Experimental overview and representative example showing supralinear dendritic integration in a neurogliaform interneuron.

(a) Summary depicting the mouse model, viral expression, and acute slice preparation with patch-clamp and imaging and uncaging.

(b) Alexa-594 fluorescence Z-stack of a representative neurogliaform NDNF+ interneuron, with uncaging locations and the position of the linescan used to measure dendritic calcium transients (dotted white line)(inset). The image was obtained after the experiment was concluded.

(c) Uncaging protocol for asynchronous (separate responses) and near-synchronous conditions.

(d) Representative somatic voltage traces across asynchronous separate response and near-synchronous conditions. Laser uncaging light stimuli are indicated by red dots above the traces. uEPSPs were elicited in the asynchronous condition with light pulses separated by an interval of 100.32 ms (left; grey traces: individual sweeps; black traces average). The arithmetic sum traces were calculated by aligning and summing an increasing number of asynchronously evoked responses (middle). Near-synchronous uEPSPs were elicited with light pulses separated by an interval of 0.32 ms (right). The families of traces for the arithmetic sum and near-synchronously evoked responses are shown as light to dark grey traces, indicating an increase in the number of uncaging loci from 1 to 12.

(e) Fluo-4 and Alexa-594 linescans during asynchronous sequential uncaging at 12 loci at times indicated by the vertical red dashes. The ratio of dendritic Fluo-4 to Alexa fluorescence is shown below (au: arbitrary unit).

(f) Linescans during near-synchronous uncaging at increasing numbers of locations (1 – 12, top to bottom).

(g) Peak amplitude of the recorded near-synchronous response plotted against the amplitude of the arithmetic sum as the number of uncaging loci was increased.

(h) Time integral of the recorded near-synchronous response plotted against the integral of the arithmetic sum.

(i) Fluo-4 fluorescence transient amplitude, normalised by Alexa-594 fluorescence, plotted against the number of locations uncaged near-synchronously. The grey line indicates the estimated separate response amplitude interpolated from the fluorescence measured between 1 and 12 locations uncaged asynchronously (see Methods).

Summary of supralinear dendritic integration in neurogliaform interneurons.

(a) Average scaled amplitude of recorded near-synchronous uEPSPs plotted against scaled amplitude of the arithmetic sum of asynchronously evoked uEPSPs as the cumulative number of uncaging locations was increased (n=11 dendrites in 11 cells from 9 animals; error bars represent SEM).

(b) Amplitude nonlinearity quantified for data shown in (a). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 56% [95%CI 27%, 108%]. P<0.001 (two-sided permutation t-test compared to 0%).

(c) Average scaled near-synchronous uEPSP integral plotted against scaled arithmetic sum of asynchronous separate responses, for the same dataset.

(d) Integral nonlinearity corresponding to panel (c). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 122% [95%CI 73%, 213%]. P<0.001 (two-sided permutation t-test compared to 0%).

(e) Average Fluo-4/Alexa-594 fluorescence transients plotted against the cumulative number of uncaging locations. The grey line indicates the interpolated values used in the nonlinearity calculation (see Methods). The dark grey diamond indicates the amplitude from the 12th asynchronous response. (n = 7 dendrites in 7 cells from 7 animals).

(f) Amplitude nonlinearity corresponding to panel (c) (dendritic calcium). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 37% [95%CI 18%, 54%]. P=0.0138 (two-sided permutation t-test compared to 0%).

For the slopegraphs and Gardner-Altman estimation plots, paired observations are connected by coloured lines. The paired mean differences between the near-synchronous (NS) and asynchronous separate response (S) groups are shown in Gardner-Altman estimation plots as bootstrap sampling distributions. The mean differences are depicted as black dots. The 95% confidence intervals are indicated by the ends of the vertical error bars.

Sublinear dendritic integration in neurogliaform interneurons with NMDARs blocked.

