Fig 1.
Somatic spikelets in a detailed biophysical model of a cortical pyramidal neuron in response to noisy input.
A: Morphology of the model neuron. Inset: excitatory (ge, red) and inhibitory (gi, blue) conductances are placed at the soma. Recording electrodes are placed at the soma (Vsoma, black) and the AIS (Vaxon,green). Basal dendrites were removed for clarity. B: Example three seconds of membrane voltage recorded at the soma (upper trace, black) and AIS (lower trace, green) during noisy stimulation. Somatic spikelets are marked with gray asterisks (*). Spikelets co-occur with APs at the AIS. C: Phase plot of ten somatic APs (black) and ten somatic spikelets (gray). D: Examples of a somatic AP (left, black) and a somatic spikelet (middle, gray) overlaid with the corresponding APs at the AIS (green traces). Right: overlay of the somatic AP (black) and the spikelet (gray). E: All somatic events generated during a 100 s simulation. Left: APs (N = 579, dark gray), aligned in time to crossing of the somatic voltage threshold (-10 mV, dashed line). The mean is shown in black. Right: spikelets (N = 63, light gray), aligned to the voltage threshold (-10 mV) crossing at the AIS. The mean is shown in dark gray. F: The all-or-none nature of APs (black) and spikelets (gray) is revealed in a plot of event amplitude against the maximum slope. G: Left: an example voltage trace recorded in a CA1 pyramidal neuron in a freely moving rat. Spikelets are marked with red asterisks (*). Right: Event amplitude plotted against the maximum slope of APs (dark green) and spikelets (red). Adapted from [2]. H: AP- and spikelet-triggered averages (solid and dashed lines, respectively), aligned to the time of crossing the voltage threshold in the AIS (vertical dashed line). H1: mean somatic AP (solid line) and mean somatic spikelet (dashed line) waveform. The horizontal dashed line accentuates the depolarization prior to AP and spikelet occurrence. H2: mean excitatory (red) and mean inhibitory (blue) AP-triggered (solid line) and spikelet-triggered (dashed) conductances. H3: the mean effective synaptic reversal potential combines mean excitatory and inhibitory conductances (see also Methods). During APs (solid line), the synaptic drive was stronger than during spikelets (dashed line).
Fig 2.
Signal attenuation in a passive-membrane model.
A: The model consists of a somato-dendritic compartment attached to a semi-infinite cable (axon). Attenuation of sinusoidal inputs was calculated according to equations given in the Methods. Attenuation of an AP waveform was determined numerically. B–G: The natural logarithm of attenuation is plotted for the antidromic, axon-to-soma (solid lines) and for the orthodromic, soma-to-axon (dotted lines) signal propagation for three input frequencies: 10 Hz (blue), 300 Hz (purple), and 1,000 Hz (red). The results for the antidromic propagation of an AP waveform are shown as black dashed lines. The triangle indicates the default value of the parameter that is varied, all other parameters are held constant at their default values (see Methods for the default parameter values). The attenuation was determined in dependence upon the following model parameters: physical distance between the stimulation and the recording sites (B), axial resistivity of the axon (C), diameter of the axon (D), surface area of the somato-dendritic compartment (E), specific membrane resistance (F), and input capacitance of the somato-dendritic compartment (G), which was varied selectively by changing the specific membrane capacitance of the somato-dendritic compartment (range 0.01–3.1 μF/cm2).
Fig 3.
Conditions of spikelet generation in an active model with reduced morphology.
A: Schematic of the neuron model. B: Left: exemplary APs and spikelets (solid line: soma, dashed line: AIS). The color bar indicates voltage amplitudes of somatic events. Right: phase plots of the exemplary somatic events shown on the left. Inset: a rapid onset (“kink”) is present for spikelets (yellow) and sh-APs (red), but not for fb-APs (orange), which arise smoothly from the baseline. Note that fb-APs reached similar maximum voltages as the sh-APs, but fb-AP amplitudes were smaller because the maximum curvature, used to define the AP onset, occurred at more depolarized voltages (see Methods for details). C–H: Amplitude of somatic events (APs or spikelets) plotted in color code as a function of the stimulus strength (ordinate) and one of the model parameters (abscissa). Default values are indicated with triangles and given in the Methods. C: Physical distance between the soma and the distal AIS. D: Axial resistivity in the proximal and distal AIS. E: Input capacitance at the soma, varied through the specific membrane capacitance (range 0.2–3.2 μF/cm2). F: Specific membrane resistance, varied only in the dendrite. G: Sodium channel density at the soma and the dendrite. Axonal channel densities were kept constant. H: Voltage shift in the activation and inactivation curves between the somato-dendritic and the axonal sodium channels.
Fig 4.
Orthodromic and antidromic spikelets in the biophysically complex model.
