The basis of sharp spike onset in standard biophysical models 

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Backpropagation Hypothesis

As a response to the Cooperativity Hypothesis, the McCormick group proposed a Backpropagation Hypothesis as a potential explanation for the kink (Naundorf et al., 2007; Yu et al., 2008). Here, the action potential follows standard Hodgkin-Huxley type model and the initiation of the action potential with a smooth onset is located at the AIS. As the action potential travels towards the soma, it sharpens with each further opening of sodium channels. When the AP reaches the soma it shows the kink. This explanation provides a simple account for the kink, which is unfortunately not completely correct (as we will argue in Chapter 3). The main aw of this hypothesis is that the distance between the AIS and the soma is not long enough to account for the kink, as distance required would be 2 mm, as shown in the paper, opposite to the 30{50 m of actual biological distance from the soma to the AIS.

Critical Resistive Coupling Hypothesis

Finally, in 2013, Brette proposed the Critical Resistive Coupling (initially called Compartmentalization) explains the kink based on two requirements: the distal initiation, and the large size dierence between the soma and the axon initial segment, leading to a current sink formation in the soma. When the action potential is initiated in the AIS, a single current loop forms between the AIS and the soma (instead of small propagating current loops as in the Backpropagation Hypothesis). Although the mechanism is very dierent, this hypothesis is mathematically very similar to the cooperativity hypothesis; In the Chapter 3, we will argue that this hypothesis indeed explains the kink correctly.

Signature of a single cell activity in the extracel- lular potential

The eld potential is composed of the activity of multiple neurons, proximal and distal to the recording electrode (Katzner et al., 2009). It is believed to re ect transmembrane currents (Einevoll et al., 2013). To model this eld, a dipole approximation is frequently used (Buzsaki et al., 2012). The action potential (AP) of a single neuron is such a large signal that it can be detected in the extracellular medium, in the scale of microvolts (Henze et al., 2000). However, the extracellular eld represents a much wider composition of signals related to other processes concomitant to, but not involved in the generation of the original AP, such as synaptic integration or network activity (Telenczuk and Destexhe, 2013). An AP recorded at various sites around the cell might appear dierent, and an AP in the extracellular medium might show the action potential peak slightly sooner than in the soma (as we predict in the simulation described in Chapter 3).
In addition to the extracellular signature of AP, synaptic activity triggered by a single cell can also be recorded extracellularly. Spikes of thalamocortical neurons arriving at cortical synapses generate a unitary excitatory synaptic eld in the cortex (Swadlow et al., 2002). Similarly, single hippocampal interneurons, such as basket cells, generate a local unitary inhibitory eld (Bazelot et al., 2010; Glickfeld et al., 2009). Interestingly, in these studies there is no record of excitatory postsynaptic potential (ePSP) in the extracellular eld being generated by single pyramidal cells in the hippocampus. Others have argued that ePSPs are the main determinant of the LFP (Reimann et al., 2013) (but see Haider et al. (2015); Telenczuk et al. (2016)). Why then would we only see inhibitory PSP in the hippocampus?
The dierence in the extracellular eld evoked by interneurons and pyramidal neurons could be due to the distribution of their synaptic terminals. While most of the synapses of inhibitory cells are clustered proximally to the cell body of the hippocampal basket cell, and are most likely to contact the cell bodies of other neurons (which in the hippocampus are in the same layer), the synpases of pyramidal neurons are more widely distributed in space (Megias et al., 2001). Also, pyramidal cells tend to make contacts in all the layers, which will have signals more likely to cancel each other out in the extracellular medium (Buzsaki et al., 2012).
Field potentials are relatively easy to record and they are often routinely used to measure neuronal population activities and to infer brain states (Cui et al., 2016; Destexhe et al., 1999).

