Initiation of simple and complex spikes in cerebellar Purkinje cells

Cerebellar Purkinje cells produce two distinct forms of action potential output: simple and complex spikes. Simple spikes occur spontaneously or are driven by parallel fibre input, while complex spikes are activated by climbing fibre input. Previous studies indicate that both simple and complex spikes originate in the axon of Purkinje cells, but the precise location where they are initiated is unclear. Here we address where in the axon of cerebellar Purkinje cells simple and complex spikes are generated. Using extracellular recording and voltage-sensitive dye imaging in rat and mouse Purkinje cells, we show that both simple and complex spikes are generated in the proximal axon, ∼15–20 μm from the soma. Once initiated, simple and complex spikes propagate both down the axon and back into the soma. The speed of backpropagation into the soma was significantly faster for complex compared to simple spikes, presumably due to charging of the somatodendritic membrane capacitance during the climbing fibre synaptic conductance. In conclusion, we show using two independent methods that the final integration site of simple and complex spikes is in the proximal axon of cerebellar Purkinje cells, at a location corresponding to the distal end of the axon initial segment.


Simulations of axonal action potential generation demonstrate that eAPs can be used to accurately locate the action potential initiation site
One of our methods to determine the site of action potential initiation in the Purkinje cell axon was based on recordings of the extracellular action potential (eAP) waveform at multiple sites along the axon. The 10 % rise point of the eAP peak was chosen as the time of action potential onset (see main text and Fig. 1). Since axonal eAP waveforms are the result of a superposition of different current sources and sinks along the axon, which might complicate the identification of the site of action potential initiation, we used a combination of compartmental modelling and calculation of eAPs to address the following questions: • Which membrane currents determine the waveform of the eAP and which membrane currents are active at the 10 % rise point?
• How strong is the influence of extracellular potentials generated by remote active sites at the 10 % rise point? Is the eAP always dominated by the local active site?
• Most importantly: do multisite eAP recordings allow us to correctly identify the site of action potential initiation?
We used the following two compartmental models to address these questions: A) Our previously published multi-compartment Purkinje cell model in which action potentials are initiated in the first node of Ranvier (Clark et al., 2005), with conductances based on Khaliq et al. (2003); and B) A modified version of the model in A) in which, due to a small number of changes in conductance densities (see Supp. Methods below), action potentials are initiated in the axon initial segment (at ~19 µm from the soma, Fig. S1A).
From the membrane currents generated by these two models, eAPs were calculated (Holt & Koch, 1999; see Supp. Methods) enabling us to link the timing of axonal action potentials and their underlying membrane currents to the waveforms of the eAPs at different locations along the axon.
The key difference between the two different compartmental models is the site of action potential initiation (Fig. S1A), and we first tested whether this site could be correctly identified in both models on the basis of axosomatic delays measured from the onset of axonal and somatic eAPs (10 % rise point). Waveforms of eAPs were calculated for multiple sites along the axon and axosomatic delays were determined in the same way as for the experimental data ( Fig. S1B, Fig. 1). For both compartmental models, the spike initiation site was identified correctly (Fig. S1B & C) confirming that eAP recordings can be used for this purpose. To ensure that this result was sufficiently general and not a consequence of the specific properties of the two compartmental models, we made two separate perturbations to both models to change the shape of the generated eAPs and tested the effect on the detection of the initiation site. Neither broadening of the eAPs by removal of all fast repolarizing potassium conductances, nor generation of briefer eAPs by acceleration of the kinetics of all channels to approximate the situation at physiological temperature (37 °C), influenced the correct localization of the initiation site (data not shown).
Further details about the membrane currents contributing to the simulated extracellular action potential are shown for the somatic compartment in Figure S2.
The sum of the capacitive and ionic currents closely resembles the extracellular action potential and indicates that the eAPs measured near the soma are a reflection of the local somatic membrane current (Fig. S2A). The initial positive deflection in the eAP waveform occurring before the onset of the active somatic membrane current is the capacitive current associated with the initial passive depolarization of the soma driven by axial current from the axon initial segment. The onset of the negative inflection of the eAP is determined by the rising phase of the sodium current (Fig. S2B). As a result the 10 % rise point of the eAP is a good predictor of the local sodium conductance activation and, therefore, of the time of action potential onset at the recording site.
Extracellular potentials generated at an active site spread in the tissue according to Φ(r) ~ 1 / (4 π r), where r is the distance from the active site (Holt & Koch, 1999).
This means that recorded eAPs at a specific site represent the sum of eAPs generated by several current sources, which could confound the accurate analysis of spike onset (10 % rise point). To test whether distant eAP sources contribute significantly to eAP waveforms at candidate sites for action potential initiation, we calculated the spatial spread of isolated eAPs from the soma, initial segment and first node along the axon. showing that the local eAP is dominated by the extracellular potential generated at this site (Fig. S2D). However, if there is no active current source at the recording site, the eAP onset is typically influenced by the nearest active compartment. For example, the eAP of the first node of Ranvier can still be seen at a distance of ~10 µm from the node (Fig. S2D). This might lead to a slight imprecision in localizing the exact position of the node, but on the other hand provides a major experimental advantage: if the axon is scanned for eAPs using a 20 µm window, nodes will not be missed.
Therefore we can draw conclusions about the initiation site of the action potential, i.e.
whether the spike initiates in the first node or the proximal axon, even though there might be uncertainty about the exact location of nodes of Ranvier.
To summarize, the simulations show that multisite extracellular recordings of action potentials reliably report the AP onset along the axon and are therefore a valid method for localizing the site of action potential initiation.

