FIGURE 13:
Our method greatly improves on the results of methods that treat noise as fixed. To compare the performance of Eq. 8 to Eq. 11, we use a 20,000-data point set of just 10 fluorophores (μf = 2.0 and σf = 0.2) photobleaching to background with aSNR = 10.0–1.0. We show the theoretical signal (thick black line) around which we added noise (light blue), our estimate (yellow line), and the result of Eq. 8 (red line). At the end of the trace, both methods do very well. However, at the start of the trace, where cumulative noise is highest, our method has only minor offset (OF = 2.4), whereas a fixed-noise model grossly overfits, finding >100 spurious steps. This is expected because the higher noise at the start of the trace is now interpreted as signal by algorithms that assume that noise is fixed. Note that both methods find all true steps (SE = 1 for both), but the overfit by the fixed-noise model leads to great disparity for precision (PR = 1 for our approach; PR ≈ 0.125 for Eq. 8). Inset, detail of the trace’s first 1000 data points, where the bulk of overfitting by the fixed-noise model occurs.