Understanding the Brain

# Bursting

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

Bursting 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 spiking are followed by quiescent, silent, periods. 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.

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 potentials, 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[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 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[11] 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.

### 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.[11] 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[6][12][13] and Ca2+[14] gated currents and spiking interplay between dendrites and the cell body.[15]

## 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. The Interspike Interval (ISI) histograms should then show a Poisson distribution.[16][17] 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.

## 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 perturbed form

\begin{align} \dot{x} =&\ f(x, u) &\mbox{(fast subsystem)} \\ \dot{u} =&\ \mu g(x, u) &\mbox{(slow subsystem)} \end{align}

where $f$ and $g$ are both Hodgkin–Huxley style relations, $\dot{x}$ is a vector representing the cell parameters relevant to the fast subsystem, $\dot{u}$ 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.[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 circle saddle homoclinic orbit supercritical Andronov-Hopf fold limit cycle
saddle node (fold) fold/ circle fold/ homoclinic fold/ Hopf fold/ fold cycle
saddle node on an invariant circle circle/ circle circle/ homoclinic circle/ Hopf circle/ fold cycle
supercritical Andronov-Hopf Hopf/ circle Hopf/ homoclinic Hopf/ Hopf Hopf/ fold cycle
subcritical 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.[11]

## 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 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.[18]

### 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][19][20] 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.

### 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. 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.[21] 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][22] Once these circuits have been activated, the subicular signal reverts to a single spiking mode.[23]

### pre-Bötzinger Complex

The pre-Bötzinger Complex (preBötC) is located in the 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 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[19] 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]

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