Dynamics of neural excitability Romain Brette Computational neuroscience
Dynamics of neural excitability Romain Brette Computational neuroscience of sensory systems romain. brette@inserm. fr
The spike threshold action potential postsynaptic potential (PSP) firing threshold temporal integration
Questions 1. Is there a voltage threshold? If yes, is it equal to the onset voltage? If yes, which one? Kole & Stuart (2008)
Questions 2. What determines the value of the threshold? 3. How does the spike threshold vary? 4. What difference does it make?
IS THERE A VOLTAGE THRESHOLD FOR SPIKE INITIATION? Brette, R. (2013). Sharpness of spike initiation in neurons explained by compartmentalization. PLo. S Computational Biology
The « sharpness » of spike initiation 1) Spikes have sharp onsets in recordings, unlike in Hodgkin-Huxley models 2) I-V relationship at soma is very sharp V Naundorf et al (2006) Badel et al. (J Neurophysiol 2008)
The « sharpness » of spike initiation 1) Spikes have sharp onsets in recordings, unlike in Hodgkin-Huxley models 2) I-V relationship at soma is very sharp 3) Integrate-and-fire models can predict precise spike trains of neurons 4) Cortical neurons transmit high frequency inputs (>200 Hz) Naundorf et al (2006)
Spikes are initiated in the axon Stuart, Schiller, Sakmann (J Physiol 1997)
Model of axonal initiation I The soma is a current sink soma Va Ra. I Vs (Ohm’s law) Brette, R. (2013). Sharpness of spike initiation in neurons explained by compartmentalization. PLo. S Comp Biol.
Model of axonal initiation I The soma is a current sink soma Va Ra. I Vs (Ohm’s law)
Model of axonal initiation Na activation I=f(Va) soma Va Ra. I Vs
Model of axonal initiation I=f(Va) I=(Va-Vs)/Ra Lateral and Na currents must match soma Vs I=( V I (n. A) a -V s )/R a Vs I=f(Va)
Distal axonal initiation I=f(Va) I=(Va-Vs)/Ra Lateral and Na currents must match soma Vs Vs I=f(Va) I (n. A) a a V ( I= /R ) s V Discrete opening of Na channels
A view from the soma Lateral current flows abruptly when a voltage threshold is exceeded m Na channels open in an all-or-none fashion
A view from the soma A fairly good phenomenological description: - below Vt, no sodium current - when Vm reaches Vt: all channels open (spike) a. k. a. the integrate-and-fire model ! with axonal initiation Vt m single compartment HH model
Answers yes 1. Is there a voltage threshold? If yes, is it equal to the onset voltage? yes X If yes, which one? Kole & Stuart (2008)
WHAT DETERMINES THE VALUE OF THE THRESHOLD?
Model of axonal initiation I=f(Va) I=(Va-Vs)/Ra Lateral and Na currents must match soma Vs Fixed point equation f(Va) = (Va-Vs)/Ra I (n. A) Spike threshold = bifurcation point (= Vs when solution jumps) Na activation The threshold equation ka V 1/2
How about other channels? I=f(Va) I=(Va-Vs)/Ra soma Vs IK Vs Va Ra. IK There also K+ channels! If the axonal threshold is unchanged, then the somatic threshold increases by –Ra. IK (Ohm’s law) The threshold equation
HOW DOES THE SPIKE THRESHOLD VARY? Platkiewicz, J. & Brette, R. A Threshold Equation for Action Potential Initiation. PLo. S Comp Biol 6(7): e 1000850. doi: 10. 1371 Fontaine B, Peña JL, Brette R (2014). Spike-threshold adaptation predicted by membrane potential dynamics in vivo. PLo. S Comp Biol
(Azouz & Gray, 2000) The spike threshold is not fixed The spike threshold is variable in vivo Membrane potential Threshold Large threshold variability (>10 m. V) Voltage (m. V)
(Wilent & Contreras, 2005) The threshold depends on depolarization speed In the visual cortex (Azouz & Gray 2003) 2 ms The threshold adapts to the membrane potential Spike threshold is inversely correlated with depolarization speed Mean membrane potential (m. V)
Two possible mechanisms Inactivation of Na channels decreases threshold Activation of K+ channels increases threshold Huguenard et al. (1988) Na inactivation: g. Na proportional to h (= non-inactivated channels) The « threshold equation »
Validation in a multicompartmental model Prediction:
Validation in a multicompartmental model
Threshold dynamics Example with linear membrane equation: « Steady-state threshold »
The steady-state threshold Inactivation curve where ka/ki 1
Testing the model In vivo intracellular recordings in barn owl IC (JL Peña) Vm Ө We fit a threshold model to predict spikes Fontaine B, Peña JL, Brette R (2014). Spike-threshold adaptation predicted by membrane potential dynamics in vivo. PLo. S Comp Biol
Testing the model Fontaine B, Peña JL, Brette R (2014). Spike-threshold adaptation predicted by membrane potential dynamics in vivo. PLo. S Comp Biol
WHAT DIFFERENCE DOES IT MAKE? Platkiewicz, J. & Brette, R. Impact of sodium channel inactivation on spike threshold dynamics and synaptic integration. PLo. S Comp Biol 7(5): e 1001129. doi: 10. 1371 Fontaine B, Peña JL, Brette R (2014). Spike-threshold adaptation predicted by membrane potential dynamics in vivo. PLo. S Comp Biol
Synaptic integration with adaptive threshold Above Vi, threshold is a low-pass filtered version of the membrane potential Threshold VT « threshold PSP » PSP
The effective PSP Threshold PSP q V Time (ms) Distance to threshold: Fixed threshold « Effective PSP » shorter integration time constant V-q
Sharpening and noise reduction PSPs « Noise » reduction Autocorrelation Effective time constant Fontaine B, Peña JL, Brette R (2014). Spike-threshold adaptation predicted by membrane potential dynamics in vivo. PLo. S Comp Biol
Summary 1) There is a sharp voltage threshold because of compartmentalization. 2) Spike threshold depends on AIS geometry, Na channel properties, K+ currents 3) Spike threshold adapts on a short timescale 4) Threshold adaptation shortens integration time constant and reduces effective variability « Effective PSP »
Thank you! Platkiewicz, J. & Brette, R. A Threshold Equation for Action Potential Initiation. PLo. S Comp Biol 6(7): e 1000850. doi: 10. 1371 Jonathan Platkiewicz, J. & Brette, R. Impact of sodium channel inactivation on spike threshold dynamics and synaptic integration. PLo. S Comp Biol 7(5): e 1001129. doi: 10. 1371 Fontaine B, Peña JL, Brette R (2014). Spike-threshold adaptation predicted by membrane potential dynamics in vivo. PLo. S Comp Biol, 10(4): e 1003560. Bertrand Fontaine B, Benichoux V, Joris PX and Brette R (2013). Predicting spike timing in highly synchronous auditory neurons at different sound levels. J Neurophysiol 110(7): 1672 -88. Brette, R. (2013). Sharpness of spike initiation in neurons explained by compartmentalization. PLo. S Computational Biology Experimental collaborators: Jose Peña (New York; in vivo electrophysiology in barn owls) Philip Joris (Leuven; in vivo electrophysiology in cats)
Alternative mechanisms of threshold variability. 1 – Remote initiation site V 1 Vm Threshold Spikes are initiated in the axon, but usually recorded at the soma. Time (ms) Depolarization slope (m. V/ms)
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