Fast, Automated Implementation of Temporally Precise Blind Deconvolution of Multiphasic Excitatory Postsynaptic Currents Daniel Andor-Ardo´ 1,2*, Erica C. Keen1, A. J. Hudspeth1, Marcelo O. Magnasco2 1 Howard Hughes Medical Institute and Laboratory of Sensory Neuroscience, The Rockefeller University, New York, New York, United States of America, 2 Laboratory of Mathematical Physics, The Rockefeller University, New York, New York, United States of America 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 ms. 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. Citation: Andor-Ardo´ D, Keen EC, Hudspeth AJ, Magnasco MO (2012) Fast, Automated Implementation of Temporally Precise Blind Deconvolution of Multiphasic Excitatory Postsynaptic Currents. PLoS ONE 7(6): e38198. doi:10.1371/journal.pone.0038198 Editor: Vladimir Brezina, Mount Sinai School of Medicine, United States of America Received September 8, 2011; Accepted May 4, 2012; Published June 26, 2012 Copyright: 2012 Andor-Ardo´ et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This research was supported by grants DC000241 and DC007294 from the National Institutes of Health (http://nih.gov). A.J.H. is an Investigator of Howard Hughes Medical Institute (http://hmmi.org). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: daa@cantab.net Introduction The deconvolution tasks involved in astronomy, fluorescence microscopy, and electrophysiology display several useful parallels (Table 1). Although the nomenclature and dimensionality are different in these three cases, the mathematical model that describes the system as a convolution of a signal with an impulse-response function is essentially the same. Reconstructing the location and intensity of each object from the superposition of blurred images is known as deconvolution. Sometimes the basis of the blurring is known theoretically; in an ideal, diffraction-limited telescope, for example, it is an Airy function. An algorithm is said to be blind if, in addition to reconstructing the positions of the objects, it also reconstructs the impulse-response function associ- ated with the blurring. An important subclass of such problems is characterized by a data set that is largely empty, peppered with only very few objects or events. Such problems are called sparse because one may safely assume that the information in the data is captured concisely by the locations and intensities of a small number of spatially point-like or temporally brief objects. Sparseness of the original signal introduces important mathemat- ical simplifications that make the reconstruction process more tractable. As a result, reconstruction of sparse signals by deconvolution has been applied to many different fields. We present here a deconvolution algorithm that aids in the analysis of complex but sparse electrophysiological recordings obtained in the course of studying synaptic transmission. Chemical synaptic transmission, which involves the exocytotic release of neurotransmitter from synaptic vesicles, results in excitatory postsynaptic currents (EPSCs) that can be measured electrophysiologically in a postsynaptic neuron by tight-seal, whole-cell recording. Records of such postsynaptic currents are often complex, with overlapping signals that display a large range of amplitudes (Fig. 1; [1]). Because this complexity results from the superposition of neurotransmitter release events from various ensembles of vesicles, the postsynaptic response to a single presynaptic release event, the unitary EPSC, provides an appropriate basis for characterizing a sparse representation. In the auditory system, an additional complication arises from the tendency of presynaptic release events to synchronize and therefore produce apparently unitary EPSCs that may in fact reflect responses to neurotransmitter from several presynaptic vesicles. Although statistical analysis of the kinetics and amplitudes of complex EPSCs is essential in the development of mechanistic models of neurotransmitter release, multiphasic waveforms PLoS ONE | www.plosone.org 1 June 2012 | Volume 7 | Issue 6 | e38198