Figure 1.
A spectrum of possible excitatory driver-modulator (classical-contextual) interactions.
Conceptual curve families illustrate: A, pure threshold-lowering, B, pure gain-boosting, and C, mixed modulatory effects.
Figure 2.
Location independence of the dendritic spike-threshold nonlinearity.
A, Experimental setup. Whole-cell recordings were performed from the soma of a layer 5 pyramidal neuron. The cell was loaded with OGB-1 (200 µM) and was visualized using fluorescence confocal microscopy. Purple “clouds” denote sites of glutamate uncaging. B, Somatic responses to increasing stimulus intensity using UV laser focal uncaging of glutamate 60 µm from the soma. Black dashed trace shows extrapolated response based on linear fit to series of subthreshold response peaks. Ratio of actual to extrapolated response at local spike threshold defines the “Nonlinearity Relative to Linear Extrapolation” (NRLE) ratio (see Materials and Methods). C, Same as (B), but for stimulus site 160 µm from soma. D, NRLE values at proximal and distal sites were equivalent (∼3) under control conditions, and were reduced to equivalent values (<1) by NMDA channel blockers APV and MK-801. Bars indicate mean ±SD. E, Model responses at soma to increasing stimulus intensity (# of synapses) at 70 µm. F, Same as (E) but for stimulus at 160 µm. G, As in the experimental data, model NRLE values under control and NMDA block conditions were nearly constant along the proximal-distal axis. Error bars indicate SD across four different dendritic branches in the model, highlighted in the inset in (E). H, Red data are same as in (G). When the NMDA-AMPA ratio is made uniformly higher or lower over the length of the dendrite (magenta and cyan dashed lines, respectively), the NRLE measure roughly follows suit (magenta and cyan points). Similarly, if the NMDA-AMPA ratio increases or decreases linearly along the length of the dendrite (diagonal green and blue dashed lines, respectively), the NRLE ratio also varies roughly linearly (green and blue points).
Figure 3.
Proximal-distal interactions: predictions of the detailed compartmental model.
A, Location pairs are indexed on outer x and y axes, and depicted by electrode icons in insets (number shown under electrodes is separation distance). Proximal and distal stimulus intensity is indexed on inner x and y axes, respectively, in each subplot. Striped lines in 3 subplots on main diagonal are shown in (B). B, Dendritic spike threshold and amplitude recorded at the soma increased markedly as electrodes approached soma. C, Superposition of curves normalized to first suprathreshold point shows nearly invariant basic shape of input-output curve. The normalization was a x,y-scaling of each curve such that the first suprathreshold data point was placed at the middle of the plot.
Figure 4.
Proximal-distal interactions in a time-invariant 2-compartmental model are nearly indistinguishable from those produced by the detailed compartmental model.
A, Schematic proximal and distal ‘stimulating electrodes’ are shown activating one highlighted terminal basal dendrite. B, Peak somatic responses for inputs at 90 and 150 µm as illustrated in (A). Plot shares color bar with Figure 3A. C, 2-compartment circuit diagram with proximal and distal NMDA conductances. D, Time-invariant responses for 2-compartment model. Parameters were hand tuned to resemble (C): Axial, distal leak and proximal leak conductances were 2.5,0.25, and 4 A.U., respectively. NMDA peak conductance was 0.5 A.U. per synapse. Overall peak response in 2-compartment model was scaled to match overall peak in (C) (Vsoma = 15.2 mV). For details on 2-compartment model see Figure S1 in Text S1.
Figure 5.
Proximal-distal interactions: experimental results.
