Fast, automated implementation of temporally precise blind deconvolution of multiphasic excitatory postsynaptic currents

Abstract

Records of excitatory postsynaptic currents (EPSCs) are often complex, with overlapping signals that display a large range of amplitudes. Statistical analysis of the kinetics and amplitudes of such complex EPSCs is nonetheless essential to the understanding of transmitter release. We therefore developed a maximum-likelihood blind deconvolution algorithm to detect exocytotic events in complex EPSC records. The algorithm is capable of characterizing the kinetics of the prototypical EPSC as well as delineating individual release events at higher temporal resolution than other extant methods. The approach also accommodates data with low signal-to-noise ratios and those with substantial overlaps between events. We demonstrated the algorithm's efficacy on paired whole-cell electrode recordings and synthetic data of high complexity. Using the algorithm to align EPSCs, we characterized their kinetics in a parameter-free way. Combining this approach with maximum-entropy deconvolution, we were able to identify independent release events in complex records at a temporal resolution of less than 250 µs. We determined that the increase in total postsynaptic current associated with depolarization of the presynaptic cell stems primarily from an increase in the rate of EPSCs rather than an increase in their amplitude. Finally, we found that fluctuations owing to postsynaptic receptor kinetics and experimental noise, as well as the model dependence of the deconvolution process, explain our inability to observe quantized peaks in histograms of EPSC amplitudes from physiological recordings.

Figure 1. Structure and responses of a hair cell’s ribbon synapse.

A, Fast exocytosis owing to the fusion of a synaptic vesicle with the presynaptic cell’s plasma membrane floods the synaptic cleft with neurotransmitter. Postsynaptic receptors, in particular AMPA receptors at the hair-cell synapse, open and allow the flow of current into the postsynaptic nerve terminal on the right. B, The impulse response of the system is the excitatory postsynaptic current (EPSC) of stereotyped amplitude and timecourse evoked by the release of transmitter from a single presynaptic vesicle. Postsynaptic AMPA receptor channels open and close stochastically; here the mean current is shown for 150 channels. Although the channels open quickly, the risetime of the measured current is limited by the time constant of the postsynaptic membrane. The reclosure of AMPA receptors is a slower process that is well approximated by a single exponential with a time constant of 1–2 ms. C, Postsynaptic-current recordings are modeled statistically in three steps. In the first row, peaks in the density of neurotransmitter in the synaptic cleft are caused by stochastic fusions of vesicles in several size classes. In the second row, these spikes of neurotransmitter produce in the postsynaptic cell bursts of current shaped by the kinetics of receptor activation and deactivation (panel B). In the third row, noise from processes in the cell and the experimental apparatus are added to the postsynaptic signal. The purpose of our algorithm is to reconstruct the first record from observation of the third record, inferring and using the response shown in panel B.

Figure 2. Processing of EPSC records.

A, Selections from three records of postsynaptic current display typical EPSCs. The bottom trace shows the deconvolution of the third record. The color coding of the records applies as well to the subsequent panels. B, Estimates of the EPSC impulse response for the three experimental records of which segments are shown in panel A reveal the variability in EPSC kinetics. For records 1, 2 and 3, we detected respectively 7799, 825, and 3800 EPSCs. C, The probability distributions display the EPSC amplitudes detected by the algorithm for the three records. D, Cumulative probability distributions of inter-EPSC intervals for the three records (continuous lines) are adequately fit by single exponential functions (dotted lines). Perhaps because of a lack of true stationarity of the process, the magenta curve deviates most from a single exponential. E–G, Scatter plots relate the time delay to the amplitude ratio of successive pairs of EPSCs for the three records. No significant correlation between these variables is apparent.

Figure 3. A test of the basis for the increased magnitude of EPSCs with progressive depolarization of the presyanptic hair cell.

A, The mean EPSC rate grows appreciably as a function of depolarization. B, The mean EPSC amplitude displays negligible dependence on the extent of depolarization. The error bars indicate 95% confidence intervals. The measured mean amplitude of about −100 pA is consistent with that reported in Figure 4C of .

Figure 4. Evaluation of the algorithm’s performance.

A, The novel algorithm reliably detects pairs of unitary EPSCs separated by about 0.25 ms, an interval about one-third that required by the MiniAnalysis program. In this and the subsequent panels, the results from the new algorithm are displayed in red and those from MiniAnalysis in blue. B, The accuracy of amplitude estimation is slightly improved by the new algorithm. C, A synthetic record consisting of 3968 EPSCs, of which three small segments are displayed, was used to evaluate the two procedures. D, The probability distribution of amplitudes determined by the new algorithm agreed more closely with the true distribution than did the result from MiniAnalysis. E, EPSC impulse-response functions were determined by the algorithms for the three schemas shown in this figure and compared to the true impulse response. “Pairs assay” and “Amplitude assay” refer to the tests plotted in panels A and B; “Complex record” refers to the test plotted in panel C. The new algorithm provided an excellent fit by all criteria. F, The new algorithm fit the true cumulative probability distribution of the inter-EPSC intervals, which was an exponential function.

Figure 5. Fits of amplitude distributions for model data from simulations.

A, The distribution of channel openings was derived for 8000 events with a model comprising 150 AMPA receptors. The magnitude of a single quantum was set to 0.1 of total receptor saturation, or 15 channels; the mean number of quanta per fusion event was 4 and the root-mean-square experimental noise was 10 pA. B, The distribution was derived from 8000 simulated events for a model with 300 AMPA receptors. The single quantum was set to 0.125 of total receptor saturation, or 37.5 channels. C, D, Convolving the data in respectively panels A and B with the kinetics of channel reclosure and the membrane time constant blurs both distributions. E, F, The final amplitude distributions, which include the additional effect of additive noise, lack distinct peaks.