Romain Brette Computational neuroscience of sensory systems The compartmentalization of spike initiation

Classic excitability theory Purves et al., Neurosciences: « The threshold is that value of membrane potential, in depolarizing from the resting potential, at which the current carried by Na+ entering the neuron is exactly equal to the K+ current that is flowing out. Once the triggering event depolarizes the membrane beyond this point, the positive feedback loop of Na+ entry on membrane potential closes and the action potential “fires”. » I Na IKIK Hodgkin & Huxley

Classic excitability theory Spikes have a smooth onset Naundorf, Wolf, Volgushev (Nature 2006) dV/dt slope = « onset rapidness » theory: (dV/dt) / ka % open Na channels C dV/dt ≈ I Na (V) V (mV) ka ≈ 6 mV Phase plot: ka slope

Sharpness of spike initiation in cortical neurons Naundorf, Wolf, Volgushev (Nature 2006) Very sharp spike onset in current-clamp Barrett & Crill (1980) (cat motoneuron) Na current measured at soma (voltage clamp) Discontinuity in voltage-clamp V (mV) As if Na channels opened as a step function of somatic voltage!

Hypothesis 1: cooperativity a channel is more likely to open if its neighbors are open => simultaneous opening Naundorf et al. (2006) (Wolf & Volgushev)Individually, channels do open discretely activation is gradual if Na channels are independent Cooperativity hypothesis:

Experimental evidence Debanne et al. (Phys Rev 2011) Prediction McCormick et al. (2007) Oz et al. (2015) soma AIS Dual soma – axonal bleb recording

Experimental evidence Debanne et al. (Phys Rev 2011) Dual soma – AIS recording Kole & Stuart (2008)

Hypothesis 2: active backpropagation Debanne et al. (Phys Rev 2011) (McCormick) 1)Spikes are initiated in the axon according to the textbook account 2) They become sharper through active backpropagation to the soma no effect for a cylinder effect with soma Problem: space length is 500 µm, initiation site is at 50 µm Yu et al. (2008)

Hypothesis 3: compartmentalization (Brette 2013) Brette, R. (2013). Sharpness of spike initiation in neurons explained by compartmentalization. PLoS Computational Biology Spike initiation, amended: The threshold is that value of membrane potential, in depolarizing from the resting potential, at which the current carried by Na+ entering the neuron is exactly equal to the resistive axial current that is flowing out to the soma. I Na IRIR soma => charge quickly accumulates at AIS then flushes to the soma

Hydraulic analogy leak soma AIS soma/dendrites = bigAIS = small thin axon

Hydraulic analogy leak soma AIS I

Hydraulic analogy leak soma AIS I

Hydraulic analogy leak soma AIS I

Hydraulic analogy leak soma AIS I

Hydraulic analogy leak soma AIS I

Hydraulic analogy leak soma AIS I

Hydraulic analogy leak soma AIS I Na+ current

Hydraulic analogy leak soma AIS I Na+ current

Hydraulic analogy leak soma AIS I even more Na+ current

Hydraulic analogy leak soma AIS I flush

Compartmentalization of spike initiation Most of the time, Vm is the same in soma and AIS Kole, Letzkus, Stuart (Neuron 2007) AIS Stuart, Schiller, Sakmann (J Physiol 1997) leak somaAIS I

Compartmentalization of spike initiation I Na x ≈ 30 µm Ra = x.raRa = λ.ra conductance ratio: λ/x ≈ 15 soma soma = « current sink »

Compartmentalization of spike initiation leak soma AIS I Na+ current At spike initiation, Vm is very different at the two sites soma I Na VsVs VaVa R a.I Na (Ohm’s law)

Compartmentalization of spike 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 Equilibrium: axial current = Na current

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

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 !

Predictions The threshold equation (modified from Platkiewicz & Brette 2010): (Debanne’s lab) +TTX threshold = -5 mV.log(gNa) + cst

Predictions At threshold: V a – V s = k a Kole & Stuart (2008)

Predictions Onset rapidness at soma ≈ maximum rapidness at AIS Onset rapidness at AIS = (1/ka).dVa/dt max slope ≈ 23 ms -1 soma AIS Yu et al. (2008)

Predictions Somatic voltage-clamp: voltage-dependent latency & stereotypical current spikes (saddle-node: hyperbolic relation) Milescu et al (2010)

Predictions axial current = axonal Na+ current => similar Na+ flux into soma and AIS Na+ from AIS Na+ from soma Fleidervish et al. (Nat Neuro 2010) « Na+ imaging reveals little difference in action potential–evoked Na+ influx between axon and soma » => much higher Na+ channel density in AIS than soma soma AIS Kole et al. (2008) « Action potential generation requires a high sodium channel density in the axon initial segment »

Predictions Initiation site ≠ peak of Na current density (potentially) Brette (2013) Initiation always at the distal end Baranauskas et al. (2013)

Summary leak soma AIS I

Summary leak soma AIS I

Summary leak soma AIS I Na+ current

Summary leak soma AIS I Na+ current

Summary leak soma AIS I even more Na+ current

Summary leak soma AIS I flush

Thank you Platkiewicz J, Brette R (2010) A Threshold Equation for Action Potential Initiation. PLoS Comput Biol 6(7): e doi: /journal.pcbi Platkiewicz J, Brette R (2011). Impact of Fast Sodium Channel Inactivation on Spike Threshold Dynamics and Synaptic Integration. PLoS Comp Biol 7(5): e doi: /journal.pcbi Brette R (2013). Sharpness of spike initiation in neurons explained by compartmentalization. PLoS Comp Biol, doi: /journal.pcbi Brette R (2015). What Is the Most Realistic Single-Compartment Model of Spike Initiation? PLoS Comput Biol Apr 9;11(4):e Maria Teleńczuk Bertrand Fontaine Jonathan Platkiewicz Dominique Debanne