Computational model of extracellular action potentials
To simulate extracellular action potentials (eAPs) in the vicinity of Purkinje cell axons we combined two modelling approaches: A) Compartmental models based on reconstructed cerebellar Purkinje cell morphologies to simulate initiation and propagation of action potentials, based on a previously published model (Clark et al., 2005) and implemented in NEURON (Hines & Carnevale, 1997). B) A MATLAB script to calculate the eAPs arising from the simulated action potentials based on the line source approximation method (Holt & Koch, 1999;Gold et al., 2006). The first compartmental model, in which action potentials are initiated at the first node of Ranvier, was the model of Clark et al. (2005), which is based on experimentally recorded currents in Purkinje cells (Khaliq et al., 2003). The second model, in which action potentials are initiated in the axon initial segment, was obtained from the first by increasing the densities of all voltage-dependent conductances in the initial segment by a factor of 4, decreasing the density of dendritic I h by a factor of 5, increasing the membrane capacitance of the first myelinated axon segment by a factor of 5 and shifting the voltage dependence of the sodium conductance in the axon initial segment by 5 mV towards more hyperpolarized potentials. The time step in all simulations was 5 µs. Corresponding extracellular action potentials in the vicinity of the model axon were calculated using the line source approximation method (Holt & Koch, 1999) implemented in MATLAB (Holt & Koch, 1999;Gold et al., 2006). Briefly, this method assumes that the net membrane current of axonal and dendritic cables comprising the model neuron can be represented as line sources projected on the centre of the cable. The electrical potential Φ(r) arising from a source at the origin and measured at a distance r in the extracellular space is: where ρ is the resistivity of the extracellular medium and I the total membrane current produced at the source. The net electrical potential Φ N at any given point in the extracellular space is the linear sum of all individual potentials Φ i at this point generated by all compartmental current sources i of the simulated cell (see also

Recording distance (µm)
First node initiation Figure S1. The action potential initiation site is reliably identified by the extracellular action potential waveform A, Simulation of spike initiation and propagation in two Purkinje cell models with different spike initiation sites (see Supp. Methods; insets: respective intracellular AP waveforms at the soma (black), initial segment (lilac) and first node (green) for the two different models). B, Somatic intracellular (wc) and somatic and axonal extracellular action potential (eAP) waveforms of the model initiating APs at the initial segment (left column) and first node (right column), respectively. The 10 % rise points are shown by red symbols. The vertical line indicates the 10 % rise point of the eAP at the initiation site. C, Latency differences between the somatic and axonal AP measured at the 10 % rise point for the models initiating APs at the initial segment (left) and first node (right). A, Simulated somatic action potential (V m ) and the underlying sodium, I Na , potassium, I K , and capacitive current (I Cap ) components (each scaled to maximum current). The sum of all currents at this location (I Sum ) is comparable to the local extracellular action potential waveform (eAP, 4 th row). The downstroke of the eAP is dominated by the somatic Na + current. The transient positive deflection of the eAP is dominated by I Cap (also observed in some experiments; data not shown) which in turn is caused by axial current from the axon initial segment. The vertical dashed line indicates the time of the peak Na + current. B, Scaling the somatic Na + conductance (dashed blue lines, 0.5x; black lines, as in A; dashed green lines, 2x) influences the somatic action potential (top), its underlying somatic Na + current (middle) and the eAP waveform (bottom). C, Extracellular potentials Φ(x) are generated at active sites and decay with distance x from their site of generation according to Φ(x) ~ 1/(4πx). The total eAP at position x along the Purkinje cell axon is the sum of all individual eAPs (attenuated according to the above relationship) generated by active sites. D, Amplitude vs distance plot of the spatial spread of the individual eAPs arising from three different source sites along the axon: soma (orange), iSeg (lilac) and first node (green). Red dots indicate the time when the extracellularly recorded simple spike reaches 10 % of its maximum amplitude. C, Axosomatic delays for cell shown (red) and 3 other cells tested (each indicated by a separate color) plotted with respect to axonal distance of the recording sites. Colored arrows mark the location of the minima for each cell. The average within-cell minimum is 20 ± 4 µm (n = 7). Calculating the moving average of all data obtained (n = 14 cells, see main text and Fig. 3) gave an average initiation location of 19.5 µm from the axon hillock. Two examples of initial segment recordings illustrate absence and presence of detectable capacitive current and the contribution of ionic current in cell-attached recordings. Cell-attached and extracellular recordings (eAP) were made from the axon of two different Purkinje neurons at 20 µm (cell 1) and 18 µm (cell 2) from the soma. For cell 1, the cell-attached current (red) is clearly dominated by positive sodium current which completely masks any capacitive negative current. In the recording from cell 2, a negative capacitive current (arrow) is followed immediately by a positive sodium and then a large negative potassium component. Red symbols mark the 10 % rise point of the eAP recorded at the same location, the green vertical line shows the location of peak somatic dV/dt.