(a) Somatic uEPSPs evoked by uncaging glutamate in a representative neuron before (top) and after (bottom) D-AP5 (50 uM) perfusion. Uncaging protocol and data representation as in Figs. 1-2.

(b) Dendritic Fluo-4 traces in the same neuron, in response to asynchronous and near-synchronous uncaging, before (left) and after NMDAR blockade (right).

(c) Scaled amplitude of the recorded near-synchronous uEPSP plotted against scaled amplitude of the arithmetic sum, as the number of uncaging locations was increased. Error bars: SEM (n=6 dendrites in 6 cells from 6 animals). The supralinear relationship became sublinear with NMDARs blocked.

(d) Amplitude nonlinearity for individual neurons shown in (c) before and after D-AP5 perfusion. The paired mean difference between the two conditions is −71% [95%CI −147%, - 41%]. P<0.001 (two-sided permutation t-test).

(e) Scaled time-integral of uEPSPs plotted against scaled integral arithmetic sum of asynchronous separate responses, before and after NMDAR blockade.

(f) Integral nonlinearity corresponding to panel (e). The paired mean difference between baseline and D-AP5 conditions is −153% [95%CI −267%, −78%]. P <0.001 (two-sided permutation t-test).

(g) Fluo-4 fluorescence transients (normalised to Alexa-594) plotted against the cumulative number of uncaging locations, before and after NMDAR blockade. Data plotted as in Fig. 1.

(h) Amplitude nonlinearity corresponding to panel (g). The paired mean difference between baseline and D-AP5 conditions is −45% [95%CI −129%, −13%]. P<0.001 (two-sided permutation t-test).

Slopegraphs and Gardner-Altman estimation plots as in Fig. 2.

Supralinear dendritic integration in neurogliaform interneurons does not require voltage-dependent sodium channels.

(a) Somatic uEPSPs evoked by uncaging glutamate in a representative neuron in the presence of TTX (200 nM), showing supralinear summation.

(b) Dendritic Fluo-4 fluorescence responses in the same neuron, showing supralinear calcium signalling.

(c) Average scaled amplitude of recorded near-synchronous uEPSP plotted against scaled amplitude arithmetic sum with increasing numbers of cumulative uncaging locations (n=7 dendrites in 5 cells from 5 animals).

(d) Amplitude nonlinearity corresponding to panel (c). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 63% [95%CI 21%, 107%]. P=0.0382 (two-sided permutation t-test compared to 0%).

(e) uEPSP amplitude nonlinearity quantified by integral, plotted in the same way as (c).

(f) Integral nonlinearity corresponding to (e). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 135% [95%CI 71%, 220%]. P=0.011 (two-sided permutation t-test compared to 0%).

(g) Fluo-4 fluorescence transient amplitude (normalised to Alexa-594) plotted against the cumulative number of uncaging locations. Data plotted as in Fig. 1.

(h) Amplitude nonlinearity corresponding to panel (g). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 48% [95%CI 9%, 123%]. P=0.088 (two-sided permutation t-test compared to 0%).

Slopegraphs and Gardner-Altman estimation plots as in Fig. 2.

L-type voltage-dependent calcium channel blockade abolishes nonlinear dendritic calcium summation.

(a) Somatic uEPSPs evoked by glutamate uncaging in one neuron in the presence of nimodipine (30 uM), showing supralinear uEPSP integration.

(b) Dendritic Fluo-4 fluorescence transients in the same neuron, showing absence of supralinear integration.

(c) Average scaled amplitude of the recorded near-synchronous uEPSP plotted against the arithmetic sum of the scaled asynchronous uEPSPs, as the cumulative number of uncaging locations was increased. Error bars show SEM (n=8 dendrites in 5 cells from 3 animals).

(d) Amplitude nonlinearity corresponding to (c). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 14% [95%CI −22%, 51%]. P= 0.505 (two-sided permutation t-test compared to 0%).

(e) uEPSP amplitude nonlinearity quantified by integral, plotted in the same way as (c).

