Simulations ('Simulation-1') showing cusp-artifacts dependence on blinking statistics. (i) Three different populations of simulated emitters with different distributions of τ on and τ off values, yielding three different distributions of ρ values P1, P2 and P3 (dashed red, blue, and black curves respectively) are plotted on top of Fig. 1v. (ii) Predictions for the signs of the resulted virtual brightnesses for P1, P2 and P3 for cumulants orders 2 to 7. (iii) SOFI processing of the simulated data. A simulated filamentous morphology was populated with emitters from either P1, P2 or P3. Signs of virtual brightnesses (red for positive, green for negative) of virtual emitters mostly follow the predictions in (ii) for the different orders, except for out-of-focus (P2) regions (details are given in Supplementary Note 2).

Contexts in source publication

Context 1

... significance of the blinking trajectories. More details describing the simulator are discussed in our accompanying manuscript [22] and posted on a public GitHub package as SR_Simu3D [27]. In the first set of simulations ('simulation-1'), we simulated three different populations of emitters (P1, P2 and P3) with different  distributions (Fig. 4i, dashed red, blue, and black curves) with the ranges of 0.49   0.51 for P1, 0.53   0.87 for P2 and 0.11   for P3 (Fig. 4i). Comparing these distributions to Fig. 1v allowed us to predict the signs of resulted virtual brightnesses (Fig. 4ii). A simulated filamentous morphology was then populated with emitters from either P1, P2 or ...

Context 2

... and posted on a public GitHub package as SR_Simu3D [27]. In the first set of simulations ('simulation-1'), we simulated three different populations of emitters (P1, P2 and P3) with different  distributions (Fig. 4i, dashed red, blue, and black curves) with the ranges of 0.49   0.51 for P1, 0.53   0.87 for P2 and 0.11   for P3 (Fig. 4i). Comparing these distributions to Fig. 1v allowed us to predict the signs of resulted virtual brightnesses (Fig. 4ii). A simulated filamentous morphology was then populated with emitters from either P1, P2 or P3 populations. And the resulting simulated movies were SOFI-processed up to 7 th order. Signs of virtual brightnesses of ...

Context 3

... three different populations of emitters (P1, P2 and P3) with different  distributions (Fig. 4i, dashed red, blue, and black curves) with the ranges of 0.49   0.51 for P1, 0.53   0.87 for P2 and 0.11   for P3 (Fig. 4i). Comparing these distributions to Fig. 1v allowed us to predict the signs of resulted virtual brightnesses (Fig. 4ii). A simulated filamentous morphology was then populated with emitters from either P1, P2 or P3 populations. And the resulting simulated movies were SOFI-processed up to 7 th order. Signs of virtual brightnesses of virtual emitters (defined in section 3) mostly follow the predictions in Fig. 4ii for the different orders, except for ...

Context 4

... predict the signs of resulted virtual brightnesses (Fig. 4ii). A simulated filamentous morphology was then populated with emitters from either P1, P2 or P3 populations. And the resulting simulated movies were SOFI-processed up to 7 th order. Signs of virtual brightnesses of virtual emitters (defined in section 3) mostly follow the predictions in Fig. 4ii for the different orders, except for out-of-focus P2 emitters regions (details are given in Fig. S1). As we can see from Fig. 4i, for P1,  is distributed in a region with positive lobes for 2 nd and 6 th order cumulants, negative lobe for 4 th order cumulant, and positive/negative transition regions for 3 rd , 5 th and 7 th order ...

Context 5

... from either P1, P2 or P3 populations. And the resulting simulated movies were SOFI-processed up to 7 th order. Signs of virtual brightnesses of virtual emitters (defined in section 3) mostly follow the predictions in Fig. 4ii for the different orders, except for out-of-focus P2 emitters regions (details are given in Fig. S1). As we can see from Fig. 4i, for P1,  is distributed in a region with positive lobes for 2 nd and 6 th order cumulants, negative lobe for 4 th order cumulant, and positive/negative transition regions for 3 rd , 5 th and 7 th order cumulants. This means that all P1 virtual emitters will exhibit positive virtual brightnesses for Feb. 10, 2019; 2 nd and 6 th order ...

Context 6

... for cumulants of 6 th order for P2. For P3,  is broadly distributed at positive/negative transition regions for all cumulants with orders higher than 2, and is purely positive only for 2 nd order cumulant. P3 is therefore predicted to exhibit cusp-artifact for all cumulants with orders higher than 2. This prediction is clearly validated in Fig. 4iii except for the 4 th order cumulant. The reason the 4 th order cumulant exhibit only negative virtual brightnesses is because the portion of positive virtual emitters is too small as compared to the negative portion, the signal is canceled out and couldn't stand out from the large portion of positive ...

Context 7

... the other hand, if large portion of the virtual emitters are negative, the negative portion could still create high contrast as a negative contrast against the positive noise background (as shown for the 7 th order cumulant in the third and fourth row). We note here that cumulants of background noise are positive for all cumulant orders higher than 2, this is because high order (>2) cumulants of a random variable that follows a Poisson distribution are constant (Supplementary Note 4). Fig. 4i (bleaching correction factor fbc = 100% means no bleaching correction). ...

Context 8

... against the positive noise background (as shown for the 7 th order cumulant in the third and fourth row). We note here that cumulants of background noise are positive for all cumulant orders higher than 2, this is because high order (>2) cumulants of a random variable that follows a Poisson distribution are constant (Supplementary Note 4). Fig. 4i (bleaching correction factor fbc = 100% means no bleaching correction). Second row shows simulated images for a bleaching correction factor of fbc = 1% (see text). The bleaching correction algorithm is effective in restoring the absolute value of the virtual brightness distribution, but not their signs. The bleaching correction ...

Context 9

... if photophysical properties (blinking and photobleaching) of emitters are more-or-less uniform across the sample, the finite acquisition time of a SOFI experiment (usually ~2,000 to 20,000 frames) is often not long enough to reach statistical significance of blinking behavior, leading to a broad distribution in  values, which in turn leads to positive and negative higher order (>2) cumulants values (Figure 1). It is only when all emitters in the sample exhibit a narrow  distribution during the data acquisition duration that cusp-artifacts could, in principle, be avoided (as shown in Figure 4 for P1 with cumulants of 2 nd , 4 th and 6 th orders.). However, narrow  distribution could still be positioned close to a zero crossing of one (or more) of the high order cumulants, leading to coexistence of positive and negative cumulants values. ...