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The peeling reconstruction algorithm can be applied to sparse trains of synaptic events as well, such as those between cPSCs in our recordings. Whereas simpler algorithms also do the job, using peeling reconstruction avoids the need of manually purging events that ride on top of each other (as we did for Fig. 3.6). Figure 3.21 compares statistics of PSCs detected during ripples and outside of ripples from recordings of cell 0 at₋66 mV. Data about other cells is presented below in the same format, in Figures 3.25 and 3.26.

Inter onset intervals during SWR peak sharply at ripple frequency The Figure

shows first in the top left panel that the distribution of inter onset intervals of the noise is rather long-tailed and does not present any peaks. A more detailed study

0 50 100 150 200 0% 3% 6% 0 5 10 15 20 0% 10% 20% 30% 0 2 4 6 8 10 0% 10% 20% 30% Fr a ct ion 0% 10% 20%

Inter onset interval (ms)

0 15 30 45

PSC amplitude (pA)

Decay time constant (ms) Rise time constant (ms)

Fr a ct ion Fr a ct ion Fr a ct ion cPSC spont.

Figure 3.21. Validation: Fit Parameters Compared to Spontaneous PSCs. The epochs for

the analysis of spontaneous events were the intervals (−180,−120 ms) with respect to each SWR peak, while in-ripple PSCs were fitted in the interval(−30,30)ms, as in all other recon- struction analyses. An independent assessment of the spontaneous PSC kinetics (Fig. 3.6) yieldedτr=1.70±0.04 ms andτd=4.04±0.08 ms.

including longer time spans would be needed to assess its Poissonian character. By comparison, the in-ripple cPSCs present a clear peak at around 4 ms. This peak is even better defined than those in the corresponding inter-slope histograms (Figs. 3.9 and 3.10), and, importantly, both are clearer than those obtained with spectral methods (Fig. 2.9 C in the previous Chapter).

Ripple-embedded PSCs many times larger than spontaneous In the top right

panel of Figure 3.21 we can appreciate that while amplitudes of the spontaneous PSCs are in the 20 pA range that we encountered in our previous analysis of Section 3.3, PSCs during ripples exhibit a long tail reaching well up to 10 times and more the size of spontaneous PSCs. This may mean that several PSCs from distinct presynaptic partners belonging in the same assembly are collated into one, so well-timed that they are inaccessible for the time resolution of peeling reconstruction on somatic voltage clamp data. Alternatively, excitatory conductances may just increase during ripples.

Exquisite accord of PSC kinetics in and out of ripples The bottom panels of

Figure 3.21 show seemingly identical distributions of both kinetic constants for in- ripple vs. out-of-ripple PSCS. A caveat is that the peeling reconstruction algorithm uses as a guess both for detection (deconvolution kernel constant) and fitting (least squares guess) the known kinetics of EPSCs, so it is not entirely unbiased in its choice of time constants. However, the success of many reconstructions (low squared area of residual, and observed match to the original) and the ultimate freedom to fix time constants are strong hints that what we see is the underlying statistical distribution, and that itisthe same for all EPSCs observed in the recording, whether ripple asso- ciated or not. The penalty function (here discouragingτd>10 ms) makes itself visible

in the little bump of decay times. The corresponding curve for spontaneous PSCs shows a small mass of events beyond the 10 ms mark. This inexactitude is a price to pay to ensure stability in the progression of the reconstruction.

Robustness of peeling reconstruction The above results are, thus, consistent in every

aspect with our previous investigation of in-ripple currents and spontaneous PSCs by independent methods. They thus add to our confidence in the performance of peeling reconstruction. We additionally stress-tested the robustness of the reconstruc- tion algorithm on individual events and at the population level by changing structural parameters (bracketing strategy, use of a second pass to catch leftover, unfitted events), signal resolution (filter bands), detection constants (deconvolution time constant and threshold), fit constraints (penalty threshold and penalty function), weighting schemes (constant bandwidth vs. adaptive; flat weighting) and by jittering parameter guesses for each PSC. No relevant changes of the fit statistics were observed. Finally, at the pop- ulation level, averages of measured currents and averages of their reconstructions agree (see Figs. 3.22 and 3.23 in the next Section), which does not guarantee correctness at the single-cPSC level but hints at absence of bias in the errors of the reconstructions.

Do synaptic inputs compound linearly during ripples? The main underlying

assumption is that individual currents sum linearly, in fact that synapses work as linear time-invariant systems. While in current clamp the arrival of a synaptic event can change the voltage of the membrane and thus affect succeeding synaptic events (through active conductances), in voltage clamp this source of nonlinearity in the tem- poral summation is absent. Another source of nonlinearity would be the arrival of PSCs in short order at the same synaptic site. The currents could engage nonlinear synaptic mechanisms, such as vesicle depletion. Though in principle possible, the low firing rates of pyramidal cells during ripples (our own observations in vitro; generally below 10 Hz in vivo, Csicsvari et al., 1999b) coupled with the extensive arborization, make it unlikely in the case of excitatory afference. From our own data (amplitude histogram in Fig. 3.21), it can be argued (admittedly, making use of the linearity assumption), that the total number of events arriving within a cPSC in our preparation is at most 50, whereas intact (not in-vitro) pyramidal cells have dozens of thousands of synaptic terminals. In support, Cash and Yuste (1999) failed to see nonlinear sum- mation due to reduction of driving force (does not apply here, under voltage clamp) or conductance shunt in hippocampal CA1 pyramidal cells, attributing the disagreement with the predictions of cable theory mostly to active, compensating conductances.

The arguments above do not establish, by far, that the currentsdocompound lin- early (much less in the high-conductance state in vivo), after all, for example, why should they distribute across synaptic terminals in a non-clustered fashion?. On the other hand, if currents compounded nonlinearly, the process would be time- and mem- brane-site dependent, and it could show hysteretic effects due to e.g. chemicals being not cleared out fast enough. Analyses would be nearly impossible. We are thus bound to see how far we can get within the limits of the necessary assumption of linearity.