(f) Integral nonlinearity corresponding to (e). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 37% [95%CI −37%, 153%]. P=0.497 (two-sided permutation t-test compared to 0%).

(g) Fluo-4 fluorescence transient amplitude (normalised to Alexa-594) plotted against cumulative number of uncaging locations. Data plotted as in Fig. 1.

(h) Amplitude nonlinearity corresponding to (g). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 4% [95%CI −6%, 19%]. P=0.561 (two-sided permutation t-test compared to 0%).

Slopegraphs and Gardner-Altman estimation plots as in Fig. 2.

SERCA inhibition abolishes nonlinear dendritic calcium summation.

(a) Somatic uEPSPs evoked by glutamate uncaging in one neuron in the presence of CPA (30 uM), showing supralinear uEPSP integration.

(b) Dendritic Fluo-4 fluorescence transients in the same neuron, showing absence of supralinear integration.

(c) Average scaled amplitude of the recorded near-synchronous uEPSP plotted against the arithmetic sum of the scaled asynchronous uEPSPs, as the cumulative number of uncaging locations was increased. Error bars show SEM (n=5 dendrites in 2 cells from 2 animals).

(d) Amplitude nonlinearity corresponding to (c). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 42% [95%CI 5%, 79%]. P=0.067 (two-sided permutation t-test compared to 0%).

(e) uEPSP amplitude nonlinearity quantified by integral, plotted in the same way as (c).

(f) Integral nonlinearity corresponding to (e). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 171% [95%CI 69%, 432%]. P<0.001 (two-sided permutation t-test compared to 0%).

(g) Fluo-4 fluorescence transient amplitude (normalised to Alexa-594) plotted against cumulative number of uncaging locations. Data plotted as in Fig. 1.

(h) Amplitude nonlinearity corresponding to (g). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 2% [95%CI −16%, 20%]. P=0.754 (two-sided permutation t-test compared to 0%).

Slopegraphs and Gardner-Altman estimation plots as in Fig. 2.

Supralinear dendritic integration in OLM interneurons.

(a) Summary depicting the mouse model and acute slice preparation with patch-clamp and imaging and uncaging. Uncaging protocol and data representation as in Figs. 1-2

(b) Alexa-594 fluorescence Z-stack of a representative OLM SOM+ interneuron with uncaging locations (inset). The image was obtained after the experiment was concluded.

(c) Representative somatic voltage traces across asynchronous separate response and near-synchronous conditions, depicted as in Fig. 1.

(d) Average scaled amplitude of the recorded near-synchronous uEPSP plotted against the arithmetic sum of the scaled asynchronous uEPSPs, as the cumulative number of uncaging locations was increased. Error bars show SEM (n=13 dendrites in 13 cells from 13 animals).

(e) Amplitude nonlinearity corresponding to (d). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 31% [95%CI 15%, 46%]. P=0.004 (two-sided permutation t-test compared to 0%).

(f) uEPSP amplitude nonlinearity quantified by integral, plotted in the same way as (d).

(g) Integral nonlinearity corresponding to (f). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 56% [95%CI 31%, 71%]. P<0.001 (two-sided permutation t-test compared to 0%).

Slopegraphs and Gardner-Altman estimation plots as in Fig. 2.

Linear dendritic integration in neurogliaform interneurons with NMDARs blocked and no effect of voltage-dependent sodium channel nor of L-type voltage-dependent calcium channel blockade.

(a) Somatic uEPSPs evoked by uncaging glutamate in a representative neuron before (top) and after (bottom) D-AP5 (50 uM) perfusion. Uncaging protocol and data representation as in Figs. 1-2.

(b) Scaled amplitude of the recorded near-synchronous uEPSP plotted against scaled amplitude of the arithmetic sum, as the number of uncaging locations was increased. Error bars: SEM (n=6 dendrites in 6 cells from 6 animals).

