Article Figures & Data
Figures
- Figure 1.
AP onset rapidness in the axon initial segment. Schematic at top depicts the model used, consisting of a spherical soma (blue) coupled to a passive cylindrical dendrite and a cylindrical axon. The latter starts with of 50 μm long, uniformly excitable AIS, followed by a myelinated cylinder (see Materials and Methods). a, Brief, 5 ms, depolarizing current pulse was injected to the soma; the resultant AP is recorded in three locations (color coded as in the schematics). The AP peaked first at a distal point, 47 μm from the soma; this is the SIP (red). Inset, Zoom in at the AP onset, which is less rapid in the SIP (red). b, AP phase plot at the corresponding locations coded by colors in a. The initial part of the phase plot is enlarged in the inset. The AP onset rapidness (the phase slope) was defined as the slope at the point where the phase slope was 10 mV/ms (horizontal dotted line in the inset). The phase slope is minimal at the SIP (red line in inset) and becomes very steep at the soma (blue line). c, AP phase slope in the AIS as a function of distance from the soma.
- Figure 2.
Dendritic load, AP onset rapidness, and the tracking of high-frequency modulation by axonal spikes. a, Schematics showing four neuron models with increasing dendritic load (increasing ρaxon; see Materials Methods). The model with gray dendrite (ρaxon = 190) was used in Figure 1. b, Top, Voltage response of the model with ρaxon = 190 to a fluctuating current injected in the soma (schematic electrode in a). The corresponding current input was composed of a DC current (lower traces, green line of 0.2 nA), a modulated sine wave, and a noisy current input, as shown in the lower traces (see Materials and Methods). c, AP phase slope as a function of distance from the soma for the four neuron models. Input current was normalized to yield similar firing rate of 10 Hz in all four models (see Materials and Methods). Colors are as the dendrites in the respective schematics. AP was initiated at the same location (the SIP) in all four models (red points). Inset, zoom in at the SIP; AP onset becomes more rapid with increased dendritic load. d, Models' capability to track high-frequency modulations via axonal spikes, as assessed using the vector strength R. Colors are as in a. Cutoff frequency is shifted to the right with increasing the dendritic load. e, Correlation between ρaxon and AP onset rapidness (black curve, left x-axis) and the cutoff frequency (green curve, right y-axis). Note the 30% increase in AP inset rapidness and the >3-fold improvement of encoding input fluctuations via axonal spikes with increasing ρaxon.
- Figure 3.
The theoretical basis for the dendritic size effect. a, Voltage response in the passive model depicted in Figure 2 schematics to current step injected at the SIP. As ρaxon increases, the transient voltage response becomes faster. Vertical dashed line depicts one membrane time constant. Color codes as in Figure 2a. b, Frequency response for the corresponding passive cases shown in a. Note the significant right shift in the cutoff frequency with increasing ρaxon. Lower dashed line is for soma alone, whereas the upper dashed curve line is for an infinite cylinder. Note the difference in scales of x- and y-axes as compared with Figure 2. c, d, As in a and b, but the current was injected at the soma and voltage response was measured at the AIS. e, Vector strength for the active model with a fixed ρaxon = 370, but with increasing the activation rate of Na+ conductance in the AIS to a required target phase slope as denoted. f, As in e, but with a fixed phase slope of 3.5/ms and with varying ρaxon values.
- Figure 4.
The relationship between axial current loss (dendritic load) and tracking of input modulation. Top, Schematics of modeled neurons. a, An RC circuit (red) representing the membrane compartment at the SIP, with a membrane capacitor (cSIP) and a resistor (gSIP). The membrane time constant, τm = cSIP/gSIP. The axial resistor (ga) represents the path by which axial current is lost from the SIP toward the soma/dendritic region (blue). b, Equivalent circuit to that drawn in a, now with the two resistors, gSIP and ga drawn in parallel. This makes it clear why the effective time constant of this circuit, τeff = cSIP/(gSIP + ga), is shorter than τm. c, Voltage response to current step onset and offset in the isolated SIP (red) and in the model shown in b (which includes axial resistance). Voltage buildup during current injection and (its mirror image) voltage decay following the end of current injection. Both the buildup and the decay are faster for the case with the shorter effective time constant (purple). The fast voltage buildup (and decay) is associated with the current loss from the SIP. d, Normalized vector strength (phase locking as function of the frequency of input modulations) for the two corresponding isopotential models with active currents as in Figure 2b. Shorter membrane time constant leads to improvement in tracking of high-frequency modulations.
- Figure 5.
Encoding of input modulations via axonal spikes in human versus rat L2/3 pyramidal cells. a, The modeled human (red) and rat (blue) L2/3 3D reconstructed pyramidal cells. Scale bar, 200 μm; see details in Materials and Methods. b, Raster plot in human (red, left) and rat cells (blue, right) for 500 Hz input modulation (60 s input duration or 30,000 sine-wave cycles as shown on top). APs were emitted in only a few such input cycles. The improved tracking (time locking) capability of human cells can be clearly seen in the corresponding PSTHs on the lower frames. c, Vector strength in human (red) and rats (blue) as a function of the frequency of input modulations. The case of in vivo condition for the human cells is also depicted; in this case the leak conductance of the dendrites was increased to take into account the shunting effect of excitatory and inhibitory synapses bombarding the dendritic tree.