Bursts of action potentials

Until now we only explained the process of the action potential (AP) initiation and propagation in dierent neuronal parts and the AP signature in the extracellular medium. However, a single AP is often directly followed by multiple other APs, forming a burst. Bursts of action potentials may play a dierent role than single APs and are worth mentioning. For instance, during the burst, interaction between soma and dendrite can be more complex. Multiple studies have showed that slow, calcium spikes or other active depolarizing events may take place in the dendrite and provide for the long depolarization driving the burst of action potentials in the soma (Helmchen et al., 1999; Kim and Connors, 1993; Larkum and Zhu, 2002; Larkum et al., 2001; Stuart et al., 1997a). The soma is not always able to follow the burst initiated in the axon initial segment appropriately, thus bursts are easier to identify in the axon (Mathy et al., 2009). In the AIS, APs display a minimal decrease in amplitude during bursts (Shu et al., 2007a; Williams and Stuart, 1999).
In the hippocampus, when sodium channels are partly blocked, the amplitude of the rst AP is not aected. This might suggest that there is an excess of sodium channels in the cell if only one action potential is red. However, the next action potentials and the overall maximal discharge frequency will be aected by this change (Fig 2.11) (Madeja, 2000).
Firing patterns vary between dierent types of neurons. Since the distribution of ionic channels with divergent properties are particular for each cell type, it is more probable that the ring patterns stem from the properties of these dierent channels. Surprisingly, Mainen and colleagues (Mainen and Sejnowski, 1996) showed in their computational study that dierent morphologies of neurons are sucient to produce variability of ring patterns (example, Fig 2.12).

Activity of single cell within population

A single cell can discharge a single action potential or bursts of action potentials to provide an input of information to other cells. But does the action of a single neuron really matter in the jungle of other cells and their activity? Some studies argue against this Recordings of pairs of action potentials at dierent concentration of TTX (no TTX on the left, 10 nmol/l TTX on the right). The amplitude of the rst action potential is hardly aected, whereas amplitude of the second action potential changes with increasing TTX concentration (arrow) (I, amplitude 0.5 nA, duration 2ms, interpuse interval is 10 ms.
Dissociated CA1 hippocampus neurons of guinea pig. Adapted from Madeja (2000). (Shadlen and Newsome, 1998) hypothesizing that it is rather the overall activity which makes an impact (so-called rate-coding). At this time, multiple studies have showed that a single action potential can have an impact on the overall network activity. For instance, stimulation of a single motor cortical neuron can evoke whisker movement (Brecht et al., 2004), and action potentials in a single somatosensory cortical neuron might induce behaviorally reportable eects (Houweling and Brecht, 2008). Also, single GABAergic cell might have an impact on population events in developing hippocampus (Bonifazi et al., 2009).
Furthermore, bursts of action potentials of a single cell can trigger a switch between brain states (slow wave and rapid-eye-movement sleep, and inversely) (Li et al., 2009). Finally, a single action potential in pyramidal neurons of the hippocampus can trigger the Sharp Wave Ripple (SPW-R) network activity (which we will discuss further in Chapter 5) (Bazelot et al., 2016).

Sharp Waves as example of network activity

In certain brain states neurons synchronize their activity, which can be recorded as dierent types of patterns in the extracellular medium and by electroencephalography (EEG) recordings. In the hippocampus there are two types of oscillations which can be found in compositions produce dierent ring patterns. Adapted from Mainen and Sejnowski (1996). the healthy brain: First is the gamma wave (40{100 Hz), modulated by the slower theta wave (4{10 Hz) as recorded in vivo when the animal is awake (Fig 2.13 A). They are believed to be responsible for memory acquisition. Second, Sharp Wave-ripples (SPW-Rs) recorded during quiet immobility or during slow wave sleep are believed to be responsible for the consolidation of memory (Fig 2.13 A-B) (Buzsaki, 1996). SPWs can be recorded in vivo and in vitro in the extracellular medium, and as input current to the recorded cell. These recordings are of 1{3 Hz with 100{200 Hz ripple oscillation imposed on the them.
It is still unclear how synchrony between multiple cells is achieved so quickly – when synaptic connections are blocked and much faster than synaptic activity would allow (Draguhn et al., 1998). Some studies conclude that this can be due to the electrical coupling through gap junctions (Traub et al., 2002) while others show the importance of excitatory (Maier et al., 2011) or inhibitory (Ho et al., 2009) recurrent circuits.

