Spike-frequency adaptation · Lobeworks/17
Spike-frequency adaptation is the slowing of a neuron's firing rate while its input stays constant: the intervals between spikes stretch, so a cell that starts at 200 Hz may settle at 40 Hz, because every spike leaves behind a small outward current that makes the next one harder.
Spike-frequency adaptation. Spike-frequency adaptation is the slowing of a neuron's firing rate while its input stays constant: the intervals between spikes stretch, so a cell that starts at 200 Hz may settle at 40 Hz, because every spike leaves behind a small outward current that makes the next one harder.
The brakes are potassium currents that outlast the spike. Each action potential lets in some calcium, which opens calcium-activated potassium channels (SK and BK) in proportion to how much has piled up, gKCa=gˉKCa s([Ca2+])g_{K_{Ca}} = \bar g_{K_{Ca}}, s([\text{Ca}^{2+}])gKCa=gˉKCas([Ca2+]). Slow voltage-gated potassium channels add the M-current (the KCNQ or Kv7 channels, named in 1980 for being shut by muscarinic receptors), and the sodium-potassium pump adds an outward current of its own. Every potassium current pulls the voltage towards EKE_KEK, around −90 mV, IK=gK(V−EK)I_K = g_K (V - E_K)IK=gK(V−EK), so the membrane dips below rest after each spike, the afterhyperpolarisation (AHP). If the next spike comes before the dip has faded, the dips add up. In the membrane equation the sum appears as one more current,
CmdVdt=−INa−IK−Iadapt−Ileak+IinputC_m \frac{dV}{dt} = -I_{\text{Na}} - I_{\text{K}} - I_{\text{adapt}} - I_{\text{leak}} + I_{\text{input}}CmdtdV=−INa−IK−Iadapt−Ileak+Iinput
and as IadaptI_{\text{adapt}}Iadapt grows, the same input takes longer to reach threshold. The adaptive exponential integrate-and-fire model of Brette and Gerstner (2005) reduces all of it to one variable www, which decays between spikes and jumps by bbb at each one:
τwdwdt=a (V−EL)−w,w←w+b at each spike\tau_w \frac{dw}{dt} = a\,(V - E_L) - w, \qquad w \leftarrow w + b \ \text{at each spike}τwdtdw=a(V−EL)−w,w←w+b at each spike
It is a filter, and neither good nor bad. A cell that adapts answers mostly to the start or the change of a stimulus and quiets down while it lasts; a cell that does not keeps signalling the stimulus for as long as it is there. Which one a circuit needs depends on the job.
It is tunable by the brain. Acetylcholine, through muscarinic receptors, shuts the M-current and so reduces adaptation, which makes cortical cells more excitable; it is one of the ways the brain's arousal systems change how neurons answer the same input.
It runs on several clocks at once. The fast AHP lasts milliseconds, the calcium-driven one tens to hundreds, and the pump and slow sodium inactivation up to seconds, so a long train slows in stages.
Every spike pulls a small brake, and when the neuron fires fast the brakes pile up.
The spacing of its spikes is the record of how much brake is on.
Questions: Is spike-frequency adaptation good or bad for a neuron? Neither: it is a computational property, close to a filter in time. A cell that does not adapt holds 200, 200, 200 Hz for as long as the stimulus lasts, which suits a signal that must be sustained and precise. A cell that adapts falls from 200 towards 40 Hz under the same stimulus, so it signals mostly the onset or a change and quiets down while the stimulus stays, much like a high-pass filter. What is it called when a neuron fires more and more slowly under a constant input, and how is it written as a model? Spike-frequency adaptation: the intervals stretch, so a cell may go from 200 Hz down through 150, 100 and 60 to 40 Hz with the input unchanged. In the adaptive exponential integrate-and-fire model it is one variable, an adapting current www, with τw dw/dt=a(V−EL)−w\tau_w,dw/dt = a(V - E_L) - wτwdw/dt=a(V−EL)−w between spikes and w←w+bw \leftarrow w + bw←w+b at each spike. Each spike adds a small brake bbb that decays with τw\tau_wτw; firing fast stacks the brakes faster than they fade. What is the dip below rest after a spike called, and why does it deepen during a train? The afterhyperpolarisation, or AHP. Potassium currents that outlast the spike pull the voltage towards EKE_KEK, around −90 mV, through IK=gK(V−EK)I_K = g_K(V - E_K)IK=gK(V−EK). Some of them are opened by the calcium each spike lets in, gKCa=gˉKCa s([Ca2+])g_{K_{Ca}} = \bar g_{K_{Ca}},s([\text{Ca}^{2+}])gKCa=gˉKCas([Ca2+]), so the more spikes in a row, the more calcium, the more open channels and the deeper the dip: when the next spike comes before the last dip has faded, the two add up. What is the M-current, which channels carry it and why is it called M? A slow potassium current that opens with depolarisation and does not inactivate, carried by KCNQ channels (Kv7, mainly KCNQ2 and KCNQ3). It was named M in 1980 by Brown and Adams because muscarinic acetylcholine receptors shut it. It builds up during a train and adds to adaptation, so shutting it with acetylcholine makes a neuron fire more and adapt less.