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. 2013 Dec 24;7:201. doi: 10.3389/fncir.2013.00201

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Copyright © 2013 Lütcke, Gerhard, Zenke, Gerstner and Helmchen.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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(A) Conceptual link between neuronal network dynamics and structure in our study. Network dynamics measurable with calcium imaging techniques is simulated to investigate how well spike trains can be reconstructed for a broad value range of the most important experimental parameters. Reconstruction performance is condensed in three key parameters (TPR, true positive rate; FDR, false discovery rate; and σ_Δt, temporal precision), which are used to analyze how well structural network properties such as topological characteristics (right) can be revealed depending on the attainable accuracy of spike train reconstruction. Missed (green) and falsely detected (red) spikes indicated by arrowheads. (B–D) Simulation of calcium traces from spike trains and subsequent reconstruction of firing pattern. (B) Top: simulated noise-free (red) and noisy (black) calcium traces for the example Poisson spike train (SNR = 2; f = 10 Hz). Bottom: reconstruction of spike train from simulated noisy calcium trace using the peeling algorithm. Reconstructed spike train and model calcium trace in blue. Gray: residual calcium trace. Note the missed (green) and two false spikes (red). Middle: same traces but with a better SNR of 4. Bottom: expanded view of example calcium transient in gray box on faster time scale. Note the timing imprecision of reconstructed spike timing due to the low frame rate. (C) Same data as in (B) but with a higher frame rate. Note the improved reconstruction, especially at the faster time scale (bottom). (D) Illustration of simulated original spike train and reconstructed spike train (SNR = 2; f = 10 Hz). Spikes are matched based on the Δt matrix of all spike-pair-intervals Δt_ij between original and reconstructed trains. After sorting the matrix according to the rank of Δt and applying a threshold Δt_max, spikes are either matched or remain as “misses” or “false discoveries.” Unmatched spikes i with Δt_ij > Δt_max for all j are undetected original spikes (misses) and unmatched spikes j with Δt_ij > Δt_max for all i are spurious reconstructed spikes (false discoveries).