Figure 1.
Masking of true motion by localization error.
A. 10,000 single points representing localized positions of a molecule were generated randomly from a normal distribution with standard deviation σloc. The distance of each point from the true location is plotted (red line). To simulate the effect of finite error on repeated localizations of a fixed object, a histogram of the distances between two randomly selected points within the same distribution is plotted as a histogram (black bars). B. Localized positions were randomly generated for pairs of molecules with true locations separated by increasing multiples of σloc. The distance between random pairs of localized positions is plotted as a histogram for each true intermolecular spacing. C. The measured distance plotted as a function of true separation. Measured distances were larger than expected due to the non-trivial localization precision, but approached the expected measurement with increasing separation of the two true points.
Figure 2.
Accurate determination of direction depends on localization precision.
A. Monte Carlo simulations were used to determine the distance of motion required to accurately determine the direction of a moving molecule localized with precision of σloc. 100 pairs of single points were generated in normal distributions with standard deviation σloc centered around two points separated by increasing distance. B. Pairs were plotted as a compass plot with the initial point (green) in the center connected to the second point (red) by a blue line. The net distance traveled parallel to the real translation of the distribution is marked by the black dot. C. The percent of vectors pointing toward the correct quadrant (within 45 degrees of the correct direction). D. The measured distance between localized points (blue) and the standard deviation of θ for the accompanying vectors (black). Each dot represents mean of 100 paired measurements.
Figure 3.
Effect of motion during image acquisition on single molecule photon distribution and localization precision.
A. Examples of random walks taken by a molecule over various timescales. Blue lines depict the path taken by the molecules, with green and red dots denoting the starting and ending position, respectively. B. Examples of photon distributions emitted from moving molecules of the indicated D over integration times ranging from 0 to 50 ms. C. The mean value of the brightest pixel (N = 1000 molecules) is plotted against integration time for molecules emitting 100, 250, or 1000 photons over the course of the integration time. D. Histogram of calculated precisions for molecules with D = 1.0 µm2/sec. E. The mean calculated precision for molecules with D = 0.1 µm2/sec (red line) and D = 1.0 µm2/sec (black line). Points represent mean of 1000 molecules. F. To examine the interaction of movement-induced error with photon-dependent precision, the mean error of molecules emitting 100 photons (black line), 250 photons (red line), and 1000 photons (blue line) were plotted as a function of exposure duration.
Figure 4.
Measurement of morphology is degraded by molecular motion during prolonged integration times.
To determine the effect of diffusion on the measurement of cell structure based on the position of localized molecules, we simulated molecules diffusing within a bounded space analogous to a filopodium. A. Random walks of molecules with D = 1.0 µm2/s were generated within a rectangle 100 nm wide (left, center). The localized position of the molecules is displayed for simulated acquisition using integration times of 0 (i.e., a fixed particle) and 10 ms (right). B. Molecules with D = 1 µm2/s (left) or 0.1 µm2/s (right) began their walks at random initial points within the bounded rectangle as in A. The density of localized positions across rectangles 150 nm in width (Top) or 75 nm (Bottom) plotted as histograms for exposures ranging from 0 to 50 ms are shown. C. The half-width of the bounded regions is quantified for D = 1.0 µm2/s (Left) or 0.1 µm2/s (Right). D. The effect of motion on the distribution of localized positions within a spine was modeled using a region consisting of a 500 nm square spine head and a neck that was 1000 nm long and 100 nm wide connected to a dendrite that was 500 nm wide and 1500 nm long (left). Plots of the paths taken by individual molecules with D = 1 um2/s and an exposure duration of 1 ms are shown (second panel). E. Localized positions of simulated imaged acquired using integration times of 0 (fixed particle), 5, and 50 ms are shown. Note the degradation of morphological accuracy with long exposure times.
Figure 5.
Short exposure time is critical for accurate measurement of diffusion for molecules within bounded space.
To determine the effect of exposure duration on measurement of diffusion of a freely moving molecule, we simulated molecules moving within bounded spaces analogous to small cellular compartments of interest. A. Molecular trajectories were generated as a series of 100 concatenated random walks. During each walk, each molecule generated an average of 1000 photons, creating an image that could be fit to localize the molecule for a single time point. Tracks were generated from sequential positions of the molecule. B. Tracks plotted for 100 sequential localizations of a molecule with diffusion coefficient of 1.0 µm2/s (top) or 0.1 µm2/s (bottom) moving within a bounded region represented by a 100 nm box. The measured path of tracked molecules was clearly affected at longer exposures, as localized positions progressively approached the center of the square. The resulting measured Deff was subsequently decreased from the expected value. C. Mean Deff for molecules of various D are plotted for several exposure times in regions of decreasing size. D. The Y axis of the final panels from C is expanded to demonstrate that within the bounded space, faster molecular motion results in decreased measured diffusion. This effect is reduced with rapid exposure times.
Figure 6.
More accurate morphology of living neurons using short, pulsed excitation during acquisition.
A. Cultured hippocampal neurons grown 10 days in vitro (DIV) expressing membrane-mEos2 were imaged at 50 Hz using excitation pulses of two durations (te = 2 ms and 10 ms) delivered in random order. The distribution of localized positions was plotted (A, enlarged in B), demonstrating a thinner appearance of neuronal processes imaged with longer te. C. Intensity profile of line scans drawn perpendicular to the neuronal process as in B. D. Cumulative frequency plot of the line scan full width at half maximum intensity. E. Paired comparison showed that the width of the processes was consistently diminished in the longer exposure. F. Measured spine neck widths (red) and spine lengths (blue) in neurons grown 11 to 12 DIV. Neurons were imaged at 50 Hz for 10,000 frames with te = 4 ms.