Supplementary for
A simple method to estimate the average localization precision of a single-molecule
localization microscopy experiment
Ulrike Endesfelder, Sebastian Malkusch, Franziska Fricke, Mike Heilemann
Institute of Physical and Theoretical Chemistry, Johann Wolfgang Goethe University Frankfurt am
Main, Frankfurt am Main, Germany
Corresponding authors:
Ulrike Endesfelder (endesfelder@chemie.uni-frankfurt.de, +49-69-798-29425, fax +49-69-798-29560)
Mike Heilemann (Heilemann@chemie.uni-frankfurt.de, +49-69-798-29736, fax +49-69-798-29560)
Monte Carlo simulations of fluorophore distributions to characterize NN adfr
In order to investigate the influence of false nearest neighbors on the distribution for a single molecule
with Gaussian distributed localizations, we simulated fluorophore distributions with distances beyond
the diffraction limit (~200 nm) and defined structures. First, a linear structure labeled with fluorophores
was simulated containing five fluorophores that are placed in equal distances along one axis
(supplementary figure 2, three representative distances). The simulation reveals periodical Gaussianshaped contributions with declining amplitude in the nearest neighbor distribution NNadfr, each
possessing a center of mass exactly at the simulated distance and its multiples (e.g. xc1 = 60 nm, xc2 =
120 nm, xc3 = 180 nm for a simulated distance of 60 nm between two fluorophores supplementary
fig.2b). They directly reflect the labeling density of the simulated linear structure. The decrease in
amplitude is explained by the nature of the nearest neighbor measurement: In case of two
localizations in the same frame, which is getting more likely for increasing distances dependent on
experimental conditions and algorithmic performances, the nearest neighbor approach favors the
closer localization.
To simulate a more densely labeled two-dimensional structure, a single cell of a rhombic Bravais
lattice with five fluorophores placed in a face centered square was chosen. The simulation results in a
single Gaussian-shaped appearance in the distance distribution NN adfr centering between the distance
of the vertex and the center and the distance of two adjacent vertexes (supplementary figure 3).
Taking the result for the linear simulation into account, the Gaussian-shaped appearance is defined by
three overlapping Gaussian distributions, each indicating one of the three distances (vertex to vertex
at the same side, vertex to center and diagonal distance of vertex to vertex) inside the lattice. Based
on the results of these two simulations we postulate that the short-range order disturbance depends,
as expected, on the structure and the labeling density of the sample. It is reasonably well
approximated by a Gaussian distribution reflecting these factors. As for real experiments the sample
and labeling properties are usually not known, we add a Gaussian correction term for short range
order with free fit parameters and estimated initial values to our distribution equation p(d).
For distances above ~ 100 nm, the nearest neighbor distance distribution NNadfr shows a constant
population of marginal amplitude that is not explained by the equation, correcting for short-range order
disturbance. We define this population as long-range order disturbance, as its significance emerges
with increasing distances, while the structural effect on the distribution NNadfr is getting smaller (see
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linear simulation). Notably, as the area scales quadratic with the distance, the detection of a
fluorophore within a distinct distance interval becomes more likely for larger distances. We simulated a
uniform distribution of localizations with a single fluorophore in the center (supplementary figure 4). We
obtain a linear shape with positive slope and an origin at zero contributing to the distance distribution
NNadfr. We defined the influence of the long-range order disturbance with a linear factor in p(d). The
gradient is depending on the structure and the degree of labeling, which typically are not known in
practice.
It is important to mention that p(d) is only approximating false nearest neighbor distributions at
distances of about the diffraction limit. For larger distances, another correction term weighting the
linear part is needed, as in case two or more molecules are fluorescent, the nearest neighbor selection
would always yield the shortest distance to the closest molecule. For a SMLM experiment only one
other molecule should reside in the fluorescent state in an adjacent frame and the range of the
diffraction-limited area. Thus there is no need for further correction terms that increase the parameter
range and would make the fitting error prone.
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Supplementary Figure 1: Monte Carlo simulation of individual blinking molecule.
By the repeated simulation (100 individual simulations per condition) of the distribution of localization
of an individual molecule ( = 10 nm, number of localizations 100, 200, 300 and 900) the precision by
measuring the Gaussian distribution of the absolute distances to the center of mass (red box plots)
and the corresponding relative distribution of the pairwise distances of all localizations (black box
𝑛𝑙𝑜𝑐 −1
plots) is verified. The box plot reveals the higher statistics of the pairwise distribution (𝑛 = ∑𝑖=1
(𝑖)) in
contrast to the statistics of the absolute distance measure (𝑛 = 𝑛𝑙𝑜𝑐 , 𝑛𝑙𝑜𝑐 number of localizations) and
the spread of localization precision which enhances significantly with the number of localizations (box:
25th to 75th percentile, square: median, line: mean, bars: 5th and 95th percentile, crosses: 1th and 99th
percentile, minus: minimum and maximum).
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Supplementary Figure 2: Monte Carlo simulation of five blinking molecules in a row.
By simulating several molecules in a row, the influence on the nearest neighbor distribution of
localizations in adjacent frames for one-dimensional structures (e.g. filaments) is evaluated (each
molecule 3000 localizations, on = 1 frame). The contribution is quantified by calculating the difference
spectrum of the nearest neighbor displacement measure of all localizations of the simulation (middle
panel, blue curve) in respect to the nearest neighbor displacement measure of the middle molecule
only (middle panel, green curve) and is depicted in the right panel. The maxima of the interfering
distributions reflect the simulated distance and its multiples of the molecules.
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Supplementary Figure 3: Monte Carlo simulation of five blinking molecules in 2D structure.
By simulating five molecules arranged in a 2D cross, the influence on the nearest neighbor distribution
of localizations in adjacent frames for two-dimensional structures is evaluated (each molecule 3000
localizations, on = 1 frame). The contribution is quantified by calculating the difference spectrum of the
nearest neighbor displacement measure of all localizations of the simulation (middle panel, blue curve)
in respect to the nearest neighbor displacement measure of the middle molecule only (middle panel,
green curve) and is depicted in the right panel. In general, the interfering distribution of distances
between different molecules can be described as a sum of all non-Gaussian distributions of pairwise
nearest neighbor distances from the different molecules which are in close proximity. This analytical
distribution nevertheless can only be described by knowing the number of molecules marking the
specific structure and the ability to assign each individual localization to its corresponding molecule. As
in a typical localization microscopy experiment localization distributions of molecules overlap, for small
distances, nearest neighbors belonging to the same molecule cannot be distinguished from those
involving localizations from different molecules. As seen in the maxima of the interfering contribution
(right panel) for different distances between the simulated molecules, they give a measure of the
average labeling density of the 2D structure.
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Supplementary Figure 4: Monte Carlo simulation of a blinking molecule and uniform
background disturbance.
By simulating uniform background (red localizations), the influence of background on the nearest
neighbor distribution of localizations in adjacent frames is evaluated (molecule blue, 3000
localizations, on = 1 frame). As seen in the progression of (a-c), the contribution of nearest neighbors
of different molecules increases with background density. The contribution is quantified by calculating
the difference spectrum of the nearest neighbor displacement measure of all localizations of the
simulation (middle panel, blue curve) in respect to the nearest neighbor displacement measure of the
molecule only (middle panel, green curve) and is depicted in the right panel. As the density of possible
nearest neighbor localizations from the background increases radically from the localization of interest,
an increasing contribution is obtained.
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