Triggered cagedSTORM microscopy

In standard SMLM methods, the photoswitching of single fluorescent molecules and the data acquisition processes are independent, which leads to the detection of single molecule blinking events on several consecutive frames. This mismatch results in several data points with reduced localization precision, and it also increases the possibilities of overlapping. Here we discuss how the synchronization of the fluorophores’ ON state to the camera exposure time increases the average intensity of the captured point spread functions and hence improves the localization precision. Simulations and theoretical results show that such synchronization leads to fewer localizations with 15% higher sum signal on average, while reducing the probability of overlaps by 10%.


Triggered cagedSTORM microscopy: supplemental document 1. FRAME DURATION PROBABILITIES
Based on photoswitching models, the ON lifetime distribution can be described by a single exponential distribution: where t is the temporal length of the blinking event and τ is the expected ON lifetime.Let us select a blinking event starting on a given frame.If the activation probability of the blinking event is uniform in the [0, R] interval, the probability of the blinking event to end in the [t l1 , t l2 ] interval is 1 τ e −t l /τ dt l dt s .(S2) To restrict the length of the blinking events to end on a given frame, the single frame case must be separated: where t s is the start time of the blinking event and T is the exposure time.These integrals are one of the following forms: leading to the following probabilities: For spontaneous activation (R = T), with K = τ/T: To determine the limit for triggered activation (R → 0), let us rephrase the probabilities in Eq.S5a and Eq.S5b: Evaluating the limit for triggered activation after applying the L'Hopital's rule: The calculated probability distributions for K = 0.5, 1, 2, 4, 8 and 16 are shown in Figure S1.

OVERLAPPING PROBABILITY
The number of the blinking events (assuming uniform labeling/blinking density) within a given time interval and region (a diffraction limited spot in this case) follows Poisson distribution: where N is the number of the blinking events, λ = ρt, ρ is the temporal density of blinking events within a diffraction limited spot and t is the length of the time interval.The probability that no blinking event will occur in the time interval can be expressed: In order to determine the overlapping probability, first, choose a blinking event with a given frame length t N .Now one has to determine the time interval within which other blinking events can not fall.The length of this time interval depends on the length of the other blinking events.First let us set the length of the other blinking event, t o to a fixed value.The density function of such blinking events can be expressed: The probability that no other blinking event with length between t o + dt o will overlap with the examined N frames can be expressed: Now consider other blinking events with t o1 , t o2 , . . ., t om lengths, too.Then the probability that neither of them will overlap with the selected blinking event's trajectory: Now let us consider other blinking events with all the possible t o lengths and switch from the summation to Riemann integral: The integral in the exponential can be evaluated: Substituting in Eq.S14: To get rid of the dependence on the arbitrarily chosen, examined blinking event frame duration, we must consider the different frame duration probabilities of the trajectories: Substituting the frame duration probabilities for the two activation types (with K = 1): Rephrasing them to get geometric series, we can arrive at the following result: The general formulas for any given K = τ T value can be derived similarly:

AVERAGE TIME DURATIONS
The average time durations of blinking events captured on a given frame number can be calculated by the following expressions:

TESTSTORM SIMULATIONS
Figure S2 shows the localized images of the simulated structures.Table S1 and Table S2 contain the labeling and acquisition parameters of the TestSTORM simulations.Quantum efficiency 0.9 0.9

Table S1 .
Labeling parameters used in TestSTORM

Table S2 .
Acquisition parameters used in TestSTORM