A, Somatic responses evoked by 50 Hz double pulse stimulation with bipolar theta electrode at distal site (210 µm from the soma), including a clearly visible dendritic spike. B, Somatic responses to proximal input alone at 120 µm, evoked by laser flash photolysis of caged glutamate. C, Distally evoked responses in the presence of constant proximal modulation activated simultaneously; modulatory input alone is indicated by asterisked trace in (B). D, Summary plot: each successive curve corresponds to a higher proximal modulation. Modulator-alone peaks are given by y-intercepts. Triangle indicates just-suprathreshold response to distal input, also shown in (E). Circle marks just-suprathreshold response for the distal stimulus when the proximal bias was simultaneously just-subthreshold for its own spike. E, Same cell as (D), with proximal and distal roles reversed. Square and pentagon correspond to just sub- and just supra-threshold response peaks, respectively, also shown in (D). F, G, Combined results of 294 stimulus pairs in 6 cells (cell-by-cell results shown in Figure S2 in Text S1). Inset, stimulus sites are indicated by black triangles (electrical stimulation) and purple clouds (laser uncaging), dendrite length in ball-and-stick cartoon is 275 µm. Blue case is same as in (A–E). Red case included TTX (1 µM) perfused from an electrode near the soma to prevent somatic spiking which would have masked the subthreshold integration process being studied. Grey and orange cases used electrical stimulation at proximal site instead of uncaging, and included CNQX (10 µM) in the bath to block AMPAR responses in order to prevent somatic spiking due to fast AMPA currents.
Figure 6.
Experimental results match model predictions.
A, B, Orthogonal views of 3D surface shown in Figure 4D for the 2-compartment model. Curves are grouped into 4 categories (colors) based on modulation strength. Averages within each category are shown in bold. Gray curves in (A) were excluded from averaging, since corresponding experimental cases were not observed. C, D, Data from Figure 5F,G was scaled vertically and horizontally using fiducial points for each cell (triangle, square, pentagon, circle; see Materials and Methods) to allow comparison to model results despite different stimulus locations, efficacy, branch input resistances, etc.
Figure 7.
Model predictions of spike rate responses also show strong proximal-distal asymmetry.
A,B, Somatic responses to 50 Hz independent Poisson inputs delivered to 3 (blue), 6 (green), and 9 (magenta) distal synapses centered at 190 µm in (A) and 17 (blue), 21 (green), and 25 (magenta) proximal synapses centered at 90 µm in (B). C, Mean firing rates for distal drive with proximal modulation increasing from curve to curve (averages of 20 runs). Slope changes are accentuated by black bars centered at point of maximum slope. Colored squares correspond to traces in (A–B). D, Same as (C), but for proximal drive with distal modulation. Black bars accentuate left shifting of i-o curve. E, F, Similar input configuration to (C–D), but with proximal and distal inputs (same distances) on two different dendrites. Modulatory effect from both perspectives is linear, as evidenced by the nearly constant additive (vertical shifting) effect of either proximal or distal cross-branch modulation acting on the driver's input-output curves. G, Diagram illustrates driver-modulator interaction shown in (C). Proximal synapses when viewed as contextual modulators (left) lower the threshold θ and increase the gain α of the dendritic sigmoid nonlinearity. Distal synapses viewed as modulators (right) exert a left-shifting (threshold lowering) effect. Note diagrams are schematic representations of the modeling results; absolute and relative positions of the driver and modulator inputs in the schematics should not be given a literal spatial interpretation.
Figure 8.
EPSP time-course analysis of L3 model neuron suggests that “modulatory” long-distance horizontal connections terminate proximally and vertical L4 “driver” inputs terminate distally.
A, L3 model morphology [89, see Materials and Methods for details] with colored markers indicating one set of the locations of the 4 synapses evoking the responses shown in (B). B, Four synaptic inputs were placed on 100 sets of 4 randomly selected dendrites 50, 150, and 250 µm from the soma, evoking 4.6, 3.6, and 2.9 mV EPSPs on average. EPSP half width and risetime grew with distance from the soma. Error bars indicate s.d. of the mean across random dendritic sets. Compare to Table 1 from Yoshimura et al. [47] showing that EPSP half widths between modulatory� long-distance horizontal and vertical L4 “driver” inputs increased (34.5±19.9 vs. 53.0±28.1ms, p<0.05, t-test) as did EPSP rise times (3.9±2.5ms vs. 5±2.5ms, p<0.04, Wilcoxon rank-sum test, Figure 2B rise time data from Yoshimura et al. [47] was digitized with Engauge Digitizer for statistical analysis in Matlab).
Table 1.
Model parameters.