Figure 6. Low ΔCa_AP dendrites have a more elaborate branch structure than high ΔCa_AP dendrites.

(A) Maximum z-projection of Alexa 594 fluorescence from a L2/3 pyramidal cell. Dots indicate location of calcium imaging sites for a high (black) and low (blue) ΔCa_AP branch. The two sites are approximately the same distance from the soma (high ΔCa_AP: 145 µm, low ΔCa_AP: 131 µm). (B) Calcium-dependent fluorescence transient evoked by bAP in high (black) and low (blue) ΔCa_AP sites from panel A. (C) Comparison of ΔCa_AP in distance-matched, within-cell pairs. N = 20/8/8, N = 12 pairs, Ratio: 0.17, (range: 0.06–0.29). (D) Comparison of the distances from the soma for each pair of recording sites. (E) Comparison of branch complexity in high (black) and low (blue) ΔCa_AP sites, using a distance-discounted measurement of nearby dendritic branches. Branch complexity was significantly higher in low ΔCa_AP sites, U-Test, U = 215, z = 3.73, p = 1.9 × 10^–4. (F) Comparison of input resistance for high (black) and low (blue) ΔCa_AP sites shown in panels C and D, measured in computational simulations of compartment models of each cell in NEURON. Input resistance was significantly lower in low ΔCa_AP sites, U-Test, U = 213, z = 3.61, p = 3.1 × 10^–4. (G) Average number of branches at a given distance from a recording site for high (black) and low (blue) ΔCa_AP dendrites. This curve was multiplied by a symmetric exponential filter with a length constant of 145 µm and then integrated to compute the branch complexity in panel E. Mean ± SEM. (H) Schematic of morphologies with same branch order but different branch complexity. The blue and black site in each neuron have the same branch order, but the branch complexity of the blue site is higher due to the number of branches distal to the site (left), the number of branches on a sister dendrite (middle), and the distance from a previous branch (right).

Figure 6—figure supplement 1. bAP-evoked calcium influx attenuates around branch points.

(A) Alexa 594 MZP showing two ROIs within a segment of dendrite or across a branch point. Blue ROI is more distal than black ROI. (B) Calcium influx evoked by bAP in ROIs from panel A. (C) Distribution of the ratio of peak calcium influx (distal/proximal) for within-segment pairs (N = 22, median = 0.798) and across branchpoint pairs (N = 41, median = 0.361). U-test: U = 874, z = p = 0.015. Width of bar indicates number of observations. (D) Comparison of dendritic bAP-evoked calcium influx and branch order (N = 202, R² = 0.178, F = 43.3, p = 4 × 10^–10).

Figure 6—figure supplement 2. Back-propagating APs span 145 µm in L2/3 cell dendrites.

(A) Alexa 594 MZP showing location of point ROI. The scan mirrors were parked at angle such that excitation light impinged directly on an ROI of interest (in this case a dendritic shaft), and fluorescence was collected at the maximal sample rate of the DAQ board. (B) Calcium-dependent fluorescence transients evoked by a bAP for 10 trials collected at the ROI indicated in panel A. (C) Average ΔF/F for the 10 trials in panel B. (D) Alexa 594 MZP showing locations of two point ROIs that were 73 µm and 111 µm from the soma. (E) Normalized and smoothed $∆\mathrm{F}/\mathrm{F}$ for the two ROIs indicated in panel D. Note the small delay for the further ROI. (F) Somatic action-potential waveform recording from the cell in panel D. (G) Smoothed derivative of ΔCa_AP in dendritic spines, color-coded by their distance from the soma (color scale in panel H). We used the derivative to accurately measure the time-course of calcium influx in each spine. (H) Conduction delay of ΔCa_AP (measured at peak of derivative) as a function of distance. The inverse of the slope gives the conduction velocity of APs as they back-propagate through L2/3 cell dendrites. (I) Waveforms of APs recorded from L2/3 cells aligned to peak of second derivative (kink of AP waveform). (J) Histogram of FWHM of AP waveform for each cell. To compute the spatial spread of APs in L2/3 cell dendrites, we multiplied the average AP width by the conduction velocity $(154.9\mathrm{}\frac{\mathrm{\mu }\mathrm{m}}{\mathrm{m}\mathrm{s}}\mathrm{*}0.94\mathrm{}\mathrm{m}\mathrm{s}=146\mathrm{}\mathrm{\mu }\mathrm{m})$.

Figure 6—figure supplement 3. Branch complexity is correlated with input resistance.

(A) Input resistance of each site, measured in NEURON, compared to the inverse of branch complexity of each site, measured based on the cell’s dendritic morphology using a length constant of 145 µm. R² = 0.93 at λ = 145. We took the inverse because branch complexity should scale linearly with input conductance, which is the inverse of input resistance. (B) Correlation (R²) between branch complexity and input resistance for each length constant used to compute branch complexity. The arrow indicates the length constant used in panel A and Figure 6, computed based on the spatial waveform of the AP in L2/3 cell dendrites. (C) Comparison of branch complexity between high and low ΔCa_AP dendrites for each length constant of branch complexity. Red dotted line indicates length constant used in panel A and Figure 6. Y-axis is on a log scale.