A: Neuron model with fluctuating somatic inputs as in Fig 1 (red: excitatory, blue: inhibitory). Additionally, the model cell was stimulated every 500 ms with a short current pulse at the distal axon (orange, see Methods). B: Left: example somatic spikelets; shown are 20 orthodromic (black, evoked with somatic inputs) and 20 antidromic spikelets (orange, evoked with distal axonal inputs). Right: phase plots of the spikelets depicted in the left panel. C: Spikelet-triggered averages for all orthodromic spikelets (N = 66, dashed lines) and all antidromic spikelets (N = 194, dotted lines) generated within 100 s of simulation. C1: Mean orthodromic (dashed black) and antidromic (dotted orange) spikelet, aligned to the voltage-threshold crossing at the AIS (as in Fig 1H). C2: Mean excitatory (red) and inhibitory (blue) conductances for orthodromic (dashed lines) and antidromic (dotted lines) spikelets. C3: Mean effective synaptic reversal potentials (as in Fig 1H) for the orthodromic (dashed line) and antidromic (dotted line) spikelets.
Fig 5.
Orthodromic and antidromic-like spikelets in a model cell with the axon attached to a basal dendrite.
A: Neuron model with fluctuating somatic inputs as in Fig 1 (red: excitatory, blue: inhibitory), except that the axon is attached to a basal dendrite. Additionally, the model cell was stimulated every 500 ms with a synaptic conductance gsyn located at the axon-carrying basal dendrite, distally to the AIS-connecting site (orange, see Methods). B: Left: example somatic spikelets; shown are 20 orthodromic (black, evoked with somatic inputs) and 20 antidromic-like spikelets(orange, evoked with dendritic input). Right: phase plots of the spikelets shown in the left panel. C: Spikelet-triggered averages for all orthodromic spikelets (N = 137, dashed lines) and all antidromic-like spikelets (N = 100, dotted lines) generated within 100 s of simulation. C1: Mean orthodromic (dashed black) and antidromic-like (dotted orange) spikelet, aligned to the voltage-threshold crossing at the AIS (as in Fig 1H). C2: Mean excitatory (red) and inhibitory (blue) conductances for orthodromic (dashed lines) and antidromic-like (dotted lines) spikelets. C3: Mean effective synaptic reversal potentials (as in Fig 1H) for the orthodromic (dashed line) and antidromic-like (dotted line) spikelets.
Fig 6.
Orthodromic spikelets evoked with somatic background inputs and dendritic current stimuli.
A: Neuron model with fluctuating somatic inputs as in Fig 1 (red: excitatory, blue: inhibitory). Additionally, the model cell was stimulated every 20 ms with a brief current pulse at the proximal apical dendrite (orange, see Methods). B: Left: example somatic spikelets; shown are 15 spikelets evoked with the dendritic stimulus (orange) and 15 spikelets evoked with the somatic background stimulus (black). Right: phase plots of the depicted spikelets. C: Spikelet-triggered averages for all spikelets evoked with the somatic background stimulus (N = 41, dashed lines) and all spikelets triggered by the dendritic input (N = 43, dotted lines) generated within 200 s of simulation, see Methods. C1: Mean spikelets evoked with the somatic background stimulus (black dashed line) and with the dendritic stimulus (orange dotted line), aligned to the voltage-threshold crossing at the AIS (as in Fig 1H). C2: Mean excitatory (red) and inhibitory (blue) conductances for spikelets evoked with the somatic background stimulus (dashed lines) and for spikelets evoked with the dendritic stimulus (dotted lines). C3: Mean effective synaptic reversal potentials (as in Fig 1H) for spikelets evoked with the somatic background stimulus (dashed line) and with the dendritic stimulus (dotted line).
Fig 7.
Mechanisms of spikelet generation in pyramidal neurons.
A: Sketch of the pyramidal-cell neuron model. The axon initial segment (AIS) can be divided in the proximal part (dark gray), where high-threshold NaV1.2 channels accumulate, and the distal part, where low-threshold NaV1.6 channels accumulate (dark green). High-threshold NaV1.2 channels are present at lower densities throughout the soma and dendrites (light gray). Low-threshold NaV1.6 channels are located throughout the axon (light green), but at lower densities than in the distal AIS (see Methods). We distinguish four different scenarios (AP, Sp1, Sp2, Sp3), which are described in detail in what follows. AP: Strong enough somato-dendritic inputs initiate an AP at the distal AIS (dark green). The AP then propagates down the axon and back to the soma and into the dendrites. Sp1: Weaker and briefer somato-dendritic inputs give rise to somatic spikelets if the AP initiated at the AIS fails to trigger a somatic AP. However, the axonal AP propagation to the postsynaptic targets remains unaffected. Sp2: Antidromic spikelets occur when an AP initiated in the distal axon propagates to the soma, but does not suffice to evoke a somatic AP. Sp3: In neurons with the axon connected to a basal dendrite, spikelets can also be evoked by inputs to the axon-carrying dendrite. These inputs can evoke an AP at the AIS without passing the soma first. The evoked AP, in turn, propagates down the axon but might fail to trigger a somato-dendritic spike, so a somatic spikelet appears. B: Mean somatic voltage threshold for the four scenarios illustrated in A: orthodromic APs (AP, N = 579), orthodromic spikelets (Sp1, N = 63), antidromic spikelets (Sp2, N = 194), and spikelets evoked by inputs to the axon-carrying dendrite (Sp3, N = 100). Error bars mark standard deviation. C: Mean somatic voltage slope in the 5-ms interval before the event, for the four scenarios illustrated in A.
Table 1.
Comparison of AP- and firing properties in the original model and the adapted model used in Fig 1.