1. Romain Brette Computational neuroscience of sensory systems romain.brette@inserm.fr Dynamics of neural excitability

2. The spike threshold firing threshold action potential postsynaptic potential (PSP) temporal integration

3. Questions 1.Is there a voltage threshold? If yes, is it equal to the onset voltage? If yes, which one? Kole & Stuart (2008)

4. Questions 2.What determines the value of the threshold? 3.How does the spike threshold vary? 4.What difference does it make?

5. IS THERE A VOLTAGE THRESHOLD FOR SPIKE INITIATION? Brette, R. (2013). Sharpness of spike initiation in neurons explained by compartmentalization. PLoS Computational Biology

6. The « sharpness » of spike initiation Naundorf et al (2006) 1) Spikes have sharp onsets in recordings, unlike in Hodgkin-Huxley models Badel et al. (J Neurophysiol 2008) V 2) I-V relationship at soma is very sharp

7. The « sharpness » of spike initiation Naundorf et al (2006) 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)

8. Spikes are initiated in the axon Stuart, Schiller, Sakmann (J Physiol 1997)

9. Model of axonal initiation soma I VsVs VaVa R a.I The soma is a current sink (Ohm’s law) Brette, R. (2013). Sharpness of spike initiation in neurons explained by compartmentalization. PLoS Comp Biol.

10. Model of axonal initiation soma I VsVs VaVa R a.I The soma is a current sink (Ohm’s law)

11. Model of axonal initiation soma I=f(V a ) VsVs VaVa R a.I Na activation

12. Model of axonal initiation soma I=f(V a ) I=(V a -V s )/Ra VsVs I (nA) I=f(V a ) I=(V a -V s )/Ra VsVs Lateral and Na currents must match

13. Distal axonal initiation soma I=f(V a ) I=(V a -V s )/Ra VsVs I (nA) I=f(V a ) I=(V a -V s )/Ra VsVs Lateral and Na currents must match Discrete opening of Na channels

14. A view from the soma m Lateral current flows abruptly when a voltage threshold is exceeded Na channels open in an all-or-none fashion

15. A view from the soma m single compartment HH model with axonal initiation A fairly good phenomenological description: -below V t, no sodium current -when Vm reaches V t : all channels open (spike) VtVt a.k.a. the integrate-and-fire model !

16. Answers 1.Is there a voltage threshold? If yes, is it equal to the onset voltage? If yes, which one? Kole & Stuart (2008) yes X

17. WHAT DETERMINES THE VALUE OF THE THRESHOLD?

18. Model of axonal initiation soma I=f(V a ) I=(V a -V s )/Ra VsVs Lateral and Na currents must match f(V a ) = (V a -V s )/Ra Fixed point equation Na activation Spike threshold = bifurcation point (= V s when solution jumps) I (nA) The threshold equation V 1/2 kaka

19. How about other channels? soma I=f(V a ) I=(V a -V s )/Ra VsVs IKIK There are also K+ channels! VsVs VaVa R a.I K (Ohm’s law) If the axonal threshold is unchanged, then the somatic threshold increases by –R a.I K The threshold equation

20. HOW DOES THE SPIKE THRESHOLD VARY? Platkiewicz, J. & Brette, R. A Threshold Equation for Action Potential Initiation. PLoS Comp Biol 6(7): e1000850. doi:10.1371 Fontaine B, Peña JL, Brette R (2014). Spike-threshold adaptation predicted by membrane potential dynamics in vivo. PLoS Comp Biol

21. The spike threshold is not fixed The spike threshold is variable in vivo Voltage (mV) Membrane potential Threshold (Azouz & Gray, 2000) Large threshold variability (>10 mV)

22. The threshold depends on depolarization speed (Wilent & Contreras, 2005) In the visual cortex (Azouz & Gray 2003) 2 ms Spike threshold is inversely correlated with depolarization speed Mean membrane potential (mV) The threshold adapts to the membrane potential

23. Two possible mechanisms Inactivation of Na channels decreases threshold Activation of K+ channels increases threshold Na inactivation: g Na proportional to h (= non-inactivated channels) The « threshold equation » Huguenard et al. (1988)

24. Validation in a multicompartmental model Prediction:

25. Validation in a multicompartmental model

26. Threshold dynamics « Steady-state threshold » Example with linear membrane equation:

27. The steady-state threshold where k a /k i  1 Inactivation curve

28. 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. PLoS Comp Biol

29. Testing the model Fontaine B, Peña JL, Brette R (2014). Spike-threshold adaptation predicted by membrane potential dynamics in vivo. PLoS Comp Biol

30. WHAT DIFFERENCE DOES IT MAKE? Platkiewicz, J. & Brette, R. Impact of sodium channel inactivation on spike threshold dynamics and synaptic integration. PLoS Comp Biol 7(5): e1001129. doi:10.1371 Fontaine B, Peña JL, Brette R (2014). Spike-threshold adaptation predicted by membrane potential dynamics in vivo. PLoS Comp Biol

31. Synaptic integration with adaptive threshold Above V i, threshold is a low-pass filtered version of the membrane potential Threshold PSP VTVT « threshold PSP »

32. The effective PSP Threshold PSP PSPV  V -  Fixed threshold « Effective PSP » Time (ms) Distance to threshold: shorter integration time constant

33. Sharpening and noise reduction PSPs Autocorrelation « Noise » reduction Effective time constant Fontaine B, Peña JL, Brette R (2014). Spike-threshold adaptation predicted by membrane potential dynamics in vivo. PLoS Comp Biol

34. Summary « Effective PSP » 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

35. Thank you! Jonathan Platkiewicz Platkiewicz, J. & Brette, R. A Threshold Equation for Action Potential Initiation. PLoS Comp Biol 6(7): e1000850. doi:10.1371 Platkiewicz, J. & Brette, R. Impact of sodium channel inactivation on spike threshold dynamics and synaptic integration. PLoS Comp Biol 7(5): e1001129. doi:10.1371 Fontaine B, Peña JL, Brette R (2014). Spike-threshold adaptation predicted by membrane potential dynamics in vivo. PLoS Comp Biol, 10(4): e1003560. Bertrand Fontaine Experimental collaborators:Jose Peña (New York; in vivo electrophysiology in barn owls) Philip Joris (Leuven; in vivo electrophysiology in cats) Brette, R. (2013). Sharpness of spike initiation in neurons explained by compartmentalization. PLoS Computational Biology 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.

36. Alternative mechanisms of threshold variability. 1 – Remote initiation site Spikes are initiated in the axon, but usually recorded at the soma. Vm Time (ms)Depolarization slope (mV/ms) Threshold V1

37. Alternative mechanisms 2 – Channel noise