Vertebrate neurons communicate primarily with action potentials or "spikes", which is why a basic neurophysiological question is to understand precisely what makes neurons spike. The question also has clinical importance, because a number of pathologies are dysfunctions of neural excitability (e.g. epilepsy and multiple sclerosis), and because neural prostheses rely on the precise stimulation of neurons (e.g. cochlear implants and retinal prostheses). Finally, the topic has a central role in theoretical neuroscience, as this is one area where we have biophysical models that have strong predictive power. It also connects with metabolism, in particular the regulation and modulation of ionic channels and energy consumption.

You can have a look at this presentation I did on this subject in Antwerp (2014): *Dynamics of neural excitability. *You can also read the first chapters of a book I am writing on the theory of action potentials (uploaded as I write them).

Axonal spike initiation

In most vertebrate neurons, spikes initiate in the axonal initial segment, a small structure near the soma, packed with ionic channels and other proteins. This is unlike the squid giant axon, the basis of the classic Hodgkin-Huxley model, which actually results from the fusion of hundreds of cells. In the textbook description of spike initiation, spikes are produced by a positive feedback loop of Na+ entry when “the current carried by Na+ entering the neuron is exactly equal to the K+ current that is flowing out” (Purves et al., Neuroscience). I defend a different version that takes into account the peculiarity of axonal spike initiation, in particular the fact that the soma is a current sink for the axonal initiation site: spikes are produced when the current carried by Na+ entering the axonal initial segment is exactly equal to the *axial** current* that is flowing out to the soma (11). This subtle variation has important consequences, in particular Na channels open abruptly as a function of somatic voltage, which in effect makes the integrate-and-fire model more realistic than the single-compartment Hodgkin-Huxley model (13, 15). These two drawings illustrate the difference between the standard account of spike initiation (left) and my proposition (right) (more detailed explanation here):

It explains why integrate-and-fire models are so good at predicting the responses of neurons to somatically injected currents, which we (and other labs) found out using optimization techniques (5,7). I previously called this account of spike initiation the *compartmentalization hypothesis*, because it is based on the fact that spike initiation is associated with a large voltage gradient between the somatic and axonal compartments, but this name seems to be confusing so I now call it *critical resistive coupling theory*, which is more explicit.

Resistive coupling theory also predicts that the current backpropagated to the soma at spike initiation scales inversely with the distance of the AIS. We have shown with M. Kole that this property seems to be used to normalize somatic spikes in the face of variations in somatodendritic geometry (14).

The mathematical modeling uses an exponential approximation of the Na+ current. I previously showed (with Wulfram Gerstner) that, when augmented with adaptative currents, this leads to a simple model that is a good approximation of (single-compartment) Hodgkin-Huxley models, the *adaptive exponential integrate-and-fire model* (1-4).

Threshold dynamics

An often neglected aspect is that spike threshold is not a fixed quantity, but varies on short and long timescales. On short timescales, we found with Jonathan Platkiewicz, using biophysical models, that most data could be explained by the inactivation of Na channels, possibly in conjunction with the subthreshold opening of K channels, and we proposed a threshold equation that predicts the value of spike threshold as a function of biophysical properties (6). Functionally, it implies that the threshold adapts to the membrane potential, which enhances the neuron's coincidence detection properties. We introduced the concept of the « effective postsynaptic potential » (difference between PSP and threshold) to understand the integrative properties with an adaptive threshold, such as enhanced coincidence detection (8). The threshold equation, initially derived in single-compartment models, was amended to take into account axonal spike initiation (11).

We then showed that our adaptive threshold model could predict spike threshold dynamics in vivo (12). I also showed how a model with adaptive threshold can produce responses that do not depend on input amplitude (9). We used this model to predict the responses of auditory neurons to sounds with various levels (10).

Ongoing work

We are currently testing detailed aspects of our theories with our experimental collaborators Dominique Debanne and Maarten Kole. We are also interested in the longer timescales (long-term changes in spike threshold and structure of axonal initiation segment), which connect to metabolism, and in relating structure (properties and location of ionic channels) and function (for example energy consumption). Finally, we are also starting to do our own patch clamp experiments on cultured neurons.

*Relevant publications* (chronological order):

- Brette, R. and W. Gerstner (2005).
*Adaptive exponential integrate-and-fire model as an effective description of neuronal activity*. - Touboul, J. and R. Brette (2008). Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. (code)
- Gerstner, W. and R. Brette (2009) Adaptive exponential integrate-and-fire model.
- Touboul, J. and R. Brette (2009). Spiking dynamics of bidimensional integrate-and-fire neurons.
- Rossant C, Goodman DF, Platkiewicz J and Brette R (2010). Automatic fitting of spiking neuron models to electrophysiological recordings.
- Platkiewicz J, Brette R (2010) A Threshold Equation for Action Potential Initiation.
- Rossant C, Goodman DF, Fontaine B, Platkiewicz J, Magnusson AK and Brette R (2011). Fitting neuron models to spike trains.
- Platkiewicz J, Brette R (2011). Impact of Fast Sodium Channel Inactivation on Spike Threshold Dynamics and Synaptic Integration.
- Brette R (2012). Spiking models for level-invariant encoding.
- Fontaine B, Benichoux V, Joris PX and Brette R (2013). Predicting spike timing in highly synchronous auditory neurons at different sound levels.
- Brette R (2013). Sharpness of spike initiation in neurons explained by compartmentalization.
- Fontaine B, Peña JL, Brette R (2014). Spike-threshold adaptation predicted by membrane potential dynamics in vivo.
- Brette R (2015). What Is the Most Realistic Single-Compartment Model of Spike Initiation?
- Hamada M, Goethals S, de Vries S, Brette R, Kole M (2016). Covariation of axon initial segment location and dendritic tree normalizes the somatic action potential.
- Teleńczuk M, Fontaine B, Brette R (2017). The basis of sharp spike onset in standard biophysical models. (Code and binder)

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