(c) Amplitude nonlinearity for individual neurons shown in (b) before and after D-AP5 perfusion. The paired mean difference between the two conditions is −32% [95%CI −53%, - 18%]. P<0.001 (two-sided permutation t-test).

(d) Scaled time-integral of uEPSPs plotted against scaled integral arithmetic sum of asynchronous separate responses, before and after NMDAR blockade.

(e) Integral nonlinearity corresponding to panel (d). The paired mean difference between baseline and D-AP5 conditions is −60% [95%CI −90%,-40%]. P <0.001 (two-sided permutation t-test).

(f) Somatic uEPSPs evoked by glutamate uncaging in one neuron in the presence of TTX (200 nM), showing supralinear uEPSP integration.

(g) Average scaled amplitude of the recorded near-synchronous uEPSP plotted against the arithmetic sum of the scaled asynchronous uEPSPs, as the cumulative number of uncaging locations was increased. Error bars: SEM (n=11 dendrites in 7 cells from 6 animals).

(h) Amplitude nonlinearity corresponding to (g). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 66% [95%CI 17%, 102%]. P=0.029 (two-sided permutation t-test compared to 0%).

(i) uEPSP amplitude nonlinearity quantified by integral, plotted in the same way as (g).

(j) Integral nonlinearity corresponding to (i). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 74% [95%CI 1%, 148%]. P=0.089 (two-sided permutation t-test compared to 0%).

(k) Somatic uEPSPs evoked by glutamate uncaging in one neuron in the presence of nimodipine (30 uM), showing supralinear uEPSP integration.

(l) uEPSP amplitude nonlinearity, plotted in the same way as (g). (n=8 dendrites in 7 cells from 7 animals).

(m) Amplitude nonlinearity corresponding to (l). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 40% [95%CI 19%, 83%]. P=0.011 (two-sided permutation t-test compared to 0%).

(n) uEPSP amplitude nonlinearity quantified by integral, plotted in the same way as (g).

(o) Integral nonlinearity corresponding to (n). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 97% [95%CI 27%, 263%]. P=0.066(two-sided permutation t-test compared to 0%).

(p) uEPSP amplitude nonlinearity quantified by integral in neurogliaform (NGF) and OLM interneurons (control and TTX experiments pooled). The mean difference between NGF and OLM integral nonlinearity is −63% [95%CI −132%, −8%]. P=0.0424 (two-sided permutation t-test).

(q) Dendritic diameter in NGF and OLM interneurons. The mean difference between NGF and OLM 0.36 [95%CI 0.20, 0.53]. P<0,001 (two-sided permutation t-test).

Slopegraphs and Gardner-Altman estimation plots as in Fig. 2.

Comparison of uEPSP time-integral and dendritic calcium in a neurogliaform cell.

(a) Alexa-594 fluorescence Z-stack, with uncaging locations and linescan position (inset).

(b) Somatic voltage traces across asynchronous separate response and near-synchronous conditions, with times of uncaging stimuli indicated by red dots). In the asynchronous condition, individual traces are shown in grey, and the average shown in black. For the near-synchronous traces, light to dark traces indicate responses as the numbers of near-synchronous uncaging stimuli was increased from 1 to 12. The arithmetic sum traces are indicated in the same way.

(c) Peak amplitude of the recorded near-synchronous response plotted against the amplitude of the arithmetic sum for increasing numbers of uncaging locations.

(d) Integralof the recorded near-synchronous response plotted against the integral of the arithmetic sum.

(e) Fluo-4 linescans in response to asynchronous stimulation. Locations 1 – 12 were sequentially stimulated at times indicated by red dots.

(f) Fluo-4 linescan in response to near-synchronous stimulation of increasing numbers of locations. The Fluo-4 fluorescence change from baseline was normalised to the fluorescence of the inert morphological dye Alexa-594 (the average linescan for Alexa-594 is shown beneath). Laser uncaging stimuli are indicated by red dots above the traces. Ratiometric calcium traces use arbitrary units (au).

