortex

Cerebellar Purkinje neurons have been proposed to have two distinct bursting modes: dendritically driven, by dendritic Ca2+
 spikes, [26] and somatically driven, wherein the persistent Na+
 current is the burst initiator and the SK K+
 current is the burst terminator. [27] Purkinje neurons may utilise these bursting forms in information coding to the deep cerebellar nuclei.

See also

Related Research Articles

<span class="mw-page-title-main">Dendrite</span> Small projection on a neuron that receives signals

A dendrite or dendron is a branched protoplasmic extension of a nerve cell that propagates the electrochemical stimulation received from other neural cells to the cell body, or soma, of the neuron from which the dendrites project. Electrical stimulation is transmitted onto dendrites by upstream neurons via synapses which are located at various points throughout the dendritic tree.

Hebbian theory is a neuropsychological 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 of brain neurons during the learning process. It was introduced by Donald Hebb in his 1949 book The Organization of Behavior. The theory is also called Hebb's rule, Hebb's postulate, and cell assembly theory. Hebb states it as follows:

Let us assume that the persistence or repetition of a reverberatory activity tends to induce lasting cellular changes that add to its stability. ... When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency, as one of the cells firing B, is increased.

In neuroscience, synaptic plasticity is the ability of synapses to strengthen or weaken over time, in response to increases or decreases in their activity. Since memories are postulated to be represented by vastly interconnected neural circuits in the brain, synaptic plasticity is one of the important neurochemical foundations of learning and memory.

Spike-timing-dependent plasticity (STDP) is a biological process that adjusts the strength of connections between neurons in the brain. The process adjusts the connection strengths based on the relative timing of a particular neuron's output and input action potentials. The STDP process partially explains the activity-dependent development of nervous systems, especially with regard to long-term potentiation and long-term depression.

<span class="mw-page-title-main">Pyramidal cell</span> Projection neurons in the cerebral cortex and hippocampus

Pyramidal cells, or pyramidal neurons, are a type of multipolar neuron found in areas of the brain including the cerebral cortex, the hippocampus, and the amygdala. Pyramidal cells are the primary excitation units of the mammalian prefrontal cortex and the corticospinal tract. Pyramidal neurons are also one of two cell types where the characteristic sign, Negri bodies, are found in post-mortem rabies infection. Pyramidal neurons were first discovered and studied by Santiago Ramón y Cajal. Since then, studies on pyramidal neurons have focused on topics ranging from neuroplasticity to cognition.

<span class="mw-page-title-main">Neural circuit</span> Network or circuit of neurons

A neural circuit is a population of neurons interconnected by synapses to carry out a specific function when activated. Multiple neural circuits interconnect with one another to form large scale brain networks.

<span class="mw-page-title-main">Purkinje cell</span> Specialized neuron in the cerebellum

Purkinje cells, or Purkinje neurons, are a class of GABAergic inhibitory neurons located in the cerebellum. They are named after their discoverer, Czech anatomist Jan Evangelista Purkyně, who characterized the cells in 1839.

Schaffer collaterals are axon collaterals given off by CA3 pyramidal cells in the hippocampus. These collaterals project to area CA1 of the hippocampus and are an integral part of memory formation and the emotional network of the Papez circuit, and of the hippocampal trisynaptic loop. It is one of the most studied synapses in the world and named after the Hungarian anatomist-neurologist Károly Schaffer.

<span class="mw-page-title-main">Neural oscillation</span> Brainwaves, repetitive patterns of neural activity in the central nervous system

Neural oscillations, or brainwaves, are rhythmic or repetitive patterns of neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms within individual neurons or by interactions between neurons. In individual neurons, oscillations can appear either as oscillations in membrane potential or as rhythmic patterns of action potentials, which then produce oscillatory activation of post-synaptic neurons. At the level of neural ensembles, synchronized activity of large numbers of neurons can give rise to macroscopic oscillations, which can be observed in an electroencephalogram. Oscillatory activity in groups of neurons generally arises from feedback connections between the neurons that result in the synchronization of their firing patterns. The interaction between neurons can give rise to oscillations at a different frequency than the firing frequency of individual neurons. A well-known example of macroscopic neural oscillations is alpha activity.

<span class="mw-page-title-main">Neuronal noise</span> Random electric fluctuations in neurons

Neuronal noise or neural noise refers to the random intrinsic electrical fluctuations within neuronal networks. These fluctuations are not associated with encoding a response to internal or external stimuli and can be from one to two orders of magnitude. Most noise commonly occurs below a voltage-threshold that is needed for an action potential to occur, but sometimes it can be present in the form of an action potential; for example, stochastic oscillations in pacemaker neurons in suprachiasmatic nucleus are partially responsible for the organization of circadian rhythms.

Neural coding is a neuroscience field concerned with characterising the hypothetical relationship between the stimulus and the neuronal responses, and the relationship among the electrical activities of the neurons in the ensemble. Based on the theory that sensory and other information is represented in the brain by networks of neurons, it is believed that neurons can encode both digital and analog information.

The preBötzinger complex, often abbreviated as preBötC, is a functionally and anatomically specialized site in the ventral-lateral region of the lower medulla oblongata. The preBötC is part of the ventral respiratory group of respiratory related interneurons. Its foremost function is to generate the inspiratory breathing rhythm in mammals. In addition, the preBötC is widely and paucisynaptically connected to higher brain centers that regulate arousal and excitability more generally such that respiratory brain function is intimately connected with many other rhythmic and cognitive functions of the brain and central nervous system. Further, the preBötC receives mechanical sensory information from the airways that encode lung volume as well as pH, oxygen, and carbon dioxide content of circulating blood and the cerebrospinal fluid.