Table of contents :

Acknowledgements
Summary 
1.1 Abstract
1.2 Resume (en francais)
2 Introduction to action potential 
2.1 Context and objective of this work
2.2 Currents during action potential
2.2.1 Hodgkin and Huxley Model
2.2.2 Voltage gated channels
2.2.2.1 Sodium channels
2.2.2.2 Potassium channels
2.2.2.3 Other voltage gated channels
2.2.3 Energy eciency
2.3 Role of dierent neuronal segments
2.3.1 Soma
2.3.2 Axon
2.3.3 Axon initial segment
2.3.4 Synapse
2.3.5 Dendrite
2.3.6 Impact of morphology on the ring pattern
2.4 Kink at the initiation, experiments vs models
2.4.1 Cooperativity Hypothesis
2.4.2 Backpropagation Hypothesis
2.4.3 Critical Resistive Coupling Hypothesis
2.5 Signature of a single cell activity in the extracellular potential
2.6 Bursts of action potentials
2.7 Activity of single cell within population
2.8 Sharp Waves as example of network activity
2.9 Malfunction of action potential
2.9.1 Epilepsy
2.9.2 Stroke
2.9.3 Alzheimer’s disease
2.9.4 Other Disease
3 The basis of sharp spike onset in standard biophysical models 
3.1 Abstract
3.2 Author summary
3.3 Introduction
3.4 Results
3.4.1 Intracellular and extracellular features of sharp spike initiation in multicompartmental models
3.4.2 Extracellular eld at spike initiation
3.4.3 Currents at spike initiation
3.4.4 Excitability increases with intracellular resistivity
3.4.5 Sharp spike initiation requires a large enough somatodendritic compartment
3.4.6 Backpropagation does not sharpen spikes
3.4.7 Active backpropagation is not necessary for sharp spike initiation
3.4.8 Sharp somatic onset is reproduced by a model with two resistively coupled compartments
3.5 Discussion
3.6 Materials and methods
3.6.1 Detailed neuron models
3.6.1.1 Morphology
3.6.1.2 Channel properties
3.6.2 Two-compartment model
3.6.3 Analysis
3.6.3.1 Voltage-clamp
3.6.3.2 Phase slope
3.6.4 Theoretical prediction of onset rapidness
3.7 Acknowledgments
4 Local eld potential generated by neurons with dierent localisation of axon initial segment 
4.1 Results
4.1.1 Soma-axon model
4.1.2 Far-eld dipole approximation
4.1.3 Dipole model { near eld
4.1.4 Two cylinder model
4.2 Discussion
4.3 Methods
4.3.1 Soma-axon model
4.3.2 Linear Source Approximation
4.3.3 Two cylinders model
5 Single CA3 pyramidal cells trigger sharp waves in vitro by exciting interneurones 
5.1 Abstract
5.2 Introduction
5.3 Methods
5.3.1 Slice preparation
5.3.2 Drugs
5.3.3 Recordings
5.3.4 Signal analysis
5.3.5 Statistical analysis
5.4 Results
5.4.1 Single pyramidal cells initiate SPWs and eld IPSPs
5.4.2 fIPSPs from perisomatic interneurones are repeated in SPW elds
5.4.3 Excitation of interneurons by single pyramidal cells
5.4.4 Comparison of spontaneous SPWs and SPWs initiated by single cells
5.4.5 Patterns of SPW spread and the activity of identied interneurons
5.5 Discussion
5.5.1 Advantages of an in vitro study
5.5.2 Initiating pyramidal cells excite perisomatic interneurones
5.5.3 Continuation, spread and cellular components of SPWs
6 Conclusions 
6.1 Uniqueness of Action Potential
6.2 Role of the axon in neuronal coding
A Recurrent synapses and circuits in the CA3 region of the hippocampus: an associative network 
A.1 Abstract
A.2 Recurrent excitatory synapses between CA3 cells: emergence
A.3 Axonal distributions of CA3 pyramidal cells
A.4 CA3 pyramidal cell axon physiology
A.5 CA3 pyramidal cell terminals: numbers, form, contents, channels and release
A.6 Pre- meets post: synapses made by CA3 pyramidal cells with other CA3 cells
A.7 Pre- meets post in dual records
A.8 Short-term and long-term synaptic plasticity in double recordings
A.9 Transmission of recurrent excitatory signals on the membrane of a postsynaptic cell
A.10 Recurrent excitatory contributions to population activities in the CA3 region
A.11 Interictal epileptiform rhythm
A.12 Sharp-wave rhythm
A.13 Theta and gamma rhythms
A.14 Comparison of recurrent connectivity in CA3 and other cortical regions .
A.15 The CA3 recurrent system as an associative network

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