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Burst firing is a pattern in which a neuron emits groups of closely spaced action potentials, separated by longer gaps. A burst criterion must specify the relevant timescale: an interspike interval counted as short in one preparation need not define a burst in another. A burst can arise from intrinsic membrane dynamics, coordinated inputs, or their interaction.

An invented spike train makes the distinction quantitative. Put five spikes at $0,10,20,30,40$ milliseconds and five more at $500,510,520,530,540$ milliseconds. There are ten spikes in the one-second observation window, as in a $10{\mathrm{s}}^{-1}$ tonic train, but most within-cluster interspike intervals are $10$ milliseconds and the gap between clusters is $460$ milliseconds. Mean count rate alone loses this organization.

A 2018 study combined recordings, pharmacology and modelling of lateral habenula neurons in rodent preparations. It linked bursting under its experimental conditions to NMDA receptors and T-type calcium channels, and manipulated firing mode by changing membrane conditions.^[ref] This is a mechanism tested in particular cells and preparations, not a definition requiring those exact channels in every bursting neuron.

An interspike interval is the elapsed time between consecutive action potentials in a spike train. Its probability distribution and dependence on previous activity can reveal a neuronal refractory period even when the average firing rate is unchanged.

A neuronal refractory period is the change in excitability following an action potential: recent firing changes whether, and how readily, a neuron can fire again. The absolute neuronal refractory period prevents a second regenerative action potential; during the relative neuronal refractory period, some stimuli that work after full recovery still fail. These are useful distinctions, but their durations are not universal constants. The preparation, temperature, starting membrane potential, stimulation protocol and criterion for detecting an action potential must accompany a measured interval.

The mechanism continues the opposing sodium and potassium electric currents described under action potential and the Hodgkin-Huxley model. After a spike, ion-channel inactivation leaves fewer sodium-selective voltage-gated ion channels available for regenerative depolarization, while persisting potassium electrical conductance opposes that depolarization. In the Hodgkin-Huxley model, recovery of $h$ restores sodium availability and relaxation of $n$ reduces potassium electrical conductance. Closed but available channels differ from inactivated channels: opening and recovery from ion-channel inactivation are different processes.^[ref]

This short memory matters for spike trains: a stimulus-only Poisson process can predict very short interspike intervals that a refractory neuron cannot produce. Neuronal paired-pulse recovery makes that memory visible. The phenomenological paired-pulse recovery example below separates a chosen recovery rule, pulse strength and event readout; refractory limits on neuronal firing then shows why an absolute bound is not a prediction of sustained firing rate.

If every interspike interval is at least $t_{\mathrm{abs}}>0$, a sustained spike train has mean firing rate at most $1/t_{\mathrm{abs}}$. Across a window of duration $T$, the event count satisfies $N(T)\le 1+T/t_{\mathrm{abs}}$; dividing by $T$ and taking the long-time limit gives the bound. The extra one accounts for a possible first event. The bound permits much slower firing and says nothing about whether stronger drive can maintain the limiting rate in a real neuron.

For the chosen phenomenological paired-pulse recovery, the hold alone gives $500\mathrm{Hz}$. Add the further assumption that every successful event resets precisely the same recovery curve, with no accumulation from earlier events. Then $0.35\mathrm{nA}$ onset-timed pulses can sustain at most $1000/4.942488\approx 202.327\mathrm{Hz}$ in that model. This repeatable reset is an extra assumption: a two-pulse result alone cannot establish it. A real neuron's sustained rate also depends on neural adaptation, input delivery and evolving ion-channel inactivation. The existing leaky integrate-and-fire model similarly adds integration time to its imposed hold.

A homogeneous Poisson process of rate $\lambda$ has interspike intervals with an exponential distribution, soWith the purely illustrative choices $\lambda =100\mathrm{Hz}$ and $t_{\mathrm{abs}}=0.002\mathrm{s}$, this is $1-e^{-0.2}\approx 0.181269$. Thus about $18.13\%$ of intervals predicted by that model violate this chosen hold. Matching a mean spike train count does not make a stimulus-only Poisson process respect recent firing.

A minimal alternative is a renewal process with independent and identically distributed intervals $S=t_{\mathrm{abs}}+X$, where $X$ has an exponential distribution of rate $\lambda$. Its hazard function is zero during the hold and $\lambda$ afterwards. Its mean interval is $t_{\mathrm{abs}}+1/\lambda$ and long-run firing rate isThe same $100{\mathrm{s}}^{-1}$ rate after a $2\mathrm{ms}$ hold gives $83.333\mathrm{Hz}$, not $100\mathrm{Hz}$. This separate stochastic example has no gradual relative recovery; it illustrates why an available-state rate differs from an observed mean firing rate. Smooth dependence on time since the last event can extend the hazard function, while longer histories require more than this simple renewal process. Time-rescaled spike-train diagnostics can test the resulting history-dependent predictions against recorded spike trains.

For a correctly specified conditional rate, transformed interspike intervals have independent unit-exponential distributions, apart from observation-boundary censoring. Their transforms $1-e^{-z_i}$ should be uniform. Distributional checks and serial-correlation checks assess a fitted spike model on held-out data. A history-dependent model must include past spikes in its conditional rate; stimulus-only Poisson spike-train likelihood fitting cannot automatically capture refractoriness.

Tonic firing is a sustained pattern of individual action potentials rather than brief, separated clusters characteristic of burst firing. In a specified preparation it may be relatively regular, but tonic does not require perfectly equal interspike intervals or one universal firing frequency. The term concerns timing, not a permanently fixed identity of the neuron.

For an invented one-second recording, ten action potentials at $0.05,0.15,\dots ,0.95$ seconds give a mean count rate of $10{\mathrm{s}}^{-1}$ and consecutive interspike intervals of $0.1$ seconds. Two clusters containing five spikes each can have the same total count with very different intervals. The average rate therefore does not specify whether a train is tonic or bursting.

Recordings from the lateral habenula in a 2018 study distinguished tonic and bursting modes and examined changes associated with membrane potential and receptor-dependent currents.^[ref] The same cell can change its temporal pattern under changed conditions. This illustrates why a firing-mode label must be attached to the recorded interval and experimental state, rather than inferred solely from the cell's name.