(g) Fluo-4 fluorescence transient amplitude, normalised by Alexa-594 fluorescence, showing a deviation from the predicted response to asynchronous stimulation when more than 4 locations were uncaged near-synchronously. Grey line indicates the estimated asynchronous response amplitude using interpolated values (see methods).

(h) Fluo-4 fluorescence transient (normalised to Alexa-594 fluorescence) plotted against uEPSP integral.

Relationships among uncaging parameters and uEPSP nonlinearity (NGF).

(a) Mean asynchronous separate response uEPSP amplitude.

(b) Mean asynchronous separate response uEPSP integral.

(c) Distance from the soma to the uncaging location along the dendrite.

(d) Separate response mean amplitude plotted against amplitude nonlinearity following near-synchronous uncaging.

(e) Separate response mean integral plotted against amplitude nonlinearity following near-synchronous uncaging.

(f) Separate response mean amplitude plotted against integral nonlinearity following near-synchronous uncaging.

(g) Separate response mean integral plotted against integral nonlinearity following near-synchronous uncaging.

(h) Uncaging distance from soma plotted against amplitude nonlinearity.

(i) Uncaging distance from soma plotted against integral nonlinearity.

(j) Dendritic order for dendrites used for glutamate uncaging. The numbers in the pie chart represent the numbers of dendrites in the respective categories.

(k) Amplitude nonlinearity split by dendrite order.

(l) integral nonlinearity split by dendrite order.

Linear regressions are depicted as black lines. Pearson correlation parameters depicted in correlation panels. Summary values are depicted as mean ± SEM. n=11 dendrites in 11 cells from 9 animals.

Relationships among uncaging parameters and uEPSP nonlinearity (OLM).

(a) Mean asynchronous separate response uEPSP amplitude.

(b) Mean asynchronous separate response uEPSP integral.

(c) Distance from the soma to the uncaging location along the dendrite.

(d) Separate response mean amplitude plotted against amplitude nonlinearity following near-synchronous uncaging.

(e) Separate response mean integral plotted against amplitude nonlinearity following near-synchronous uncaging.

(f) Separate response mean amplitude plotted against integral nonlinearity following near-synchronous uncaging.

(g) Separate response mean integral plotted against integral nonlinearity following near-synchronous uncaging.

(h) Uncaging distance from soma plotted against amplitude nonlinearity.

(i) Uncaging distance from soma plotted against integral nonlinearity.

(j) Dendritic order for dendrites used for glutamate uncaging. The numbers in the pie chart represent the numbers of dendrites in the respective categories.

(k) Amplitude nonlinearity split by dendrite order.

(l) integral nonlinearity split by dendrite order.

Linear regressions are depicted as black lines. Pearson correlation parameters depicted in correlation panels. Summary values are depicted as mean ± SEM. N= 13 dendrites, in 13 cells, from 13 animals.

SERCA inhibition does not affect supralinear dendritic summation in OLM interneurons.

(a) Somatic uEPSPs evoked by glutamate uncaging in one neuron in the presence of CPA (30 uM), showing supralinear uEPSP integration.

(b) Average scaled amplitude of the recorded near-synchronous uEPSP plotted against the arithmetic sum of the scaled asynchronous uEPSPs, as the cumulative number of uncaging locations was increased. Error bars show SEM (n=5 dendrites in 4 cells from 4 animals).

(c) Amplitude nonlinearity corresponding to (b). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 27% [95%CI −40%, 54%]. P= 0.239 (two-sided permutation t-test compared to 0%).

(d) uEPSP amplitude nonlinearity quantified by integral, plotted in the same way as (b).

(e) Integral nonlinearity corresponding to (g). The paired mean difference between near-synchronous (NS) and asynchronous separate responses (S) is 84% [95%CI −7%, 158%]. P=0.123 (two-sided permutation t-test compared to 0%).

Slopegraphs and Gardner-Altman estimation plots as in Fig. 2.