Neural backpropagation is the phenomenon in which, after the action potential of a neuron creates a voltage spike down the axon, another impulse is generated from the soma and propagates towards the apical portions of the dendritic arbor or dendrites. In addition to active backpropagation of the action potential, there is also passive electrotonic spread. While there is ample evidence to prove the existence of backpropagating action potentials, the function of such action potentials and the extent to which they invade the most distal dendrites remain highly controversial.

<span class="mw-page-title-main">Biological neuron model</span> Mathematical descriptions of the properties of certain cells in the nervous system

Biological neuron models, also known as spiking neuron models, are mathematical descriptions of neurons. In particular, these models describe how the voltage potential across the cell membrane changes over time. In an experimental setting, stimulating neurons with an electrical current generates an action potential, that propagates down the neuron's axon. This axon can branch out and connect to a large number of downstream neurons at sites called synapses. At these synapses, the spike can cause release of a biochemical substance (neurotransmitter), which in turn can change the voltage potential of downstream neurons, potentially leading to spikes in those downstream neurons, thus propagating the signal. As many as 85% of neurons in the neocortex, the outermost layer of the mammalian brain, consists of excitatory pyramidal neurons, and each pyramidal neuron receives tens of thousands of inputs from other neurons. Thus, spiking neurons are a major information processing unit of the nervous system.

<span class="mw-page-title-main">Subthreshold membrane potential oscillations</span>

Subthreshold membrane potential oscillations are membrane oscillations that do not directly trigger an action potential since they do not reach the necessary threshold for firing. However, they may facilitate sensory signal processing.

<span class="mw-page-title-main">Dendritic spike</span> Action potential generated in the dendrite of a neuron

In neurophysiology, a dendritic spike refers to an action potential generated in the dendrite of a neuron. Dendrites are branched extensions of a neuron. They receive electrical signals emitted from projecting neurons and transfer these signals to the cell body, or soma. Dendritic signaling has traditionally been viewed as a passive mode of electrical signaling. Unlike its axon counterpart which can generate signals through action potentials, dendrites were believed to only have the ability to propagate electrical signals by physical means: changes in conductance, length, cross sectional area, etc. However, the existence of dendritic spikes was proposed and demonstrated by W. Alden Spencer, Eric Kandel, Rodolfo Llinás and coworkers in the 1960s and a large body of evidence now makes it clear that dendrites are active neuronal structures. Dendrites contain voltage-gated ion channels giving them the ability to generate action potentials. Dendritic spikes have been recorded in numerous types of neurons in the brain and are thought to have great implications in neuronal communication, memory, and learning. They are one of the major factors in long-term potentiation.

<span class="mw-page-title-main">Nonsynaptic plasticity</span> Form of neuroplasticity

Nonsynaptic plasticity is a form of neuroplasticity that involves modification of ion channel function in the axon, dendrites, and cell body that results in specific changes in the integration of excitatory postsynaptic potentials and inhibitory postsynaptic potentials. Nonsynaptic plasticity is a modification of the intrinsic excitability of the neuron. It interacts with synaptic plasticity, but it is considered a separate entity from synaptic plasticity. Intrinsic modification of the electrical properties of neurons plays a role in many aspects of plasticity from homeostatic plasticity to learning and memory itself. Nonsynaptic plasticity affects synaptic integration, subthreshold propagation, spike generation, and other fundamental mechanisms of neurons at the cellular level. These individual neuronal alterations can result in changes in higher brain function, especially learning and memory. However, as an emerging field in neuroscience, much of the knowledge about nonsynaptic plasticity is uncertain and still requires further investigation to better define its role in brain function and behavior.

Developmental plasticity is a general term referring to changes in neural connections during development as a result of environmental interactions as well as neural changes induced by learning. Much like neuroplasticity, or brain plasticity, developmental plasticity is specific to the change in neurons and synaptic connections as a consequence of developmental processes. A child creates most of these connections from birth to early childhood. There are three primary methods by which this may occur as the brain develops, but critical periods determine when lasting changes may form. Developmental plasticity may also be used in place of the term phenotypic plasticity when an organism in an embryonic or larval stage can alter its phenotype based on environmental factors. However, a main difference between the two is that phenotypic plasticity experienced during adulthood can be reversible, whereas traits that are considered developmentally plastic set foundations during early development that remain throughout the life of the organism.

<span class="mw-page-title-main">Theta model</span>

The theta model, or Ermentrout–Kopell canonical model, is a biological neuron model originally developed to mathematically describe neurons in the animal Aplysia. The model is particularly well-suited to describe neural bursting, which is characterized by periodic transitions between rapid oscillations in the membrane potential followed by quiescence. This bursting behavior is often found in neurons responsible for controlling and maintaining steady rhythms such as breathing, swimming, and digesting. Of the three main classes of bursting neurons, the theta model describes parabolic bursting, which is characterized by a parabolic frequency curve during each burst.

An autapse is a chemical or electrical synapse from a neuron onto itself. It can also be described as a synapse formed by the axon of a neuron on its own dendrites, in vivo or in vitro.

References

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Izhikevich E. M. (2006) Bursting. Scholarpedia, 1(3):1300

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